topographic rossby waves in the gulf of mexico

Progress in Oceanography 82 (2009) 1–31

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Progress in Oceanography

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Topographic Rossby waves in the Gulf of Mexico

Peter Hamilton *

Science Applications International Corporation, 615 Oberlin Rd., Suite 100, Raleigh, NC 27605, United States

a r t i c l e i n f o

Article history:Received 28 October 2008Received in revised form 3 April 2009Accepted 5 April 2009Available online 8 May 2009

Keywords:Gulf of MexicoDeep currentsTopographic Rossby wavesLoop CurrentBaroclinic instability

0079-6611/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.pocean.2009.04.019

* Tel.: +1 919 836 7565.E-mail address: [email protected]

a b s t r a c t

Observations of topographic Rossby waves (TRW), using moored current meters, bottom pressure gauges,and Lagrangian RAFOS floats, are investigated for the deep basin of the Gulf of Mexico. Recent extensivemeasurement programs in many parts of the deep gulf, which were inspired by oil and gas industry explo-rations into ever deeper water, allow more comprehensive analyses of the propagation and dissipation ofthese deep planetary waves. The Gulf of Mexico circulation can be divided into two layers with the�800–1200 m upper layer being dominated by the Loop Current (LC) pulsations and shedding of large(diameters �300–400 km) anticyclonic eddies in the east, and the translation of these LC eddies acrossthe basin to the west. These processes spawn smaller eddies of both signs through instabilities, and inter-actions with topography and other eddies to produce energetic surface layer flows that have a rich spectrumof orbit periods and diameters. In contrast, current variability below 1000 m often has the characteristics ofTRWs, with periods ranging from�10–100 days and wavelengths of�50–200 km, showing almost depth-independent or slightly bottom intensified currents through the weakly stratified lower water column.These fluctuations are largely uncorrelated with simultaneous upper-layer eddy flows. TRWs must be gen-erated through energy transfer from the upper-layer eddies to the lower layer by potential vorticity adjust-ments to changing depths of the bottom and the interface between the layers. Therefore, the LC and LCeddies are prime candidates as has been suggested by some model studies. Model simulations have alsoindicated that deep lower-layer eddies may be generated by the LC and LC eddy shedding processes.

In the eastern gulf, the highest observed lower-layer kinetic energy was north of the Campeche Bankunder the LC in a region that models have identified as having strong baroclinic instabilities. Part of the60-day TRW signal propagates towards the Sigsbee Escarpment (a steep slope at the base of the northerncontinental slope), and the rest into the southern part of the eastern basin. Higher energy is observed alongthe escarpment between 89�W and 92�W than either under the northern part of the LC or further south inthe deep basin, because of radiating TRWs from the western side of the LC. In the northern part of the LC,evidence was found in the observations that 20–30-day TRWs were connected with the upper layer throughcoherent signals of relative vorticity. The�90� phase lead of the lower over the upper-layer relative vorticitywas consistent with baroclinic instability. Along the Sigsbee Escarpment, the TRWs are refracted andreflected so that little energy reaches the lower continental slope and a substantial mean flow is generatedabove the steepest part of the escarpment. RAFOS float tracks show that this mean flow continues along theescarpment to the west and into Mexican waters. This seems to be a principal pathway for deepwater par-cels to be transported westward. Away from the slope RAFOS floats tend to oscillate in the same general areaas if primarily responding to the deep wave field. Little evidence of westward translating lower-layer eddieswas found in both the float tracks and the moored currents. In the western gulf, the highest deep energy lev-els are much less than in the central gulf, and are found seaward of the base of the slope. Otherwise, the sit-uation is similar with TRWs propagating towards the slope, probably generated by the local upper-layercomplex eddy field, being reflected and forcing a southward mean flow along the base of the Mexican slope.Amplitudes of the lower-layer fluctuations decay from the northwest corner towards the south.

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1. Introduction

It is 30 years since Thompson’s (1977) seminal analysis ofobservations of topographic Rossby waves (TRW) at Site D in the

ll rights reserved.

northwest Atlantic. Since then, more extensive moored arrays havebeen deployed in and around the Gulf Stream (Hogg, 1981, 2000;Hamilton, 1984; Watts et al., 2001) and the current variabilitybelow 1000 m has been shown to be dominated by TRWs thatconform to the dispersion relation first derived by Rhines (1970).Comprehensive long-term deep current measurements frommoorings were not made in the Gulf of Mexico until the 1980’s.

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2 P. Hamilton / Progress in Oceanography 82 (2009) 1–31

These were analyzed by Hamilton (1990) who showed that thevariability under the Loop Current (LC), in the north central andnorthwest gulf had the characteristics of TRWs including highcoherence through the lower water column, bottom intensifica-tion, and period and wavevector agreements with the dispersionrelation. Hamilton (1990) speculated that pulsations of the LC,which is a branch of the Gulf Stream system that enters the gulfthrough the Yucatan Channel and exits through the Straits of Flor-ida (Fig. 1), was the primary source of the lower-layer TRWs. Heevoked the Malanotte-Rizzoli et al. (1987) model of broadbandradiation from a pulsating meander in a channel over a sloping bot-tom as an explanation of the observations. A significant correlation,with a lag of 106 days, was found between deep currents under theeast side of the LC and a mooring in the northwest gulf that implieda minimum group speed of �9 km d�1 in rough agreement withgroup speeds estimated from the dispersion relation (Hamilton,1990). The dispersion relation indicates that TRW-trains propagatewith shallower depths on their right (i.e., generally westward inthe northern gulf) at higher group speeds than LC eddies. The latterare large anticyclones, with diameters of �300–400 km, that areshed from the LC at irregular intervals (Sturges and Leben, 2000)and translate westward and southwestward, at �3–6 km d�1, intothe western gulf (Elliott, 1982; Kirwan et al., 1984). The differencein propagation speeds and the different characteristic periodicitiesof the lower layer TRWs and the upper-layer eddies means thatflows in the upper and lower water column are largely decoupled.

Deep currents were measured due south of the Mississippi deltaat the base of a steep 500-m escarpment (the Sigsbee Escarpment)in 2000 m water depth (I1 in Fig. 1) between September 1999 andSeptember 2001 (Hamilton, 2007). The flows were highly energetic(a maximum speed of 90 cm s�1 was observed 100 m above thebottom; Hamilton and Lugo-Fernandez, 2001) with characteristicperiods of �10–20 days, which were much shorter than the previ-ously observed �20–100 days (Hamilton, 1990). Moreover, a char-

I1

L3

L6

L5

L4GGV4V3

W3W2

W4W5

3500 m

3000 m

2000 m

1000 m

200 m L1L2

V2U2

U3 U4T5

TexasLouisiana

YucataPenins

LC eddy

CamB

M

Fig. 1. Locations of the principal full-depth moorings used in the analyses. The SST imagCurrent (LC) and a detached LC eddy (named eddy El Dorado). Image courtesy of John H

acteristic of these currents were that 4–5 wave trains wereobserved over the 2-year interval, generally beginning with ahigh-energy burst (speeds > 50 cm/s) and decaying over the next3–4 months. Each wave train had slightly different characteristicwavelengths and periods, indicating a probable difference in geo-graphical source regions. Some could be associated with the localpresence of LC eddies; however, at least one occurred whenupper-layer eddy activity was weak. Hamilton (2007) speculatedthat these short period waves were being reflected from the steepescarpment rather than refracted by the changing bottom slopes,and suggested that the TRWs were locally generated and possiblytrapped by the bathymetry.

Hofmann and Worley (1986) derived a deep mean anticlock-wise circulation from an analysis of a gulf-wide hydrographic sur-vey. Numerical model results by Oey and Lee (2002) and Lee andMellor (2003) also showed deep mean cyclonic gyres with rela-tively strong (�5–10 cm/s) westward flows along the base of thenorthern slope. Mizuta and Hogg (2004) theoretically modeledTRWs propagating onto a shoaling slope. The shoaling slope in-duces a reflected wave component and a principal result is that amean flow develops over the slope, forced by convergence ofboundary layer Reynolds stresses. DeHaan and Sturges (2005)came to similar conclusions in that they attributed the observedanticlockwise (i.e., westward) deep mean flow along the base ofthe northern slope to rectification of TRWs.

Numerical modeling studies of Oey (1996) and Oey and Lee(2002) showed that simulated deep currents could be interpretedas TRWs, and the results suggested that long period (�60–100 days) TRWs radiated towards the northern slope as LC eddiestranslated across the western basin. Oey and Lee (2002) also sug-gested that the topography and the anticlockwise deep mean flowsof the northern slope provided sufficient refraction of the TRWsthat most of energetic deep waves were confined to the deep basin.Oey (2008) extended his numerical studies with a higher resolution

GL7

Y3Y2

Y1

Florida

nula

Cuba

LC

Frontal Eddy

pecheank

15 20 25 30Temperature oC

ississippiFan

e is a 3-day composite centered on February 5, 1998, and shows an extended Loopopkins University Applied Physics Laboratory.

P. Hamilton / Progress in Oceanography 82 (2009) 1–31 3

model of the gulf and investigated the generation of deep eddies bythe LC. In this model, one preferred site of deep cyclogenesis isnorth of the Campeche Bank, and another off the west Floridaslope. These deep regions of baroclinic instability are coupled tothe LC expansion and retraction cycles. Generated cyclones eithermigrate around the LC and develop as frontal cyclones, or propa-gate off to the northwest, sometimes accompanying an extendingLC or recently shed LC eddy. Significant results from Oey’s analysisof the model currents are that the propagating deep eddies radiateTRWs that propagate towards the northern slope and the SigsbeeEscarpment, and that the TRWs receive energy from the deepeddies through linear wave-eddy coupling. In Oey (2008), charac-teristic TRW periods were much shorter (�20 days) than in Oeyand Lee (2002), and also their origin was related back to the LCinstability regions.

Malanotte-Rizzoli et al. (1995) proposed wavenumber couplingbetween a propagating surface feature, such as a frontal eddy, anddeep flows as an alternate generation mechanism for TRWs. Pickart(1995) showed that this mechanism could account for the genera-tion of 40-day TRWs that are observed at Cape Hatteras by 40-dayeastward propagating meanders of the Gulf Stream. Wave trains ofTRWs propagate westward and southwestward along the slope inthe northwest Atlantic, with phase propagation southeastwards to-ward deeper water. The coupling to eastward propagating mean-ders requires that the bottom slope has a direction such that a40-day TRW wavenumber has an eastward component thatmatches the eastward wavenumber of the meanders. This couplingmechanism may be important for short period TRWs in the gulf be-cause energetic cyclonic eddies are observed on the LC front and onthe edges of LC eddies (Vukovich, 1986; Zavala-Hidalgo et al.,2003). However, because waves are observed to have wide rangeof periods between�10 and 100 days, the generation of broadbandTRW radiation by the large scale movements of the LC and LC ed-dies (Malanotte-Rizzoli et al., 1987) should not be discounted,though the mechanisms of energy transfer to the TRWs may becomplex and involve the generation of accompanying deep eddies(Oey, 2008). Hogg (2000) indicates that energetic near-bottom cur-rents, with TRW characteristics, observed over the tail of the GrandBanks seems to better agree with broadband radiation by the GulfStream and warm rings, rather than through meander coupling.

Over the last 7 years, three major observational programs havetaken place in the deep waters of the north central, northwest andnortheast gulf. These studies deployed closely spaced arrays of cur-rent meter moorings and pressure equipped inverted echo sounders(PIES). The central gulf study also deployed 36 RAFOS floats at depthsbetween 1000 m and the bottom. These observations allow a morecomprehensive analysis of deep-water circulations, and extendand refine the descriptions of the lower-layer TRW regime in thegulf. Thus, the aim of this paper is to review these new data as theypertain to the lower layer below 1000 m, particularly in regard tothe generation, propagation and dissipation of TRWs, deep meanflows, and possible couplings to upper-layer LC and LC eddy circula-tions. A comprehensive approach using all available recent observa-tional studies was felt to be more appropriate at this time thananalyzing each program individually. The gulf has several featuresthat make it suitable for this analysis, including energetic deep flows,abyssal depths (>3700 m at the deepest point), a relatively small(compared to the NW Atlantic) basin that is almost closed below1000 m, and a dominant source of energy, namely the LC, which islargely confined to the eastern half of the basin. Other importantcharacteristics of gulf bathymetry are the steep escarpments sepa-rating the abyssal basin from many sections of the lower continentalslope, and the extremely rough and complex topography of thenorthern continental slope (Lugo-Fernández and Morin, 2004).

In the following, the phrase ‘‘nearly depth independent” is oftenused with respect to current velocity profiles. In all cases ‘‘depth

independent” refers to the current profile from 1000 m to the topof the bottom boundary layer. The often strongly sheared eddy cur-rents of the upper water column are implicitly excluded from themajority of the analysis. Similarly, reference will often be madeto upper and lower layers. However, the interface between the sur-face intensified eddies and the bottom intensified TRWs is rathernebulous as these circulations can overlap. However, the transitionfrom upper to lower layer is usually characterized as a region ofminimum kinetic energy that occurs between �800 and 1200 m,and roughly corresponds to the depth of the 6 �C isotherm. Thevarying depths of the ‘‘interface” and the bottom have importantconsequences for eddy interactions with the bottom-trapped cur-rents (e.g., LaCasce, 1998; LaCasce and Brink, 2000).

After presenting data sources, an overview of deep currentsfrom selected full-depth moorings from most parts of the gulf (Sec-tion 3) is given, followed by more detailed analyses of the centraland eastern gulf experiments (Section 4), and the northwesternstudy (Section 5). Section 6 discusses the evidence for coupling be-tween upper and lower layers, after which the major results aresummarized.

2. Data

2.1. Moorings

The majority of recent full-depth sub-surface, taut-line moor-ings deployed in the gulf have been instrumented with combina-tions of ADCPs, single point current meters, and temperature andsalinity sensors. Generally ADCPs are deployed in the upper layerwith a common configuration being an upward-looking 75 kHz at450–500 m, and below this, point current measurements at fixedintervals of 250 m and 500 m above and below 1000 m, respec-tively. Moorings in Mexican waters (W2, W3, W4, W5 and L6:Fig. 1) were also instrumented with upward-looking 75 and300 kHz ADCPs at �1200 m and�10 m above bottom, respectively.Table 1 lists the studies used in this paper and their originatinginstitutions. A subset of these moorings are located in Fig. 1. Someof these studies also deployed bottom moorings with either 1 or 2current meters at 500 and/or 100 m above the seabed (mab) andPIES as part of their array designs. The latter are discussed below.Moorings G and GG (Fig. 1) were deployed prior to 1990, and werepreviously analyzed by Hamilton (1990). The Minerals Manage-ment Service (MMS) of the US Department of the Interior funded,either wholly or in part, all the in situ observations used in thispaper. MMS technical reports (see references) may be found athttp://www.gomr.mms.gov/homepg/regulate/environ/techsumm/rec_pubs.html.

All time series records from these moorings underwent basicquality assurance where suspect data values were flagged. Shortgaps of a few hours caused by flagged data or the rotation of themoorings were subsequently filled by linear interpolation. Longgaps of up to 2 days were filled with a procedure that preservesthe spectral content and has similar energy levels to the rest ofthe records. In the mooring rotation gaps, care was taken thatthe vertical coherence between levels were similar to other por-tions of the mooring’s records. This is particularly important forthe closely spaced depth levels generated by the ADCPs. The re-cords at each depth level were merged into continuous time serieswhere possible. All records were filtered with 3 and 40-h low-pass(HLP) Lanzcos kernels and decimated to 1 and 6 h intervals, respec-tively. The latter are the basis for subsequent analyses. Unlessotherwise noted, velocity components (u, v) are east and north,respectively. The convention on coordinate axis rotations is suchthat the v-component is usually aligned with the general trend ofthe isobaths at the site, and the rotation is defined as the clockwise

http://www.gomr.mms.gov/homepg/regulate/environ/techsumm/rec_pubs.html

http://www.gomr.mms.gov/homepg/regulate/environ/techsumm/rec_pubs.html

Table 1Moorings deployed by observational studies in the Deep Gulf of Mexico.

Name reference Institution Dates Locations (Fig. 1) Numbers

Full-Depth Bottom PIES

DeSoto Extn., Hamilton et al. (2003) SAIC 8/99–8/01 I1 1 4 3Exploratory, Donohue et al. (2006) SAIC 4/03–4/04 L1 to L4 4 15 27Exploratory, McKone et al. (2007) LSU 4/03–6/04 L5 1 – –Canekito, Sheinbaum et al. (2007) CICESE 5/03–8/04 L6 1 – –SEBSEP, Donohue et al. (2006) Industry 4/03–5/04 Escarpment Transect North of L4 – 6 –LSU long-term, Inoue et al. (2008) LSU 4/03–6/04 L7 1 – –NW Gulf, Donohue et al. (2008) SAIC 4/04–7/05 T5 to V4 13 – 10W Gulf CICESE 8/04–11/05 W2 to W5 5 – –NE Gulf EHI 1/05–1/06 Y1 to Y3 3 1 8

SAIC – Science Applications International Corporation, Raleigh, NC.EHI – Evans Hamilton Inc., Seattle, WA.LSU – Louisiana State University, Baton Rouge, LA.CICESE – Centro de Investigación Científica Y Educación Superior de Ensenada, Ensenada, Mexico.Industry – DEEPSTAR Oil Industry Consortium.


angle the y-axis (or v-component) makes with true north. In gen-eral current meter moorings will be referred to by 2 character ID,where the first letter is a transect or group identifier, and the sec-ond character is the mooring number within the group (Fig. 1 andTable 1). Groups with the same first letter were deployed at similartimes. Because various subsets of the observations are used in thefollowing sections, the depth levels will be identified as they areemployed.

2.2. RAFOS floats

RAFOS floats were deployed in the Exploratory program, andthis was the first time such instruments have been used in the gulf.RAFOS floats (Rossby et al., 1986) are neutrally buoyant glass-tube

Fig. 2. Spaghetti plot of all 36 RAFOS float smoothed trajectories at all depths (1000–250the beginning of each track is indicated by a square. Arrowheads are at 10-day intervals.the program.

floats that can be ballasted in the laboratory to drift with the cur-rents below the surface at a user selected pressure (roughly depth)or density for extended periods. The floats are equipped with tem-perature and pressure sensors, and with an acoustic hydrophonethat listens to the arrival times of acoustic signals sent from threesound sources deployed at the sites shown in Fig. 2. The soundsources were programmed to transmit every 8 h. At the end ofthe deployment, the floats surfaced and transmitted their data toshore via satellite. The focus of the study was on deep currents,so all the floats were configured to follow pressure as opposed todensity surfaces. The initial deployment of 30 floats was in April2003, followed by six more in October 2003. The former surfacedin April 2004, and the latter at the end of May 2004. The floats werelaunched on a grid pattern over the lower slope in the region

0 m) in the exploratory study. Sound sources are given by the large diamonds, andMost floats have two tracks because of sound source failures in the first 3 months of


encompassed by the L1 to L4 moorings (Fig. 1). Nominal launchdepths were at 500-m intervals between 1000 and 3000 m, withthe majority (15 out of 36) at 1500 m.

During the course of the experiment, monitoring showed thattwo of the sound sources failed after 3 months in the water. Theywere replaced about 6-months into the study. Therefore, most ofthe float tracks have two sections, the first 3 months and the last6 months of the 1-year deployments. Float positions were recordedevery 8 h, and more details can be found in Donohue et al. (2006).

After the travel times were converted to geographical positions,individual float tracks were smoothed using the successive correc-tions method of Pedder (1993) using a time scale of 1-day, andresampled at 6-h intervals. This is the same as the procedures usedby Hamilton et al. (1999) for near-surface drifters in the gulf. Aspaghetti diagram of all the smoothed tracks produced by the 36floats is given in Fig. 2.

2.3. PIES

A pressure equipped inverted echo sounder is a bottommounted instrument that emits 12 kHz sound pulses and measuresround trip travel times of these acoustic pulses from the seas sur-face and back. These measurements can be converted to profiles oftemperature, salinity and specific volume anomaly utilizing empir-ical relationships established by historical hydrography (Meinenand Watts, 2000). In this study, however, only the precision bottompressure measurements will be utilized in the form of low pass fil-tered anomalies, after long-term drifts are removed (Meinen andWatts, 2000). In the central gulf study, a large-scale atmosphericsignal with a period of �14–16 days was present, with uniformamplitude, in all the pressure anomaly time series, but was negli-gible in the bottom currents. Therefore, the area-averaged pressurerecord was subtracted from each anomaly, which effectively re-moved the atmospheric signal (Donohue et al., 2006).

3. Gulf-wide overview of deep currents

Generally, in the gulf, the current velocity variability is highlycoherent through the lower water column at depths greater than1000 m. One of the fundamental questions is the spatial distribu-tion of the depth-integrated eddy kinetic energy (EKE) over the

Table 2Lower-layer EOF analysis of currents by mooring.

Mooring Depth levels (m) Mode 1 percent of total

CEOF Frequency b

0.01–0.03

G 1565, 2364, 3174 97.7 63.2/35.3a

GG 725, 1650 71.8 71.6

I1 1000, 1200, 1600, 1800 88.9 83.7

L3 1000, 1500, 2000, 2500, 2900 97.7 94.0L4 1000, 2000, 2500, 2900, 3250 97.0 97.8L5 1165, 1415, 1677, 1925, 2175, 2625, 2925 95.0 96.1L6 1005, 1479, 1985, 2490, 2995, 3308 97.2 80.6L7 500, 2000, 3000, 3187,3256 85.5 70.4/23.6a

V3 1000, 1500, 2000, 2400 77.3 79.9V4 1000, 1500, 2000, 2500, 3000 92.5 84.5W2 1000, 1110, 1544, 1965 76.4 83.0W3 1007, 1541, 2048, 3038, 3518 90.9 89.9W4 1572, 1941 84.4 –W5 1025, 1125, 1572, 1998 61.8 –

Y1 729, 1224, 1472, 2479 84.5 –Y2 1037, 1284, 1532, 2035 81.0 66.6/20.0a

Y3 987, 1234, 1482, 1985, 2489, 2689 92.7 89.2

a Mode 2.

lower water column that can be attributed to TRWs. This quantityis a more complete measure of wave EKE than using EKE at a singledepth level. The former was estimated for each full-depth mooringthat was deployed in water depths of 2000 m or greater, by calcu-lating the first complex empirical orthogonal function (CEOF) usingthe available velocities from depth levels in the lower part of thewater column (Table 2). Thus,

Uðz; tÞ ¼X

n

AnðtÞ � enðzÞ ð1Þ

where all quantities are complex and the mode amplitude, An, isnormalized to unit variance (i.e., hA�nAni ¼ 1, where hi denotes timeaverage). The record means of U are removed before the analysis.The mode amplitudes and eigenvectors, en, are orthogonal and or-dered by variance explained, but their orientation is relative to anarbitrary reference (Kundu and Allen, 1976). The usual practice(Merrifield and Winant, 1989) is to rotate the spatial eigenvectorinto the frame of the semi-major principal axis of the correspondingamplitude time series. The depth-integrated EKE between 1000 mand 50 mab is given by:

EKEH ¼ 1=2Z

U�Udz� �

¼ 1=2X

n

hA�nðtÞAnðtÞiZ H�50

1000e�nðzÞenðzÞdz ð2Þ

where the integral is approximated by using the trapezium rule forthe discrete measurement levels. The integral is terminated 50 mabove bottom (H) so as to exclude the bottom boundary layer,and for the practical reason that the majority of moorings had nomeasurements there. In the following, only the first mode (n = 1)is used because for most moorings, this accounts for a high percent-age of the total variance of the input records (Table 2), has the char-acteristics of TRWs with nearly depth-independent, verticallycoherent fluctuations (guaranteed by the use of a single CEOFmode), and principal axes that are at a small angle to the generaltrend of the local isobaths. Departures from the depth indepen-dence mainly involve bottom intensification in some profiles.Changes of eigenvector direction with depth are generally negligi-ble. The use of depth levels above 1000 m was sometimes necessaryto properly characterize the lower-layer velocity profile. In these

variance Start date (yy-mm-dd) Length (days)

ands (cpd)

0.024–0.05 0.05–0.2

77.3/20.9a – 84-07-24 552

80.8 87-11-15 346

87.9 84.8 99-09-02 525

83.2 73.5 03-04-09 36377.0 – 03-04-05 36596.7 84.4 03-04-22 41187.9 – 03-05-16 46569.9/21.6a – 03-04-24 410

92.8 – 04-03-25 45692.4 – 04-03-24 45683.3 – 04-08-31 43162.4/33.4a – 04-08-31 431– – 04-08-30 433– – 04-08-30 434

– – 05-01-26 27676.9/14.0a 53.3/28.4a 05-01-25 35978.8 – 05-01-24 361


cases, the percent of total variance accounted for by the mode wasreduced somewhat over other similar locations, because theseupper-levels contain some surface layer eddy signals (e.g., GG andL7 in Table 2).

The mode 1 eigenvectors for moorings in Table 2 that have largeamplitude fluctuations are shown in Fig. 3a. At each site the vectorsare unidirectional indicating that turning with depth of the princi-

20 c

3500 m3000 m

2000 m

1000 m

200 m

I1

L3

L6

L5

L4V4

W3

(a)

10 m3s-2

20 c

3500 m

3000 m

2000 m

1000 m

200 m

(b)

Fig. 3. (a) CEOF lower layer mode 1 eigenvectors from selected mooring analyses displaycurrents at the locations identified in Table 2 (thick vertical bars). The standard deviationgiven by the arrow).

pal axes is negligible. Some sites show strong bottom trapping(e.g., I1 and L3), whereas others are nearly depth independent(e.g., G, L6 and L7). For TRWs, the degree of bottom trapping isdependant on the dominant periodicities, wavelengths and thedepth of the water column. Most of the depth variation of currentamplitudes occurs between 1000 and 2000 m, and is therefore con-sistent with Reid and Wang’s (2004) calculations of TRW velocity

m s-1

GL7

Y3

1000

2000

3000

0

Height(m)abovebed

m s-1

ed as pseudo-3D profiles. (b) Depth-integrated EKE for the CEOF mode 1 lower-layerellipses are representations of the depth-average lower-layer mode 1 currents (scale


profiles for exponentially stratified water columns that are charac-teristic of the gulf.

The lower-layer depth-integrated EKEH for the locations in Ta-ble 2 are given in Fig. 3b, which also shows the depth-mean stan-dard deviation ellipses obtained from the eigenvectors. The highestEKEH is under the LC at G and L7, with the west side having themaximum observed energy. Energy levels decrease towards thewest and also north of L7; however, relative higher energy levelsare observed moving into the escarpment from L7 through L3and L5, suggesting a wave propagation path with lower EKEH tothe north (Y3) and south (L6). The base of the escarpment isapproximately delineated by I1, L5, L4, GG and V4. It is somewhatsurprising that the energy level at Y3, which was close to thenorthern LC front for most of 2005, is less than at the escarpmentfurther to the west, though Oey (2008) also shows decreasing deepEKE towards the northern part of the eastern basin. Moreover, atY1, which is near the steep west Florida escarpment has essentiallynegligible lower-layer EKEH. In the west, the two deeper locationsat V4 and W2 have EKEH comparable to that at 92�W (GG), butagain the moorings at the base of the steep Mexican slope havesmall variances with that at W5 also being essentially negligible.Oey and Lee’s (2002) numerical model studies had the result that20–100-day deep energy was primarily restricted to a band acrossthe northern gulf between the �3000 and 3500-m isobaths, whichhas some correspondence to Fig. 3b. Radiation by the model LC and

Nor

mal

ized

Ampl

itude

Elapsed Tim

NE Gulf

NW Gulf

East & Central Gulf

Fig. 4. CEOF mode 1 normalized amplitudes for lower-layer currents. The abscissa is emooring IDs are the lower-layer integration depths below 1000 m.

westward translating LC eddies were the attributed sources of thisdeep energy. The standard deviation ellipses (Fig. 3b) tend to showmajor principal axes approximately aligned with the isobaths nearthe escarpment and steep topography. In the abyssal basin thefluctuations are less rectilinear and the principal axes are at a smallangles to the isobaths (e.g., at L3).

The normalized amplitude time series for each location are gi-ven in Fig. 4. TRW theory (Rhines, 1970) defines a cut-off fre-quency, Na, where N is the lower-layer Brunt–Väisälä frequencyand a the local bottom slope, above which waves are not supportedby these dynamics. The deep gulf topography is roughly bowlshaped and therefore locations with the deeper water depthsshould tend to have the largest fluctuations at longer periods. Thisrule holds quite well in both the eastern and western parts of thegulf basin, with the dominant periods being shorter closer to thecontinental slope (e.g. W2, Y2 and I1) and longer in deeper water(e.g., L7, L6, Y3 and W3). The spectra of the normalized amplitudesare given in Fig. 5, where the relative contributions to the varianceclearly show that longer periods tend to dominate in deeper water.Two dominant peaks of 50–60 days, and 25–30 days can be identi-fied with water depths of >�3000 m, and �2500–3000 m, respec-tively. The latter peak was prominent in the early central andwestern gulf deep current data (Hamilton, 1990), and clearly theyearlong records resolve most of the variance at these sites. Thisis not the case for the very deep locations, including the site in

e (days)

G2200 m

L72250 m

L31950 m

L51900 m

L62300 m

L42300 m

GG1900 m

Y31750 m

Y21500 m

I1900 m

Y11500 m

W32500 m

V42050 m

V31450 m

W2950 m

W4950 m

W5950 m

lapsed time in days from the beginning of each time series. The depths below the

G 2200 mL7 2250 mL6 2300 mL4 2300 m

W3 2500 m

V3 1450 mY3 1750 mL5 1900 m

GG 1900 mV4 2050 m

52 29 days

I1 900 mY2 1500 mL3 1950 m

52 29 days52 days

Fig. 5. Spectra, in variance preserving form, for the normalized CEOF mode 1 amplitudes of the lower-layer currents. The color codes give the mooring location and lower-layer thickness, and red is used for the largest depth-integrated EKE in each group. The thick gray lines are the subjectively averaged spectra.


the western gulf (W3), where the low frequency tails, with periodslonger than 100-days, are not resolved. Some of these deep records(W3 and L6) have energy also at the 25–30 day period peak.

In the eastern gulf, the LC pulsation and eddy shedding haveirregular intervals ranging from about 3 to 18 months (Sturgesand Leben, 2000), and it would be expected that some of this var-iability would be transferred to the lower-layer. However, theyearlong records preclude a statistical examination of the effectsof LC extensions and LC eddy presence or absence on the ampli-tudes of the short period (<100 days) bottom fluctuations thatdominate the deep observations (e.g., at I1, Y2 and L3). Short periodwaves at I1, and associated near-bottom moorings, have been pre-viously analyzed by Hamilton (2007) who suggested that wavetrains with periods of �8–12 days were generated fairly local tothe eastern Sigsbee Escarpment and were trapped there by thetopography. At least four distinct wave trains were observed, ofwhich three could be associated with the presence of major LCanticyclones, however, one wave train occurred when upper oceanconditions were quiescent. Thus, a direct connection of TRW occur-rence with LC eddy presence or eddy shedding from the LC is notclearly established in these data (though there are hints in the var-iability of the amplitudes of the TRW fluctuations). It is noted that,unlike other spectra in the eastern gulf, L3 shows fairly uniform en-ergy over a broad band with periods from 10 to �100 days (Fig. 5).

Based on this analysis, frequency domain EOFs were calculated,in a similar manner to the CEOFs above, for some or all of three fre-quency bands, 0.01–0.03, 0.024–0.05, and 0.05–0.2 cpd, respec-tively, based on the spectral content at each location (Fig. 5).Table 2 gives the percentages of total variance in each frequencyband, accounted for by the modes, for each mooring. In most cases,one mode suffices, but in a few cases two modes were significantaccording to the eigenvalue criteria of North et al. (1982). Thedepth integrated EKEH and depth mean standard deviation ellipsesare calculated using similar formulae to those used for the time do-main CEOF analyses, and are given in Fig. 6. The distribution ofEKEH with frequency band shows that the lowest frequencies(52-day) tend to have the most energy in 3000 m or more with de-cay towards the west from the west side of the LC (L7). The centerfrequency band (29-day) also has some power at L7 and has a moreuneven distribution with most of the larger relative contributionsto the total energy being near the escarpment (e.g., L5, GG andV4, but not L4). The shortest period (10-day) band is mainly signif-icant in a small region south of the delta (L3, I1, and L5). Differ-ences in the frequency band distribution of EKEH by location arealso seen in the time series (Fig. 4) and spectra (Fig. 5).

The depth-average modes (Fig. 6b) contain a great deal of infor-mation on rms particle displacements as a function of frequency.The hodograph ellipses are much more rectilinear than their equiv-alent CEOF modes (Fig. 3), and this is to be expected as TRWs arefrequency dependant transverse waves (Rhines, 1970). Other prop-erties are obtained from the dispersion relation under the assump-tion that fa/H� b, where b is the gradient of the Coriolisparameter, f. For the wavevector, K, with components (k, l), direc-ted parallel and perpendicular to the bottom isobaths (a = dH/dy),the wave frequency, x, is given by:

x ¼ �kaN=K cothðNHK=f Þ ð3Þ

The along-isobath wavenumber, k, must be negative so the wave-vector must point into the 2nd or 3rd quadrants with the y-axis di-rected up-slope. It can be shown that the wavevector isperpendicular to the transverse velocities, and therefore perpendic-ular to the major axes of the ellipses in Fig. 6b. The group velocity,cg (= ox/ok, ox/ol) is directed normal to the wavevector, such thatcg is directed clockwise (upslope) or anticlockwise (downslope)with respect to K when the latter points downslope (i.e., into the3rd quadrant) or upslope (i.e., into the 2nd quadrant), respectively.Therefore, the energy propagates along rays that coincide with thedirection of the major axes of the ellipses in Fig. 6b such that shal-lower water is to the right (Oey and Lee, 2002). Another conse-quence of (3) is that the wavevector rotates such that it becomesmore perpendicular to the isobaths as the frequency decreases. Atthe cut-off frequency, Na, the wavevector points along the negativex-axis and the particle displacements are normal to the isobaths.This rotation of the wavevector with frequency is one of the diag-nostics of TRWs (Thompson, 1977) and occurs at locations withgentle bottom slopes such as L3, L6, and L7 (Fig. 6b). Closer to theescarpment, the ellipse major axes are more constrained to be alongthe trend of the steep slope, as has been noted in previous studies(Hamilton, 2007). This implies that the wave energy propagatesalong, rather than across, the escarpment.

Unlike the CEOF modes, some locations, particularly underthe LC at G and L7, have more than one significant mode (Table2) in some of the frequency bands. The inclination of the ellipsesat L3 implies energy flux towards the northwest and the escarp-ment at 52 and 29 days. The mode 2 ellipse at L7 has about thesame EKEH and ellipse inclination as the 52-day mode 1 at L3.Therefore, part of the L7 fluctuations at this period could be con-tributing to the northwest propagation of TRWs towards theescarpment. However, the larger proportion of the 52-day energyis in mode 1, and this ellipse, and the 29-day mode 1 ellipse, im-

3500 m

3000 m

2000 m

1000 m

200 m

5 m3s-2

Mode121212

0.010-0.03

0.024-0.05

0.050-0.20

Band (cpd)

3500 m

3000 m

2000 m

1000 m

200 m

10 cm s-1

Mode121212

0.010-0.03

0.024-0.05

0.050-0.20

Band (cpd)

a

b

Fig. 6. (a) Depth-integrated EKE as a function of frequency band. Where more than 1 mode is present, the height of the bar represents the total EKE, and the colors show thesplit between the modes. (b) Depth average mode eigenvectors represented as hodographs for each frequency band. Mode and band colors are the same as for (a).


plies energy flux towards the Campeche Bank, where the topog-raphy slopes up to the south and TRWs would presumably re-fract into the southeast corner of the eastern basin. It ispossible that the lower magnitude northeastward 52-day andthe northwestward 29-day fluxes at G may have originated fromsuch TRWs on the west side of the LC, propagating anticlockwise

around the deep southern half of the eastern basin. If the direc-tion of cg at L3 is towards the escarpment, then the direction atL6 of the much weaker fluctuations is southwestward towardsthe center of the western basin and therefore may be a manifes-tation of reflected TRWs from the northward shoaling topogra-phy (Mizuta and Hogg, 2004).


The periodicities of the records are reasonably consistentthrough time but can have large amplitude variations (Fig. 4). Thiswill be discussed later using wavelet analysis on a couple of re-cords. Hamilton (2007) calculated the spectra for the distinct wavetrains in the 2-yearlong record at I1, and found similar spectralcontent for all events and for the total record. The spectra and fre-quency domain EOFs show average responses over an interval ofapproximately 1 year that may include a number of differentevents.

The overall view of TRWs in Fig. 6 suggests considerable com-plexity in both the frequency and energy content of the fluctua-tions, and also possible propagation paths of wave packets. Theindication from the available observations is that deepwater regionon the west side of the LC, just north of the Campeche Bank hasvery high lower-layer kinetic energy and may be radiating towardsboth the west and south. The region around L7 was identified inOey’s (2008) model as having strong baroclinic instabilities. Theescarpment between 90�W and 92�W turns the northwestwardpropagating waves into along-slope fluctuations that will be ex-plored in more detail in the next section. In the northwest corner,energy levels are small compared to eastern gulf and the centralparts of the escarpment.

Further evidence for the dominance of TRWs in the lower-layercomes from the deep Lagrangian float tracks. If linear TRWs werethe only process operating in the lower-layer, then to first order,floats placed in such a field would simply oscillate in a rectilinearfashion about their deployment point with the direction andamplitude of the displacements changing with changing periodof the waves propagating through the area. Examination of Fig. 2shows that the deep float tracks have some similarity to these ide-alized waves rather than the translating loops expected in an eddydominated regime (e.g., Kirwan et al. (1984) and Hamilton et al.(1999) for drifters in LC anticyclones). However, it is possible thatsimilar tracks could be produced by a quasi-stationary or rapidlydissipating field of deep eddies (e.g., Oey, 2008). The wave inter-pretation is favored herein because the Eulerian current oscilla-tions are generally in good agreement with (3). Eddy-waveambiguities remain to be resolved by more comprehensive obser-vations than are presently available. In particular, float tracks inthe eastern basin, under the LC, show large amplitude displace-ments that have both clockwise and anticlockwise motions, whichare often adjacent in time. There are several tracks (to be discussedin more detail in later sections) that begin less than half a degreeapart, and after 6 months, end in the same vicinity, still less thanhalf a degree apart. Of the 36 floats deployed, only one has a sec-tion of track that is consistent with a translating cyclonic eddy.In Fig. 2, three anticlockwise loops are observed moving in towardsthe western slope between 24�N and 25�N, and 93–96�W. Theother exception to the general meandering over the same regionare the tracks that move close to the northern escarpment, wherethey get transported westwards in a relatively narrow stream. Thisappears to be the main route by which floats, initially deployedaround 91�W, get to the western part of the basin. It is also note-worthy that almost no floats cross the escarpment from the abyssalbasin to the northern slope. The 4 tracks north of the escarpment inFig. 2 are all at 1000 m and therefore are more likely to be influ-enced by the lower circulations of surface-layer eddies.

Mizuta and Hogg (2004) modeled the refraction and reflectionof up-slope propagating TRWs onto uniform shoaling topography.Their principal result was the incident and reflected waves pro-duced a convergence of Reynolds stresses in the bottom boundarylayer that forced an along-slope mean current that would be con-centrated where the bottom slope (a) begins to increase. The depthstructure of this mean flow was similar to, but not necessarily ex-actly the same as the incident TRWs. DeHaan and Sturges (2005)used more heuristic arguments on the rectification of TRWs by a

topographic slope to explain the limited observations of cyclonicmean flow along the base of the northern slope in the gulf. Thepresent expanded currents database, including the deep Lagrang-ian floats, can be used to extend and further confirm the existenceof substantial westward mean flows along the Sigsbee Escarpment.

Means and standard deviations of float velocities are calculatedby defining rectangular areas that are adjacent to, and alignedalong, the escarpment. The sections of all smoothed floats tracks,excluding the two deployed at 1000 m, which pass through andare within the rectangle, are used to calculate velocities using cen-tered finite differences. The ensemble average of these velocityestimates produces the statistics for the box location. The methodis similar to DiMarco et al.’s (2005) estimation of gulf-wide velocitystatistics using near-surface drifters. In addition, Lagrangian veloc-ity statistics were estimated for 1� latitude–longitude squares cen-tered on selected mooring locations for the purpose of comparingwith Eulerian estimates using current meter measurements. Thenearly barotropic nature of flows below 1000 m means that mixingfloats from 1500, 2000, 2500 and 3000 m, into a single lower-layerestimate, is unlikely to bias the results. The means and standarddeviation ellipses from both floats and moorings are shown inFig. 7, with supporting data in Table 3. The degrees of freedom(dof) are estimated using velocity time series from nearby moor-ings to calculate the autocorrelation time scales, and given thevarying dominant periodicities with location, the estimates are lessreliable in deeper water depths. The standard error of the mean isgiven by:

SE ¼ rv=ffiffiffiffiffiffiffiffidofp

ð4Þ

where rv is the standard deviation along the principal major axis ofthe ellipse. For the western boxes 1 and 2, the time scale was inter-polated from moorings W2 and W3 to the 3000-m isobath (Fig. 7).

Mean currents from both moorings and floats show consistentwestward flows along the escarpment that seem to form a contin-uous current from around 89�W to below 24�N on the Mexicanslope. The variances are also reasonably consistent between floatsand moorings even where the measurements were taken in differ-ent years. In the western gulf, the float mean for box 2 is in thesame direction (SSW) as that at W2, but has a smaller magnitude,which is either a consequence of different measurement periods orthe mean flows are concentrated close to the base of the slope. Jet-like mean flows over the steepest part of the escarpment are dis-cussed in the next section for a transect around 91�W. It is perhapssignificant that floats that move southwards from the northwestcorner near 26�N, follow the 3000-m isobath (Fig. 2). This helpsto explain why the EKE at W5 is so weak if the source of TRW en-ergy is in the northwest corner and is refracted offshore in the gen-eral direction of the 3000-m isobath, so leaving shallower areas ofthe lower western slope in a shadow zone. Presumably the de-crease in mean flows southward of the northwest corner implies,through continuity, a mean flux from the Mexican slope towardsthe interior of the western basin.

4. The Loop Current and Sigsbee Escarpment in the central gulf

4.1. Near bottom fluctuations near the Sigsbee Escarpment

TRWs were investigated at smaller scales in the vicinity of theSigsbee Escarpment, south of the Mississippi delta, in the 1-yearlong Exploratory experiment. Some of the observations from thefull-depth moorings (L1 through L5; Table 1) were used for theoverview, however, the complete array included 12 near-bottommoorings (M1 through Q2) with current meters at 100 and 500mab, similar moorings with a single instrument 100 mab (M3,M4 and M5), and a closely spaced transect across the escarpment

200 m

1000 m

2000 m

3500 m

10 cm/s

5 cm/s

Lagrangian Eulerian1

2

34

5

Fig. 7. Lower-layer mean currents from RAFOS floats (red) and lower-layer current meters (purple). Mean velocity scale is 5 cm/s. The dashed boxes are the averaging areasfor the floats, and the escarpment box location numbers refer to Table 3. The float (blue) and current meter (cyan) standard deviation ellipses use a scale of 10 cm/s. The lightgray shaded area shows the steepest slope (500 m descent) of the Sigsbee Escarpment.


at 91�080W of six near-bottom moorings (S1 through S6) with asingle instrument three mab. Two of these latter moorings (S3and S5) had additional current meters at 200 mab. Their locationsare given in Fig. 8, which also shows the locations of the comple-mentary array of 27 PIES. Details of the array deployments, instru-mentation and data processing methods for this study are given inDonohue et al. (2006).

The average EKE and mean velocities for the 40-HLP currents at100 mab (exceptions are 200 mab for S3 and S5, and 500 mab forN3 and O3) are given in Fig. 8. Major features are the rapid de-crease of EKE above the escarpment compared to below, the twolobes of high EKE in the northeast (N2 and M1) and southwest(O3 and N4) sections of the escarpment, a general convergence ofmean flows towards the escarpment, the southwestward meanflow along the escarpment, and the exceptional high mean speedsin the middle of the steep escarpment slope at S3. The high EKE en-ergy in the northeast of the array corresponds to the high lower-layer speeds observed by Hamilton (2007) at I1 (located betweenM5 and M2) between September 1999 and September 2001, whichwere attributed to distinct trains of short period (�10 day) TRWs.The stronger southwesterly mean flows along the escarpment inFig. 8 are consistent with the earlier estimates made with a limitednumber of moorings, and also consistent with convergences ofboundary layer Reynolds stresses and the reflection of TRWs bythe steep slope as modeled by Mizuta and Hogg (2004) and dis-cussed by Hamilton (2007). A more detailed view of the along-escarpment mean flows is given in Fig. 9, where both the meanand standard deviation of the flow appear to be a maximum overthe middle to lower part of the steepest part of the escarpment.Most of the other moorings were located either below or abovethe escarpment and so it is not known whether there is a narrow(<10–20 km wide) escarpment jet over other sections. It is alsonot clear whether the jet extends farther up into the water columnabove the steep slope. However, the presence of a deep escarpment

jet helps to explain the relatively rapid translation of the RAFOSfloats to the west as indicated in Figs. 2 and 7. The standard devi-ation at 200 mab at S3 is slightly less than the mean and the year-long observations show that the southwestward flow at thislocation rarely reverses. Fig. 9 also shows the reductions of boththe mean and standard deviations above as compared to belowthe escarpment.

4.2. Lagrangian analysis

Neglecting mean flow, particle displacements in deep flowsdominated by linear TRWs are expected to be rectilinear. There-fore, displacements by RAFOS floats should have characteristicssimilar to velocity hodographs derived from Eulerian current me-ters. Examples of four tracks from floats that remained in the gen-eral vicinity of the Exploratory array for an interval of �5.5 monthsare shown in Fig. 10, along with standard deviation ellipses fromnearby current meters at similar depths. The Eulerian statisticswere calculated for the same length interval (167 days) that wasavailable from the float tracks, but beginning 10 days earlier. Floats0456 (1500 m) and 0476 (2500 m) were found close to the escarp-ment near L5 when the sound sources were restored, and as a con-sequence they moved rapidly to the southwest with the mean flow.However, after 10–20 days, they moved southwards out of the jetand began to oscillate where the displacements had a similar direc-tion to the principal axes of the L4 and L6 currents, with displace-ments along the general trend of the isobaths being much largerthan across. Both the 1500-m and 2500-m floats had similar ampli-tude displacements and their paths overlap with the 1500-m beingabout 1� east of the 2500-m float. Floats 0470 (1000 m) and 0466(1500 m), during the same time interval, oscillated over the Missis-sippi Fan to the east of the array. The mean positions of these twofloats were nearly coincident and it is clear that the deeper 1500-mfloat had larger amplitude displacements than the 1000-m float.

Table 3Time scales and degrees of freedom for Lagrangian and Eulerian velocity statistics.

Location Longitude latitude Box size Number tracksin box

Mean float/CM depth(m)

Number 6-h velocityestimates

Auto-correlation timescale (h)

dof SE (cm/s)

1-L 95.60�N 1.5� � .5� 23 2053 2810 60 281 0.223.37�W

2-L 95.42�W 1.5� � .5� 15 1796 1577 60 158 0.525.18�N

3-L 93.70�W 1.5� � .5� 25 2108 1468 95 93 0.525.99�N

4-L 92.16�W 1.5� � .5� 22 1810 1151 100 69 0.725.67�N

5-L 90.66�W 1.5� � .5� 34 1761 1375 122 68 0.926.28�N

L5-E 90.82�W 2625 1644 122 81 1.526.34�N

L7-L 86.97�N 1� � 1� 29 1656 1465 240 37 1.8

L7-E 25.52�N 3187 1642 41 2.2

Y3-L 87.53�W 1� � 1� 12 1856 1071 140 46 1.1

Y3-E 27.61�N 2689 1436 62 1

Y1-E 87.55�W 2479 1444 79 110 0.328.35�N

L1-E 89.22�W 1400 1523 62 147 0.827.60�N

L2-E 91.11�W 1650 1485 45 198 0.327.10�N

L3-E 88.96�W 2900 1451 61 143 126.09�N

L4-E 91.13�W 3250 1462 100 88 0.925.92�N

L6-E 90.50�W 2995 1861 190 59 0.925.09�N

V3-E 94.95�W 2400 1823 90 122 0.526.05�N

V4-E 94.09�W 3000 1823 95 115 0.726.04�N

W2-E 95.44�W 1965 1725 40 259 0.325.39�N

W3-E 94.89�W 3518 1727 175 59 0.825.27�N

W5-E 96.30�W 1998 1735 35 297 0.224.04�N

–L, estimated from Lagrangian floats.–E, estimated from moored current measurements.


The standard deviation ellipses in Fig. 10 all show evidence of thebottom-trapping characteristic of TRWs.

The Lagrangian and Eulerian velocities from these four floatsand nearby current meters are given in Fig. 11. The float velocitieshave more rotary fluctuations when compared to the moored cur-rents, however, there is not a preferred rotation and an anticy-clonic loop is often followed by a cyclonic loop (see also Fig. 10).Otherwise, the current vector time series from the floats have sim-ilar amplitudes and periodicities to their Eulerian counterparts.The KE spectra for both the Eulerian and Lagrangian velocity timeseries are also given in Fig. 11, which shows that the major low fre-quency peak is shifted to higher frequencies for the Lagrangian re-cords. Middleton (1985) investigated the differences betweenLagrangian and Eulerian sampling of ocean currents in terms ofthe ratio of the Lagrangian to Eulerian timescales, g = TL/TE, andtheoretical geophysical turbulence models, where:

TL;E ¼Z 1

0

u0L;EðtÞu0L;Eðt þ sÞD E

hu02L;Eids; ð5Þ

and u0 are the Lagrangian or Eulerian velocities with means re-moved. In geophysical flows, g < 1 (Chiswell et al., 2007) such thatthe characteristic length scales of the fluctuations or eddies areshorter than the distance that drifters traverse in one Eulerian time-scale. Therefore, a drifter’s velocity becomes decorrelated in timefaster than the Eulerian timescale because the drifter advects intoregions that are spatially decorrelated. This results in Lagrangiantimescales that are shorter than Eulerian timescales. Middleton(1985) further suggests that under homogeneous isotropic condi-tions, the Lagrangian spectrum should be related to the Eulerianspectrum by a variance preserving transform:

PLðxÞ ¼ gPEðgxÞ ð6Þ

200 m

500 m

1000 m

2000

m

3000 m

3500

m

cm2 s-2

5 cm/s

O1

N2

N3

O2

Q2

O3

N4N5N6

O4

M1

M5

M4

M3M2

L2

L1

L3

L4

L5

S1S3S5S6

Fig. 8. Contours mean kinetic energy, overlaid with mean velocity vectors, for 1-year 40-HLP currents at 100–500 mab. The labeled solid squares and dots show the locationsof full-depth and near-bottom moorings, respectively. Moorings S2 and S4 are midway between S1 and S3, and S3 and S5, respectively. The PIES locations are given by thesolid diamonds. The gray shaded region is the steep part of the Sigsbee Escarpment.


where the Lagrangian and Eulerian velocity spectra are given by PL

and PE, respectively. Although the conditions for the validity of (6)are violated by the wave-like and inhomogeneous space and timescales of the deep currents, it nonetheless provides a basic explana-tion for the shift to higher frequencies of the peak energy, and a pos-sible broadening of PL with respect to PE.

Estimating TL directly from the autocorrelation function of sin-gle drifter velocities is difficult because of spatially inhomogeneousmean currents and the wave-like nature of the float displacements.Chiswell et al. (2007) take an ensemble approach for surface layerdrifters in the Tasman Sea, but this not feasible for the relativelyfew numbers of tracks in a given region that are available fromthese RAFOS floats. Estimation of g from the spectra (Fig. 11) givesa range of 1.0 (0476) to �0.65 (0470) implying that the floats andcurrent meters are sampling similar velocity fields over a 6-monthinterval. Chiswell et al. (2007) obtain g � 0.1–0.2 for eddies in theTasman Sea. The Lagrangian and Eulerian velocity comparisonswere also performed for mooring L7 and two 1500-m floats(0467 and 0458) for the same time interval (Fig. 10). The floatsoscillated around under the west side of the LC, north of the Cam-peche Bank slope, with similar characteristics to the floats dis-cussed above. Displacements were larger than those to the northand west, which is not surprising considering the large velocityvariances at L7. These two float paths under the LC provide a goodillustration of the low dispersion of deepwater parcels as they be-gan and ended their 6-month sojourn about the same distance(�70 km) apart. PL was also shifted to higher frequencies with re-spect to PE, and g was estimated to be �0.6. Details may be foundin Donohue et al. (2006).

In Oey’s (2008) model predictions of deep cyclonic eddies prop-agating westward or northwestward of the Loop Current, the dissi-pation time scale is about one month during which the eddiestransfer energy to deep TRWs (Oey, 2009; personal communica-tion). This is a plausible mechanism that the observations are notextensive enough to attempt to verify. However, some aspects ofthe deep float tracks are not entirely compatible with this picturein that little evidence of eddy propagation is seen under and westof the LC. The Eulerian and Lagrangian integral timescales at1500 m in the model are about 1 month and 1 week, respectively(Oey, 2009; personal communication). These model estimates arefrom much more robust ensemble averages than are possible withthe observational data. However, estimates of TE in Table 3 are inthe range of 5–10 days, and the ratio g is �0.6–1.0, which impliesmore low frequency energy and shorter space scales in the modelthan in the eastern deep gulf. It might be speculated that deep cy-clones spun up by the LC through baroclinic instability processesare more transitory and give up their energy to TRWs faster thanshown by Oey’s (2008) model. Connections between upper andlower layers are explored in Section 6 where there is observationalevidence that baroclinic instabilities off the west Florida slopecould be directly exciting narrow band TRWs of 20–30 day periods.

4.3. Wavelet analysis

The amplitudes of the deep current fluctuations are quite vari-able in time as can be seen from Figs. 4 and 11. This variability isexamined for the 2500 m level at L3, which has a fairly broad KEspectrum (see Fig. 5) for periods longer than 10 days, using the

N5 S6 S5 S4 S3 S2 S1 L4

Sigsbee Escarpmentat 91o 08'W

-10

-5

0

5

10

15

Alon

g Sl

ope

Velo

city

(cm

/s)

<V>

<V'2>1/2

Dep

th (m

)

Distance (km)

North South

Fig. 9. Upper panel: contoured mean along-slope 40-HLP current velocity component (065 T) across the Sigsbee Escarpment (section S). Measurement positions are indicatedby the solid squares. Lower panel: Along slope mean velocity (lower line) and standard deviation (upper line) from the bottom most instruments on each mooring. Negativevelocities are towards the southwest.


wavelet power spectrum. The methodology follows Torrence andCombo (1998) with the use of the complex Morlet continuouswavelet transform (CWT), which is suited for feature extractionand revealing patterns. The time scale of a Morlet wavelet verynearly equates to its equivalent Fourier period. Torrence and Com-bo (1998) estimate the significance levels for the wavelet powerspectrum using a standard method that employs the theoreticalred-noise spectrum for a univariate lag-1 autoregressive process.The lag-1 autocorrelation coefficient (a) in this study is estimatedby the least-square fit of the Fourier spectrum of the time series tothe non-linear theoretical red-noise spectrum (Eq. (16) in Torrenceand Combo, 1998). This works better than a direct estimate fromthe time series because it removes guessing the optimum lag.The time-averaged or global wavelet spectrum has been shownto provide an unbiased and consistent estimation of the true Fou-rier power spectrum of a time series. Torrence and Combo (1998)also define a ‘‘cone of influence” where end of time series effectscan distort the analysis and the regions of the time-frequencyspace where this occurs increase with the time scale of thewavelet.

The u- and v-component wavelet power spectra for L3 are givenin Fig. 12, where the cross-isobath u-component has significantpower at shorter periods compared with the along-isobath v-com-ponent. The global power in Fig. 12 shows that the u- and v-com-ponents dominate at periods of 10–30 days and 40–100 days,respectively. The distribution of power with time and frequency

shows that there is more significant variance at shorter periodsin the u- than the v-component, and that the v-component domi-nates at longer periods. This is to be expected from the dispersionrelation (3), because the principal major axis of the fluctuations(and thus the group velocity vector) rotates from across- toalong-isobath as the wave period increases. Such behavior of thelower-layer current fluctuations is consistent with TRWs, as sucha pattern would not be expected from translating eddies or fromisotropic fluctuations of a quasi-stationary eddy field. For eddies,u- and v-component fluctuations would tend to be isotropic. Thepower in both period bands has higher amplitudes during the Juneto September, 2003 interval while eddy Sargassum formed andseparated. The initial location of Sargassum, before translating intothe western gulf, was in the northern part of the eastern basin.Eddy Titanic, on the other hand, detached in January 2004 muchcloser to the Campeche Bank, and its initial southwestward pathwas close to and parallel to the steep southern slope. The floatpaths in Fig. 10 took place while the LC was moderately extendedand eddy Titanic was separating. The wavelet power at L3 showssome increase around the time of Titanic’s separation, particularlyin the u-component, but the amplitudes are not significant at the95% level. Therefore, there are some indications that TRW activitynorth and west of the LC increases during a LC extension and LCeddy separations as would be expected from the models of TRWgeneration by a pulsating meander over a uniform sloping bottom(Malanotte-Rizzoli et al., 1987).

200 m

1000 m

2000

m

3000

m

3500

m

L2

L1

L3

L6

L7

Y3

L4

L5

5 cm/s

0466

0456

0470

0476

0458

0467

10/30/2003 to 4/15/2004

Fig. 10. Smoothed RAFOS float paths at 1000 (red), 1500 (blue) and 2500 m (green) for the indicated interval. The arrow heads are at 10-day intervals, and the start of thepath is given by a solid square. For 0467 and 0458, end points are marked with a solid diamond. The 40-HLP velocity standard deviation ellipses for the same length intervalbeginning 10 days earlier are shown for the L3, L4 and L6 moorings at the same depths as the floats (1000 m, dashed; 1500 m, thin; and 2500 m, thick). At L7, the ellipse is forthe 2000 m velocity record. The other mooring locations are given for reference. The Sigsbee Escarpment is shaded gray.


4.4. Variability along the escarpment

In the overview above, it was emphasized that the dominantperiods of the deep current fluctuations change with location andwater depth. The KE spectra (Fig. 13) from three moorings, M1,N4, and L4 (see Fig. 8 for locations), which are just seaward ofthe steep slope, illustrate this particularly well. In the northeast,at M1, short period fluctuations of �8–12 days dominate. This issimilar to the spectra for the nearby I1 site, discussed by Hamilton(2007) and attributed to the local trapping of high frequency TRWs.In the middle of escarpment, at N4, 10-day fluctuations are largelyabsent and there is a broad peak with periods around 20–30 days.In the southwest, at L4, the energy levels are less and long periodfluctuations with periods >35 days dominate. This ‘‘filtering” ofthe variability westward along the escarpment is examined belowin terms of TRW rays. In the southeast corner, at L3 (Fig. 13), abroad band of periodicities greater than 10 days is present and sug-gests that this region could be upstream of the differing dominantperiodicities along the escarpment.

The wave like nature of the bottom fluctuations is best illus-trated by the frequency domain EOF analysis of the PIES bottompressure anomalies, where the area average signal has been re-moved. Phases for scalars are easier to interpret than for vectors.The amplitudes and phases of the first EOF modes for �60 and�25-day fluctuations are given in Fig. 14. The bottom pressure ar-ray has a little better horizontal resolution than the bottom currentmeter moorings except near the escarpment. For the �60-day per-iod fluctuations, the largest amplitudes are in the southern part ofthe array below the escarpment and phase propagation is south-wards (positive phases lead) approximately normal to the isobaths.For the 25-day fluctuations, the center of the largest amplitudes

has shifted to the east and the phase propagation there is more to-wards the southwest. Closer to the escarpment around 26�N, thephase propagation is more towards the northwest implying reflec-tion and offshore propagation of energy. These changes in thephase contours are entirely consistent with the dispersion relation(3) and are further evidence that bottom fluctuations below theescarpment are dominated by TRWs. The 25-day mode 1 map(Fig. 14) also shows a band of lower amplitudes across the north-ern part of the array that appears to be separate from the high-en-ergy region in the south. This seems to be an indication of weakersources more to the east or northeast of the array. This will be ex-plored in more detail below.

4.5. TRW ray tracing

To initiate TRW ray tracing, an estimate of the wavelength andwavenumber direction at a start location is required. These initialparameters are obtained from a horizontal frequency domainEOF modes where the records are from instruments 100–500mab for 3 or 4 closely spaced moorings. The wavenumbers are thenestimated by least squares to the mode phase angle differencesacross the array in the same manner as Hamilton (1990). For theExploratory array, L3, O1, O2 and Q2, and in the northeast gulf,Y2, Y3 and Y4 were utilized (see Figs. 8 and 15 for locations). Theresults for two frequency bands are given in Table 4. Wavelengthscan also be estimated from vertical profiles of mode amplitudes,assuming constant N, using:

k ¼ NK=f ð7Þ

where the trapping depth (1/k) is from the least-square fit of themode eigenvector magnitudes to A0 cosh(kz), where z is measured

04661500m

04701000m

04762500m

04561500m

L31000m

L31500m

L42500m

L41500 m

L61479 m

L62490 m

cm/s

cm/s

cm/s

cm/s

L4 1500 m

L4 2500 m

L6 1479 mL6 2490 m

04762500 m

04561500 m

L3 1000 m

L3 1500 m

04701000 m

04661500 m

(x2)

Kinetic Energy Spectra

Fig. 11. Velocities derived from the smoothed RAFOS float tracks in Fig. 10 with 40-HLP current vectors from adjacent moorings. Float numbers and current meter locationsand depths are on the RHS of the figure. The RH panels show the KE spectra for the indicated float (dashed) and moored (thin solid) currents in variance preserving form, usingtime series lengths of 167 days and 14 dof.


upwards from the ocean surface. The results for L3 (Table 4) areconsistent with the direct calculation using phase differences. Table4 also includes the vertical mode analysis of the records at L7 for thetwo intervals corresponding to the Exploratory and Eastern Gulfstudies. The former are repeated from Table 2 for convenience,and the latter only overlapped the Y mooring records by 8 monthsand so does not resolve the lowest frequencies as well as the earlierdata.

Ray tracing uses the complete TRW dispersion relation and theWKB approximation where changes in wavenumbers and groupvelocity are caused by changes in the environment, which are as-sumed to vary on scales larger than the local wavelength. Theimplementation follows Pickart (1995) and the details are givenin Appendix A. Ray path calculations are principally dependenton the degree of smoothing used for the topography, and so pathsare approximations of energy propagation. Previously Oey and Lee(2002) and Hamilton (2007) have employed essentially the samemethod in the gulf. The results of the eastern gulf analysis forthe 60 or 61-day period bands are shown in Fig. 15. The EKE andthe velocity hodographs for mode 1 are from an EOF analysis ofall the near-bottom currents in the Exploratory array. The highestamplitudes are in the southern part of the array with low ampli-tudes above the escarpment and in the northeast corner, very sim-ilar to the 60-day bottom pressure EOF mode 1 in Fig. 14.

For mode 1, calculated from the Y2, Y3 and Y4 array, the highest60-day energy is at Y3. The wavelength calculated from the mode 1phase differences is 162 km (Table 4), which is within the range ofpreviously derived estimates in the deep gulf (Hamilton, 1990,2007). The direction of the major axes of the mode 1 ellipses indi-cate that phase propagation is south or southeastwards, which wasthe predominant direction of the eastern LC front that was close to

the array for much of 2005. The second mode is barely significantand the derived wavelength is larger than expected, and suggeststhat this weak signal is not a propagating wave. TRW ray tracingfrom the Y locations, using the 162 km initial wavelength and a60-day period, shows that a TRW could reach the upper escarp-ment in about 40–45 days, but the region of impact is an area oflow energy as measured by the earlier study. However, if the rayis moved slightly southward so it favors the larger fluctuations atY3, then it is apparent that this northeastern gulf region could po-tential supply some energy to the northern part of the high KE re-gion below the escarpment. Southward displacement of the raycould also be caused by the westward mean flow along the escarp-ment as discussed by Oey and Lee (2002). This effect is not in-cluded in the ray tracing calculations given here. Hamilton(2007) did attempt to crudely model a mean escarpment currentand found some displacement of the rays near the escarpment;however, not including this effect does not significantly changethe results. The long transit times and the relatively low energycompared to the southern edge of the Exploratory array, however,probably favor dissipation of these 60-day TRWs before they im-pact the escarpment region. Backward ray tracing of this 60-daywave indicates the source region is probably between the 3000and 2500-m isobaths, because deeper than 3000 m, the groupvelocities become very small, causing the ray to be terminated.

In the escarpment region the ray path was initiated in thesoutheastern corner (Table 4) and the forward ray follows the gen-eral trends of the large amplitude major axes of the hodographellipses towards and then along the escarpment. The ray is re-flected at the escarpment by reversing the sign of the upslopewavenumber, as in Hamilton (2007), and the dashed line gives thispath, which corresponds more with the direction and amplitude of

S T

S TU-cmpt (210°T) Variance: 72.25 Red Noise α: 0.695

V-cmpt (120°T) Variance: 113.32 Red Noise α: 0.905

L3 at 2500 m

Fig. 12. RH panels show the local wavelet power spectrum of the velocity components from L3 at 2500 m for the indicated time interval using the Morlet wavelet normalizedby the variances of the respective series. The thick solid contours enclose regions of greater than 95% confidence for a red-noise process with the indicated lag-1 (a)coefficients. The lighter shades indicate the ‘‘cone of influence” where edge effects become important. The red event lines show the detachment dates of LCE’s Sargassum andTitanic (from Leben, 2005). The LH panels show the respective global (time-averaged) wavelet spectrum (solid lines). The dashed lines show the mean red-noise spectrum(lower), and the 95% confidence levels (upper) for the global wavelet spectra, given their respective a’s.


the ellipses in the southwest corner than the transmitted ray. How-ever, the transmitted ray does correspond to the direction of thefluctuations at S5 above the escarpment on the 91�W meridian,but appears to rapidly dissipated to the west (i.e., by O4) by therough topography. Therefore, the forward ray paths imply thatlong period waves are refracted away from the northeast parts ofthe escarpment, and the majority of the energy is reflected fromthe escarpment back towards the deep western basin.

The backward ray-trace from the southeast corner shows thatL7 lies on the energy propagation path and the mode 2 oscillationsfrom the L7 lower layer analysis from the same interval as theExploratory program (Table 4 and Fig. 15) line up with ray quiteclosely. The wavelength at L7 from the backward ray path is300 km, and this is consistent with the almost depth independentnature of the fluctuations of both modes, which imply a trappingdepth (1/k) of order the water depth (3340 m). The transit time

M1

N4 L3

L4

Fig. 13. Kinetic energy spectra in variance preserving form for 40-HLP currents 100mab along the Sigsbee Escarpment at M1 (thick solid line), N4 (thick dashed line),and L4 (thin dashed line). Additionally the KE spectrum for L3 at 100 mab (thin solidline) in the SE corner of the array is also included.


from L7 to the escarpment is�25 days, which is much less than thetransit time from the northern Y array. The L7 modes from 2005are very similar to those in the earlier interval except for about30� clockwise rotation of the major axes, which indicates throughthe dispersion relation (3), shorter wavelengths. In 2003 and 2004,the LC axis was more northerly directed than the more northwest-erly trend in 2005, and this perhaps has an influence on the genesisof the TRW modes along the west side of the LC. The slightly differ-ing results at L7 suggest, not surprisingly, that there is inter-annualvariability in the deep TRW regime. If the west side of the LC, nearthe Campeche slope, is the primary generation zone for longer per-

200 m

500 m

1000 m

2000

m

3500

m

cm

335-33 Day EOF Mode 1 Bottom Pressure Anomaly (cm)

55.0% Total Variance

33

Fig. 14. EOF mode 1 amplitudes (shaded in cm) and phases (contour lines in degrees; neon 60 and 25 days from the exploratory array of PIES bottom pressure anomalies. The S

iod TRWs that propagate to the west as indicated by these results,then the northern (from the Y moorings) and southern (from L3and L7) rays in Fig. 15 imply a reduction in horizontal area be-tween the rays as the escarpment is approached. This would indi-cate an increase in energy if dissipation is disregarded, and couldaccount for the large amplitude 60-day fluctuations observed nextto the escarpment.

Similar EOF analysis of wavelengths and their use in initializingray tracing were conducted for 20–25 day period band (Table 4 andFig. 16). In the horizontal EOF analysis of the three Y moorings, thefirst two modes are significant and the directions of the major axesof the ellipses at Y3 and Y4 imply that energy is propagating up-slope (mode 1) and down-slope (mode 2). With the estimatedwavelengths from the phase analysis, the ray tracing producestwo similar ray paths towards the escarpment because thedown-slope ray is reversed by the topography. The backward raypaths are also similar and point to the Y1 location, which has verylow energy in this frequency band. This implies again that the gen-eration zone is fairly local to the deeper parts of the study area. The25-day forward ray paths imply that the Y moorings could be anupstream source for the relatively weak fluctuations at the shal-lower eastern end of the escarpment with transit times of �12–15 days (see also Fig. 14).

The mode 1 EKE and hodograph ellipses for the Exploratorystudy (Fig. 16) again show that the largest amplitude fluctuationsare below the escarpment between 90�W and 91.5�W. The 23-day ray paths initiated in the southeast corner of the Exploratoryarray align nicely with the more energetic ellipses with an indica-tion that both reflected and transmitted rays contribute to the var-iance in the west. Again the effects of persistent mean flows nearthe escarpment have been neglected. The rapid damping of thefluctuations above the escarpment seems to show that the trans-mitted ray is dissipated by the rough topography there. Comparingthe 23-day and 60-day forward ray paths shows the 23-day energypenetrates farther north along the escarpment, and the relativeamplitudes at N4 with respect to L3 confirm this, and explainswhy more 20–30-day variance is observed at N4 than at L4(Fig. 13).

The backward ray path implies that the L7 site is too far east tocontribute to the 20–25 day energy at the escarpment. At L7 during2005, mode 1 dominates and the direction of the ellipse major axisimplies that TRWs with this period at this location are primarily

200 m

500 m

1000 m

2000

m

3500

m

cm

-17 Day EOF Mode 1 Bottom Pressure Anomaly (cm)


gative values dashed; positive phase differences lead) for frequency bands centeredigsbee Escarpment is shaded gray.

cm2 s-2

5 cm/s 51.7% Total Variance100-33 day EOF Mode 1 Bottom Current Fluctuations

200 m

500 m

500 m

1000 m

2500 m

1500

m20

00 m

3000 m

3500

m

Mode % Total Variance Wavelength 1 62.7 162 km 2 17.6 338 km

EOF Analysis of 60-day TRW’s

Modes1

Modes 2

61 day period TRW path Wavelength 203 km

Y3

Y4

Y2

L7

Fig. 15. West of 89�W, the near-bottom (100–500 mab) EKE is contoured for the 100-33 day EOF mode 1 velocities from the Exploratory Program. The elliptical hodographsshow the mode 1 currents at each mooring with arrow heads giving relative phase. The EOF modes for similar near-bottom currents at the Y moorings in the Eastern Gulf arealso shown. At L7, the red and orange modes 1, and the blue and green modes 2 ellipses are for the lower-layer velocities for the eastern Gulf and Exploratory time intervals,respectively. The thick black lines are TRW ray traces initiated at the blue dots with the indicated periods and wavelengths. The reflected ray is given by the dashed line.Arrowheads are every 5 days.

Table 4EOF and wavenumber analysis of Gulf Deep Currents.

Mooring group (with depths (m)) Analysis interval dates Frequency band(cpd)

Center period(days)

Modenumber

% Totalvariance

Wavelength(km)

L3 (2900), O1 (2725), O2 (2916), & Q2(3113)

2003-04-28 to 2004-03-29

0.030–0.058 23 1 58.2 207 (185a)0.010–0.030 61 1 57 203 (187a)

L7 (500,2000,3000, 3187,3256) 2003-04-24 to 2004-06-07

0.024–0.050 27 1 69.90.010–0.030 61 1 70.4

2 23.6 300b

Y2 (2035), Y3 (2489), & Y4 (2530) 2005-01-27 to 2006-01-19

0.033–0.045 25 1 64.1 2222 30 146

0.010–0.033 60 1 62.7 1622 17.6 338

L7 (875,1200,1500, 2000,2500,3000) 2005-06-03 to 2006-01-28

0.033–0.045 25 1 78.90.010–0.033 60 1 72.7

2 25.1

V3 (2000), V4 (2500), & W3 (3038) 2004-09-01 to 2005-06-23

0.030–0.060 23 1 66.8 902 18.3 90

0.010–0.030 66 1 47.2 1352 43.3 75

a Estimated from trapping depths for lower layer L3 currents.b Estimated from backward ray trace given in Fig. 15.


propagating towards the Campeche Bank and are likely to be re-fracted into the southern part of the eastern basin as discussedabove. However, ray tracing by Oey (2008; his Fig. 10) shows that20-day period TRWs could reach the eastern end of the escarpment(location near I1) from the region north of the Campeche Bank, butthis is not supported by the direction of the dominant mode 1 fluc-tuations with similar 25-day periods at L7. Therefore, these shorterperiod TRWs in the Exploratory region would appear to have morethan one source with the shallower part of the escarpment being

more likely to be influenced by the northeast, and the deeper partseems to have source regions further south but not under the LC aswould seem to be the case for the longer period waves.

The shortest period 10-day TRWs were investigated by Hamil-ton (2007) and are primarily confined to the northeast part ofthe escarpment. Ray tracing of these 8–14-day waves (see Fig. 11in Hamilton (2007)) shows that reflection by the escarpment islikely, and that reducing bottom slopes to the south could trapthese waves and may therefore account for the exceptional high

Mode % Total Variance Wavelength 1 64.1 222 km 2 30.0 146 km

5 cm/s

cm2 s-2


200 m

500 m500 m

1000 m

2500 m

1500

m20

00 m

3000 m

3500

m

EOF Analysis of 25-day TRW’s

33-17 day EOF Mode 1 Bottom Current Fluctuations

22.4 day period TRW path Wavelength 207 km

Mode 178.9% Total

Variance

Fig. 16. West of 89�W, the near-bottom (100–500 mab) EKE is contoured for the 33-17 day EOF mode 1 velocities from the Exploratory Program. The elliptical hodographsshow the mode 1 currents at each mooring with arrow heads giving relative phase. The EOF modes for similar near-bottom currents at the Y moorings in the Eastern Gulf arealso shown. At L7, the 3000-m ellipse is from the 25-day EOF analysis of the lower-layer currents using the eastern Gulf time interval. The thick lines are TRW ray tracesinitiated at the blue dots with the indicated periods and wavelengths. The reflected ray is given by the dashed line. Arrowheads are every 5 days.


velocities observed at I1 and to a lesser extent at M1 and M2. Thisassumes that generation is fairly local to these sites by fluctuationson the west side of an extended LC and/or the westward transla-tion of recently separated LC eddies. Oey (2008) comes to similarconclusions from his numerical model analyses. Figs. 8 and 14–16 confirm that the escarpment effectively insulates the shallowerslope from energetic TRWs propagating from deep water, and thishelps to explain why hardly any of the RAFOS floats in Fig. 2 crossthe escarpment west of 90�W.

The ray tracing (Figs. 15 and 16) and the spatial variation of thewave amplitudes allow some first order estimates of dissipationtime scales. In Fig. 15, the 60-day northern ray indicates a decaytime of �40 days, whereas the southern ray implies that energeticfluctuations from under the LC will penetrate west of 93�W inabout 35 days. The propagation times for the 25-day waves inFig. 16 imply that decay takes place at scales greater than 15–20 days. The distinct wave trains observed at I1 over the 2 yearsof observations (Hamilton, 2007) lasted about 3–4 months on aver-age. Therefore, the dissipation time scale of TRWs in the abyssalbasin is estimated to be about 1–4 months.

5. The northwestern gulf

The northwestern gulf moorings are from two complementarystudies in US and Mexican waters, respectively, with the divisionat the 26�N parallel. The studies were each of 15-months duration,but the overlap was just 11 months (see Table 1). The locations ofthe moorings in the array with instruments below 1000 m are gi-ven in Fig. 17, which also shows the steep escarpment at the baseof the continental slope. In US waters this is the westward contin-uation of the Sigsbee Escarpment, which becomes known as thePerdido Escarpment south of 26�N. In many respects, because ofthe bathymetric configuration, the distribution of means and vari-ances across the slope are similar to but weaker than the same

quantities in the central gulf (compare Figs. 17 and 8). The EKE isgreatest in the gently sloping deep basin below the escarpmentand attenuates (within the resolution of the array) over the conti-nental slope. Higher magnitude mean flows, which are also bottomintensified, are also observed at the base of the escarpment as com-pared to both above and farther below (W3). Therefore, the energysources seem to be in deep water with the escarpment and steeplower Mexican western slope acting as effective barriers. Interpre-tation in terms of refracting and reflecting TRWs, in analogy withthe previous analysis, is appropriate.

For the energetic deep currents at V3, V4, W2 and W3, the CEOFanalysis (Table 2) shows that single modes account for most of thevariance below 1000 m at each location. Except for 20–30 day per-iod motions at W3, single modes also account for a large majorityof the variances in the intermediate and low (60–100 days) fre-quency bands (Table 2). Though not shown, the coherent motionsare bottom intensified somewhat similar to the mean flows inFig. 17 (Donohue et al., 2008). A similar wavelet analysis to thatperformed for the deep velocities at L3 (Fig. 12), was performedfor the 3000 m currents at W3, and apart from smaller variances,the results are similar (Fig. 18). The global wavelet spectra showtwo dominant period bands, 20–30 days, and 60–100 days, whichdominate the cross- and along-isobath components, respectively.This again implies rotation of the principal axis of variance withthe period of the motions as expected for TRWs.

The time series of wavelet power (Fig. 18) show significantpower between December 2004 and June 2005. At the end ofNovember a major LC anticyclone (eddy Ulysses) crossed the92�W meridian, interacted with a pair of cyclones, and split intotwo parts. The splitting of LC eddies in the western gulf has beenobserved before and a similar event, involving eddy Triton in1992, was documented by Biggs et al. (1996). The northern partof eddy Ulysses interacted with another cyclone against the wes-tern margin, and a lobe of the eddy intruded over the northwesternslope and was identified by satellite imagery and the presence of

200 m

1000 m

2000 m3000 m

1500 m

3500 m

3 cm/s

cm2 s-2

1000

2000

3000D

epth

(m)

W2

W3

W4

W5

V2 V3 V4

U2U3 U4

T5

Fig. 17. Mean 40-HLP currents plotted as pseudo-3D profiles where the red arrow is the deepest measurement (�60–100 mab), and contoured EKE at 100 mab. The grayshaded region is the Sigsbee Escarpment.


the high salinity Subtropical Underwater (SUW) core water around150-m depth that is characteristic of the LC and LC eddies (Don-ohue et al., 2008). This intrusion took place between Decemberand February. At the end of February, the center of the northernpart of Ulysses was at �25.5�N, 94�W, and through the end of Juneit slowly translated due westward towards the slope, with its pas-sage partially blocked by the slope cyclone. After reaching the wes-tern slope, the eddy rapidly dissipated. Selected satellite oceancolor images overlaid with upper-layer currents and satellitealtimeter derived SSH contours that show some of these interac-tions of Ulysses with surrounding cyclones in the western gulf,are given in Fig. 19. Thus, during this interval of intense LC eddyinteractions in the western gulf, there is an increase in TRW activ-ity over the abyssal depths of the deep basin. Again, as with LCeddy separations in the eastern gulf, the connections betweenTRW intensities and eddy interactions in the upper layer are sug-gestive but not necessarily statistically significant.

The analysis of coherent lower-layer fluctuations is similar tothe previous section on the central gulf. The wavelengths for thetwo dominant period bands were obtained from least-square fitsto the phase differences using records at 500 mab for V3, V4 andW3. These locations had the largest variances of all the deep wes-tern gulf records. Two modes are significant and the details are gi-

ven in Table 4. Ray tracing was initiated at the center of the V3–V4–W3 triangle, using the estimated wavelengths and periods forthe modes. EOFs were also calculated for the two frequency bandsusing all locations with records below 1000 m with records at�100 mab on the slope and 500 mab over the abyssal plain. The re-sults are given in Fig. 20 for both down- and up-slope propagatingTRWs. The shorter period band, centered on 23 days, has twomodes, though the second mode is only important at V4 and W3.The first mode corresponds to energy propagating westward alongthe escarpment and decaying rapidly southward, while the secondmode appears to be more compatible with energy propagatingdown the northern part of the slope. The ray paths show a similarpattern with the forward up-slope ray being close to the ellipses atW2, W4 and W5, however the magnitudes of these latter fluctua-tions, compared to V3 and V4, would indicate that such waveswould be rapidly attenuated. The energetic mode 1 ellipses aremost compatible with up-slope propagation from the deepwaterto the east with reflection back into deepwater at the corner regionof the escarpment. However, down-slope waves, originating on theshallower parts of the northern slope to the east are also possible.

The longer period (66-day) fluctuations have similar patternswith less significant magnitudes on the slope regions (Fig. 20).The two modes for the complete array account for 72.1% of the to-

U-cmpt (135°T) Variance: 13.09 Red Noise α: 0.92

V-cmpt (045°T) Variance: 35.6 Red Noise α: 0.92

W3 at 3040 m

Fig. 18. RH panels show the local wavelet power spectrum of the velocity components from W3 at 3040 m for the indicated time interval using the Morlet waveletnormalized by the variances of the respective series. The thick solid contours enclose regions of greater than 95% confidence for a red-noise process with the indicated lag-1(a) coefficients. The lighter shades indicate the ‘‘cone of influence” where edge effects become important. The LH panels show the respective global (time-averaged) waveletspectrum (solid lines). The dashed lines show the mean red-noise spectrum (lower), and the 95% confidence levels (upper) for the global wavelet spectra, given theirrespective a’s.


tal variance of the near-bottom currents and unusually both modesare of almost equal importance. This was true also for the 66-dayEOFs using just the three deep moorings (Table 4) for the TRWwavelength estimates from phases of modes. The mode 1 wave-length estimate is larger than for the 23-day period waves andhas a very similar distribution of energy with large amplitudes atV3, V4 and W3 that decay southwards along the slope. The direc-tions of the ellipse axes are more compatible with an up-slopepropagating wave originating from deep water to the east that isrefracted by the topography towards the south. Comparing the

phase angle (given by the arrow heads on the ellipses) at V4 andW3, it can be seen that W3 lags V4, which indicates off-slope phasepropagation. Mode 2 is primarily observed at V4 and W3, and thewavelength is about half that of mode 1. The major axis directionsof the ellipses indicate offshore propagation and this is confirmedby the phase lead of W3 over V4. In terms of amplitude thismode-2 wave dominates over mode 1 at W3 and implies thatsource may be the lower slope region of the central gulf.

The directions of wave propagation and the distribution of var-iance are compatible with wave generation in deepwater, propaga-

98° W 96° W 94° W 92° W

23° N

24° N

25° N

26° N

27° N

28° N

29° N98° W 96° W 94° W 92° W

2.5 3.0 3.5 4.0 4.5 5.0 000 m50 m250 m000 m50 m250 mChlorophyll Concentration ln(100 mg • m-3)

50 cm s-123° N

24° N

25° N

26° N

27° N

28° N

23° N

22° N

24° N

25° N

26° N

27° N

28° N

Fig. 19. Chlorophyll concentration 8-day composite images overlaid with 50 and 250-m daily averaged 40-HLP current vectors from the northwest Gulf array, and SSHcontours from altimeter mapping (images and SSH maps courtesy of R.R. Leben, University of Colorado).


tion towards the slope, refraction and reflection by the steepescarpment, with rapid attenuation to the south. Generation ofthe TRWs appears to be relatively local for short period wavesbut could extend eastwards into the central basin for longer peri-ods. The lower northern slope region to the east of the array couldalso be a generation region and the time series of wavelet power(Fig. 18) is compatible with eddy Ulysses moving into the regionand a lobe of the eddy intruding onto the lower slope. The resultof this western basin TRW activity is similar to the central gulf witha strong mean flow along the base of the escarpment (Fig. 17) thattrends southward along the isobaths (Fig. 7). However, accordingto the RAFOS floats, the energy south of 25�N appears to remainseaward of the 3000-m isobath, with very weak fluctuation ampli-tudes on the lower Mexican slope above this.

6. Upper and lower layer coupling

Establishing relationships between observations of upper andlower circulations in the deep gulf has proved to be difficult. Gen-erally, currents above 800 m and below 1200 m are not correlatedat time scales (<1 year) resolved by the measurements (Hamilton,1990). There are intriguing events where flows appear to be similarthrough the whole water column, however, they are not long last-ing and quite rare, and so have no statistical significance. A fewexamples are noted for the I1 mooring in Hamilton (2007), wherethey were mostly associated with peripheral cyclones or frontaleddies on LC eddies. The three full-depth moorings Y1, Y2 and Y3(Fig. 1 and Table 1) are in deepwater, strongly influenced by theLC, and sufficiently closely spaced to make estimates of relative

200 m

1000 m

2000 m3000 m

1500 m

3500 m

3 cm/s

200 m

1000 m

2000 m3000 m

1500 m

3500 m

3 cm/s

Fig. 20. EOF mode amplitudes of near-bottom currents for the indicated interval using all moorings (LHS: 23-day period, RHS: 66-day period). Red lines represent ray tracesof TRW paths for the indicated periods and wavelengths. The blue dot is the start location for the ray tracing. Arrowheads are at 5-day intervals and solid and dashed linesrepresent onshore and offshore propagating waves, respectively.


vorticity, 1, in both the upper and lower layers. The latter proves tobe dynamically linked through the water column, unlike the obser-vations of the currents. For much of the 1-year deployment in2005, the LC was well extended and to the west of the array, withthe LC front often in the vicinity of Y2 and Y3. Also during 2005, LCeddy Vortex formed and detached and reattached a number oftimes before breaking free of the LC in the late summer. Thus, LCand LC eddy flows were predominantly southeastward (i.e., to-wards the Florida Straits) near Y3.

CEOF analysis in the time domain of the depth profiles of cur-rents is used to establish the two-layered nature of the flows. Timedomain CEOFs are preferred because the 1-year time series ofupper-layer currents do not resolve the �6–18 month fluctuationsof the LC eddy shedding cycle. The analysis of the vertical currentprofiles uses the Y3 mooring, because it has the best 1-year cover-age of the three full-depth moorings. Similar analyses for the Y1and Y2 moorings are qualitatively the same as for Y3. Initiallyupper and lower layer CEOFs were calculated for six levels of de-meaned currents in each layer with the 987-m level being commonto both. The results are given in Fig. 21a, and the first mode foreach layer accounts for >90% of the total variance of each set ofsix records. The upper-layer mode is strongly sheared, and approx-imately unidirectional with the principal axis directed approxi-mately north–south. Clearly the 987-m level currents are onlyweakly coherent with the mode. The lower-layer currents arehighly coherent with the lower-layer mode 1 from 1000-m to thebottom. The mode CEOFs are again unidirectional, with the princi-pal axes being more along the isobaths trending southwest tonortheast, and show an increase in amplitude towards the bottom.Therefore, it is reasonable to associate the upper-layer mode 1 fluc-tuations with the LC and its peripheral cyclones, and the lower-layer mode 1 with TRWs.

The bottom mode has weak decay with height above the bedand this seems to be at odds with the bottom trapped characterof short-wavelength TRWs. However, the CEOF mode contains allTRW frequencies and long period waves are less bottom-trapped.Almost all the observations from full-depth moorings show al-

most depth independent fluctuations below 2000 m, weak decayfrom 2000 to 1000 m and strong decay above 1000 m. This con-forms to the amplitude profiles calculated by Reid and Wang(2004) using more realistic exponential N profiles that are moreappropriate for the gulf than using the constant N of the stan-dard theory.

The complex amplitude time series of the modes (normalized tounit variance) are given in Fig. 22, which also shows the observed40-HLP currents at Y3. It is clear that the upper and lower layermodes closely resemble the observed currents from the upperlayer (179 m) and lower layer (987 and 1985 m), respectively. Cor-relations between the mode amplitude time series are not signifi-cant for the v-component at any lag and barely significant (�0.26:99% significance level = 0.16) at zero lag for the u-component.

This two-layer analysis indicates that there is minimal connec-tion between the modes that account for >90% of the variance ineach layer. To analyze the total water column at Y3, the CEOFsare calculated for 5 levels in each layer with the addition of the987-m level. Because the velocity variances are an order magni-tude larger in the upper water column than near the bottom, the(complex) velocities are normalized to unit variance, so that eachlevel is equally weighted and the parts of the water column aboveand below 1000-m have the same number of records. Two modesaccount for 93.3% of the total normalized variance of the 11 veloc-ity records (Fig. 21b). The mode velocity profiles are plotted withnormalized magnitudes, and also after being ‘‘denormalized” bymultiplying by the standard deviation of each velocity record. Cur-rents at 983 m and below are highly coherent with mode 1. Thecorrelations then decay towards the surface. Therefore, this isessentially the bottom trapped TRW signal, even though theupper-layer denormalized magnitudes increase towards the sur-face. The latter is not significant and is a result of weighting bythe much larger upper layer variances. However, this mode doesindicate that some of the signal above 1000 m is attributable toTRW motions.

Mode 2 is primarily surface intensified and is clearly similar tothe upper-layer mode 1 in Fig. 21a. However, it also has a weak al-

Upper Layer

Lower Layer

a

b

Fig. 21. Depth profiles of CEOF amplitudes (cm/s) from (a) separate analyses of upper and lower-layer currents at Y3, and (b) full water column analysis of normalizedcurrents at Y3. The solid and dashed lines are the denormalized and normalized amplitudes, respectively.


most depth-independent expression, in the opposite direction, be-low 1000 m that has small, barely significant correlation coeffi-cients. The zero crossover point is at about 800 m, and this modeclosely resembles the dynamical normal mode 1 calculated frommean vertical profiles of Brunt–Väisälä frequency for this regionof the deep gulf (DiMarco, 2008; personal communication). Thelower layer has a small contribution from upper-layer LC or eddyfluctuations through dynamical coupling, just as the upper layerhas a small contribution from TRW flows decaying upwards

through the water column. Therefore, the separate layer and fullwater column CEOF velocity modes are essentially equivalentand indicate only very weak interactions.

The measurements on the three full-depth moorings allow cal-culations of layer potential vorticity. The Ertel potential vorticity(PV) for a layer bounded by isopycnals, or material surfaces, is con-served in the absence of dissipation, and is defined as:

PV ¼ fþ fh

ð8Þ

cm/s

cm/s

Nor

mal

ized

Nor

mal

ized

Upper Layer Mode 1

Lower Layer Mode 1

N

N

N

179 m

987 m

1985 m

Fig. 22. Mode 1 amplitude vector time series (top panel: upper-layer; bottom panel: lower-layer) from the Y3 CEOF layer analysis. The middle panels show 40-HLP currentobservations from 3 depths on Y3, where the two lower records have been rotated into the same principal axis coordinates as the lower layer mode 1.


where f = ov/ox � ou/oy is the relative vorticity, f is the Coriolisparameter, and h is the layer thickness, bounded by isopycnal sur-faces. The relative vorticity, f, is calculated for fixed depth levelsfrom current measurements by fitting planes to the three measure-ments. Thus,

uðx; y; z; tÞ ¼ u0 þ x@u=@xþ y@u=@yvðx; y; z; tÞ ¼ v0 þ x@v=@xþ y@v=@y

ð9Þ

where (x, y) are measured from the center position of the subset ofthe array used for the estimates. The results are normalized by thelocal Coriolis parameter (f = �6.5 � 10�5 s�1). The north–south andeast–west extents of the array are 82 and 30 km, respectively, andtherefore, the calculation of f has these implicit scales that areappropriate for the larger frontal or peripheral eddies. The potentialvorticity anomaly is defined as:

PVA ¼ fþ fh� f

Hð10Þ

where H is a constant and represents the thickness of the layer atrest. Normalizing by H/f,

PVA ¼ Hh

ffþ H

h� 1

� �ð11Þ

where the term in parentheses represents the stretching effect(sometimes defined as the Sverdrup PVA) as a fraction of f/H. PVAis a linear function of PV and is therefore also a conserved quantity.

Layer thicknesses, h, are estimated by averaging isothermdepths, calculated by linear interpolation between temperaturesensors, at the Y1, Y2 and Y3 locations, and the appropriate f isfound by vertically averaging f(x, y, z, t) between delineating iso-therms, using common depths for the three moorings and equation(9) for the horizontal velocity gradient estimates. Common velocitydepths were between 76 and 428 m with 8 m spacing, and at anominal 750, 1500 and 2300 m. In the calculations below, onlytwo layers are considered: between the surface and the 8 �C iso-therm, and between the 8 �C isotherm and the bottom. Ideally,the 6 �C isotherm is a better divider between the upper and lowerwater columns because its mean depth is just below the sill depth(800 m) of the Florida Straits, which contains the outflow of the LC(Bunge et al., 2002). However, the temperature sensor distributionon the Y moorings resolves the depth of the 8 �C surface much bet-ter than deeper isotherms, and the majority of the energetic LCflows occur above this depth. The statistics for the two layers aregiven in Table 5.

Time series of f, for the upper and lower layers, along with thedepths of the 15 and 8 �C isotherms are given in Fig. 23, where the

Table 5Potential vorticity parameters from Y1, Y2 and Y3.

Layers Mean thickness H (m) Depths of 8 �C isotherm (m) Layer mean h1/fi Layer std. dev. hð102=f 2Þi1=2 Maximum correlationcoefficient

Lag (days)

Surface to 8 �C 550 Minimum 0.052 0.103 0.42 (0.16)a 1 (Surface lags)428

8 �C to bottom 2150 Maximum 0.008 0.021758

a 99% Significance level.

15°C

8°C

fract

iona

l f

Relative Vorticity (fractional f )-0.4 -0.3 0.3-0.2 0.2-0.1 0 0.40.1

Fig. 23. Relative vorticity (as a fraction of f) contoured for the upper layer, and as time series for the lower layer (1500 and 2300 m) calculated for the Y1, Y2 and Y3 moorings.The upper layer contour plot is overlaid with the depths of the 15 and 8 �C isotherms.


color shading differentiates between cyclonic (cold) and anticy-clonic (warm) eddies (f > and < 0, respectively). Relative vorticityis a maximum near the surface and decreases with depth throughthe upper layer and then shows a slight increase towards the bottom,similar to the vertical profile of velocity variances. There is some cor-respondence between the lower and upper layer peaks in f, indicat-ing a connection that is not apparent in the velocity fluctuations. Asnoted above, the depth of the 8 �C isotherm has been used to delin-eate the lower parts of LC eddies, and here it is a reasonable choicefor the interface between the upper and lower layers. For the most

part, the 8 �C isotherm lies between 400 and 750 m where f hassmaller magnitudes, and shows the expected relations with deepand shallow excursions corresponding to anticyclonic and cyclonicflows in the surface layer, respectively. Mean relative vorticity inboth layers is positive. In the upper layer the relatively large meanvalue (5% of f) is a consequence of the array being on the east andcyclonic side of the LC front for most of the study interval, as wellas from the frequent passage cyclonic frontal eddies.

The upper and lower layer vertically averaged relative vorticitiesare significantly correlated (Table 5), though some of the correlation

Total Stretching

ζ

Upp

er L

ayer

Low

er L

ayer

Potential Vorticity Anomaly

Upper Layer Total PVAversus

Lower Layer Total PVA

Upper Layer ζversus

PVA Stretching Term

Lower Layer ζversus

PVA Stretching Term

Upper Layer versus Lower LayerAveraged ζ. 300 versus 2300 m ζ.Y3 Upper Layer Mode 1 versus Y3 Lower Layer Mode 1 V-cmpts.

a) b)

Fig. 24. Upper panels: Coherence squared and phase differences between (a) layer averaged f, f at 300 and 2300 m, and along-isobath components (V) of velocity from the Y3upper and lower layer mode 1’s (see Fig. 20); and (b) layer PVA and constituent terms as indicated. Lower panel: Time series of potential vorticity anomalies and theircomponent relative vorticity and stretching terms for the upper and lower layers with interface defined by the 8 �C isotherm.


is caused by the upper layer f leaking below the 8 �C isotherm depth(Fig. 23). The coherence squared and phase differences between theupper and lower layer averaged f, as well as f at the 300 and 2300-mdepth levels, are given in Fig. 24a. There is significant coherence atTRW frequencies in the 20–35 day period band with the upper layerlagging the lower layer by�90� that is suggestive of baroclinic insta-bility mechanisms (McWilliams, 2006). These frequencies dominatethe spectra of lower-layer Y3 and Y2 currents (Fig. 5), and ray tracingshows that 25-day TRWs can propagate across the Mississippi Fantowards the eastern part of the Sigsbee Escarpment (Fig. 16). Theexistence of baroclinic instability in the lower layer that triggers25-day TRWs is also consistent with Oey’s (2008) analysis of modelresults that shows a region of persistent baroclinic energy conver-sion, related to LC frontal eddy propagation, along the west Floridaslope in the vicinity of the Y moorings. Fig. 24a also shows the coher-ence squared between the upper and lower layer CEOF along-isobathcomponent mode amplitudes, given in Fig. 22, which confirms thecomplete lack of connection for velocity fluctuations at energeticTRW periods.

Time series of PVA (Eq. (11)) and its constituent terms (f andstretching: H/h � 1) are given for both layers in Fig. 24, whichshows that for many events the stretching term dominates (e.g.,the warm and cold eddy events in May–June and October–Novem-ber, respectively). Because the stretching terms are inversely corre-lated in the two layers, this will contribute to the overall coherenceof the total PVA of the layers, but not to energy transfer betweenthe layers. However, there are other events when the stretchingis weak and f dominates the total PVA (e.g., the events in March–April, and at the beginning of August and the middle of December).

The coherence squared and phase differences between the layerPVA, and for each layer between f and the stretching term(Fig. 24b) show that, for the upper layer, f correlates quite wellwith stretching as can be visually ascertained in Fig. 23. In the low-er layer, only the 25–30 day period band is coherent, which corre-sponds to the same frequencies for which f is coherent betweenthe layers (Fig. 24a). The relation between lower layer stretchingand relative vorticity at 25–30 days indicates active TRW genera-tion by the upper layer, because the total layer PVAs are coherent


at these frequencies (Fig. 24). Wavelet power analysis of lower-layer currents at Y3 (not shown) showed that 16–32 day periodfluctuations were prevalent and significant during June to August2005 when eddy Vortex was attaching and detaching from the ex-tended LC. It is not obvious that 25-day period fluctuations domi-nate the isotherm depths in Fig. 23 as might be expected if thelower layer was coupled to southeastward propagating cyclonicLC frontal eddies. The upper-layer cyclonic relative vorticity fluctu-ations must arise from combinations of displacements of the LC,frontal eddies, and eddy detachments, rather than be attributedto a single mechanism. Therefore, there is some evidence that ed-dies, and their local upper-layer PV fluctuations that have a sub-stantial stretching component, have a relation to 25–30 dayTRWs in the lower layer. The latter will radiate westward towardsthe escarpment as indicated by the ray paths in Fig. 16.

7. Discussion and conclusions

Analysis of vertically coherent currents below 1000 m in thedeep basins of the Gulf of Mexico has shown that low frequencyfluctuations with periods greater than �7–10 days are mostlyattributable to TRWs. The database consisted of measurementsfrom both full-depth and near-bottom moorings, PIES pressuregauges, and deep RAFOS Lagrangian floats that were made for ma-jor observational programs in the deep gulf by a variety of institu-tions and entities. Evidence for the dominance of TRWs in at leastthe northern half of the deep basin comes from (1) the coherent,nearly barotropic and sometimes bottom intensified fluctuationsthat generally account for >80–90% of the total variance below1000 m. (2) The frequency content of the motions that tends to fa-vor longer and shorter period fluctuations in deeper water withweak topographic slopes, and shallower depths with steeperslopes, respectively. When broken down by period, fluctuationsare generally rectilinear with clockwise rotation of the principalaxes with increasing frequency as predicted by the TRW dispersionrelation (3). (3) The lack of dispersion and long-term transport ofdeep Lagrangian floats when in regions that are not adjacent tosteep slopes such as the Sigsbee Escarpment. A field of lower-layertranslating eddies, as indicated by Welsh and Inoue (2000) forexample, would not be compatible with these observedcharacteristics.

In the eastern gulf, there is strong support for the LC being thesource of deep TRWs with the highest, lower-layer energy beingfound at L7 under the LC, which appears to be a source for a bandof higher energy fluctuations stretching northwest towards theSigsbee Escarpment. Ray tracing confirms this for �60-day waves,and suggests that the other dominant periodicities of �20–30 daysoriginate further north or west of L7. However, the fluctuations atL7 also suggest that only part of the observed energy radiates tothe northwest, and the larger fraction may radiate anticlockwisetowards the Campeche slope and the Yucatan Channel, and possi-bly around to the lower west Florida slope. Energy levels and ob-served periodicities at mooring G on the east side of the LC arecompatible with the west side being a possible source, even thoughthe observations were taken two decades apart.

Observations under the LC and along the Sigsbee Escarpmentgenerally support the analysis of high-resolution numerical modelruns by Oey (2008), though they are not able to confirm the exis-tence of deep lower layer eddies that either become LC frontal cy-clones or break free of the LC and translate to the west, which, inthe model, are the sources of TRW radiation. The observed deepRAFOS float tracks are consistent with TRWs in this region, butcould also be interpreted as having some eddy-like characteristics.Oey’s (2008) analysis of the model LC shows areas of high baroclin-ic energy conversion and flow instability north of the Campeche

Bank and off the west Florida slope. The very high lower-layer KEat L7 could be a manifestation of the Campeche instabilities. How-ever, more support for direct connections between upper and low-er layers comes from a vorticity analysis at the Y moorings that arenear the model west Florida slope instability region. As is usual inthe gulf, only minimal connections between upper and lower-layercoherent velocity fluctuations can be seen. However, significantcoherence is found between upper and lower-layer relative vorticityat 20–30 day periods, which are the periods of the most energeticradiating TRWs at this site. Moreover, lower-layer f leads theupper-layer f by �90� at these frequencies, which is a basic indica-tion of flow instabilities and upper to lower layer energy transfer.The transfer is restricted to a narrow frequency band but seemsnot to be related to the wavenumber coupling mechanism ofMalanotte-Rizzoli et al. (1995) between southeastward propagat-ing LC frontal cyclones and TRWs. Baroclinic instabilities, however,do seem to generate a narrow band TRW response in this case.

The observations along the Sigsbee Escarpment between 89�Wand 92�W show the deepwater TRWs refracting and being reflectedby the shoaling topography, with a narrow jet-like mean currentfound immediately above the steep escarpment slope. The distri-bution of KE with frequency from east to west along the slope, withshort periods (�10 days) in the east, long periods (�60 days) in thewest, and�20–30 day periods in the center of the observational ar-ray, are difficult to explain except by TRWs of different frequenciespropagating from deep water with group velocities nearly alignedwith, and more across the isobaths, for long and short periods,respectively. Short �10-day period TRWs are confined to the east-ern end of the array, and previously Hamilton (2007) from observa-tions at I1, and Oey (2008) from his model suggest that generationof these short period waves must be local, because of restrictingtopographic slopes, and are trapped near the escarpment. It is clearfrom the observations that little lower layer energy penetratesabove the escarpment onto the lower continental slope, implyingreflection of TRW energy by the steep escarpment wall. Accordingto Mizuta and Hogg (2004), TRWs propagating northward overshoaling topography will generate a westward mean flow by con-vergences of Reynolds stresses in the bottom boundary layer.Strong mean southwesterly flows were observed at the one sectionwhere moorings were deployed across the escarpment.

The RAFOS float tracks at 1500 m and below also do not crossthe escarpment from the deep basin to the northern slope. If thefloats move close to the escarpment, they get caught in the meanflow and move rapidly off the west following the escarpment. Thisis in contrast to their more general behavior in deep water ofmeandering around in the same general area. The escarpmentmean flow appears to be the main mechanism by which deepwater parcels are transported into the western gulf.

For the deep currents in the western gulf, the observations arequite similar in character to the central gulf except that energy lev-els are much less and longer periods are more prevalent. There ispropagation of TRWs towards the escarpment (in this case the Per-dido, which is an extension of the northern slope escarpment intoMexican waters) and a mean flow to the south exists along thebase of the western slope. It is speculated that the complexeddy–eddy interactions in the western gulf are the source of theobserved deepwater TRWs. The western gulf also produced theonly direct evidence to date of a lower-layer translating cyclonethat was observed in a RAFOS float track approaching the westernMexican slope. However, this was only one partial track out of the36 floats deployed originally in the central gulf around 90�W.

Acknowledgements

First of all, thanks are made to all the principal investigators andtheir colleagues who made the measurements in the various pro-


grams that have been collected together for this review. They in-clude Masamichi Inoue, Sue Welsh, and Nan Walker, LouisianaState University, Antonio Badan and Julio Candela, CICESE, KevinLeaman, University of Miami, George Forristall, formerly of ShellOil Company, and Jeff Cox at Evans-Hamilton, Inc. The MineralsManagement Service has consistently funded comprehensivephysical oceanographic studies in the Gulf of Mexico over threedecades, and special thanks go to program managers Alexis Lugo-Fernandez (MMS) and Evans Waddell (SAIC) for their support dur-ing the writing of this paper, as well as over the years that I havebeen looking at gulf data. Special thanks are due to my fellowPI’s, Kathy Donohue, Randy Watts, and Bob Leben, on these deep-water programs for their insights and many discussions. Principalsupport for this review came from MMS contract number 1435-01-03-CT-71562 to Science Applications International Corporation.

Appendix A. TRW ray tracing

TRW ray paths in this study are calculated using the full disper-sion relation. The basis of the method is given in Meinen et al.(1993) and previously used by Pickart (1995) to calculate TRWray paths generated by the deep Gulf Stream in the Middle AtlanticBight, and Hamilton (2007) in the gulf. The dispersion relation forTRW’s is given by the coupled equations (Pickart, 1995):

k2 ¼ ðk2 þ l2 þ bk=xÞðN=f Þ2 ðA:1Þk tanhðkhÞ ¼ N2=ðxf Þðkhy � lhxÞ ðA:2Þ

Under the WKB approximation, where changes in wave amplitudeand phase caused by the environment are assumed to vary on scaleslarger than the local wavelength, the equations governing the pathof a wave and its wavenumber are (LeBlond and Mysack, 1978):

Dtx ¼ @x=@k ¼ cg ðA:3ÞDtk ¼

X�@x=@circi ðA:4Þ

where

Dt ¼ @=@t þ cg � ris the derivative following the wavegroup, x is the path of the ray,and cg is the group velocity. The ci are the environmental parame-ters that cause refraction of the wave. There are three such param-eters for TRWs: h (water depth), rh (bottom slope), and N (Brunt–Väisälä frequency). N is assumed constant for these calculations.The WKB assumption is marginal though it is often used under con-ditions that have sharp changes in the environmental parameters.Therefore, the topography must be smoothed over at least thewavelength scale for the method to apply. The ray tracing equa-tions, (3) and (4), are solved using 4th order Runge–Kutta methodsto determine ray paths, and the change in the wavenumbers alongthe rays. Oey and Lee (2002) used essentially the same method foran investigation of TRW’s generated by a numerical circulationmodel of the Gulf of Mexico basin. For this study, a bicubic splinesmoothed version of the GTOPO30 world ocean bathymetry dataset (Smith and Sandwell, 1997) was used in the same way as inHamilton (2007).

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