Wave-current interaction near the Loop Current Edge

Leonel RomeroEarth Research Institute, UCSB

Luc Lenain and W. Kendall Melville Scripps Institution of Oceanography (UCSD)

data source: http://hycom.org/dataserver/goml0pt04/expt-31pt0

Motivation• Surface waves and particularly wave breaking are important

for engineering applications, including offshore structures• Improve models of wave breaking including the effects due

to surface currents• Test numerical wave models in conditions with strong wave

current interactions.

http://www.euroinvestor.com/ei-news/2012/09/03/hurricanes-could-affect-the-price-of-oil/20827

Wave Current Interaction

• Effects of waves on currents– For example:

• Vortex force: Langmuir circulation• Stokes-Coriolis force (wave-induced inertial motions)• Direct forcing by breaking waves

• Effects of currents on waves– Including:

• Direct forcing due to collinear waves and currents• Wave refraction• Enhanced wave breaking• Modification of the wind input due to relative winds• Modulation of surface waves statistics

Focus of this study

Experiment in the Gulf of Mexico October 2011

- Atmospheric Fronts with Southerly winds- Predictable and frequent fronts in the Fall and Winter

(Henry 1979)- The Loop Current was within range of a small aircraft based

from Jack Edwards Airport ( )

Example of an atmospheric front &associated southerly winds from model winds

Gulf of Mexico Experiment (October 2011)

- Scanning Lidar (400kHz)

Sea surface elevation (waves)- Infrared camera (50Hz, 640x512px)Sea surface temperature and breaking waves- Color Camera (8Mpx,

15fps)Breaking waves- Inertial Motion Unit

w/GPS (200Hz)Georeferencing

+Flights out of Jack Edwards airport (KJKA), Gulf Shores, Alabama

AspenHelo Partenavia

Main Instrumentation

Reanalysis Surface Currents & Flight Tracksfor October 29 and 30, 2011

*Current data: MITgcm- MIT general circulation model (Cornuelle and Gopalakrishnan- SIO)

Wind directionMean wind direction

Lidar Measurements of Broadband Directional Wavenumber Spectrum

Directional OmnidirectionalSpectrum: F(k,θ)Spectrum: ϕ(k)

h= flight elevation

€

φ(k) = F(k,θ )k d∫ θ• Up to 3 orders of magnitude in wavenumber range• At lower flight elevations the lidar data can resolvethe directional spectrum up to 60 cm wavelengths

Power-lawTransition atk= 1 rad/m ( 6 m )

60 cm

1.25 m

Significant Wave Height and Peak Direction( )along flight track on 10 /29 and 10/30

• The blue arrows show the mean wind directions• Maximum wave height observed: 2.7 and 1.9 m on 10/29 and 10/30.

- Opposing waves and currentsat Loop Current Edge showstronger wave height modulation

- Waves nearly orthogonal to theLoop current

Enhanced Breaking Near the Loop Current Edge• Opposing waves and currents on 10/30

• Whitecap Coverage (fractional area covered by whitecaps)

is on average larger near the area of opposing waves and currents

PeakDirection( )

Modulation of the Wave Field near the Loop Current

• Wave slope

(measure of the wave

amplitude times the

peak wavenumber)

* r is the correlation coefficient against WCC

• Peak directional spreading

(measured of the directional half

width of the spectrum

near at the spectral peak)

• Whitecap Coverage

*WCC correlates with wave slopeand is negatively correlated with peakspreading ( not statistically significant).*Wave slope is better correlated toWCC than peak spreading

It is well known that wave breaking correlates with waves slope but it relationship to the directional spreading is not well understood and some studies suggest it may be inversely related (Banner 2002)

r=.33 r=-.05

Numerical Simulations of Directional Spectra

WaveWatch III(Romero and Melville 2010; Sullivan et al. 2012)

5 km horizontal resolution

Current ModelsHycom-

Hybrid Coordinate Ocean Model(GOMI0.04/exp_31.0 )

5km – horizontal resolution&

MITgcm-10km – horizontal resolution

Surface WindsWRF-

Weather Research and Forecasting ModelCharles Jones (ERI)

4km – horizontal resolution

Validation:Lidar Wave Data

• Modeling framework: surface current models & wind model force the wave model which is validated against the observations

Doppler-Shifted frequency:

Intrinsic frequency:

Sin: wind input (Snyder , 1981)Snl : nonlinear fluxes due to resonant wave-wave interactions (Webb-Resio-Tracy, Resio

& Perrie 1991, van Vledder 2006)Sds : dissipation primarily due to wave breaking (Alves and Banner, 2003; Romero and Melville 2010; Sullivan et al. 2012)

dsnlinHHcg SSSk

NNUc

t

N

)()(

)(

)()(

k

kFkN

Wave action:

kUk c

)(

Forcing:)tanh(|| khkg

Advection Refraction Forcing

cU

: ocean current

Numerical Wave Model with Current Effects**Numerical Framework: WAVEWATCH III

Relative winds:

€

rU R =

r U 10 −

r U c

Simulated Wave Height vs. Observations for 10/29 and 10/30

- Scatter diagram color coded by the number of observations per bin- The model shows good agreement with obs. particularly for 10/30- Comparison not significantly sensitive the surface current productnor the effects due to relative winds (not shown)

Wave Field Modulation as function of time along the flight track in and out of the Loop Current Edge

Significant wave height

Wave Slope

Forcing Currents

Wave simulationsForced with MITgcm

Wave simulationsForced with MITgcm(without relative winds)

Wave simulationsForced with Hycom

-Without relative winds (forced with U10 insteadOr UR), the simulated waveheight is smaller by 15%.-All three wave simulationsare well within the scatter of the data

Omnidirectional (1d) Spectrum, Saturation, and Spreading at the Loop Current Edge

• Hs= 1.7 m

€

φ(k) = F(k,θ )k d∫ θ

kp : peak

wavenumber

€

B(k) = φ(k)k 3

Saturation:

Directionalspreading:

€

θ (k) =F(k,θ )θ 2 d∫ θ

F(k,θ )d∫ θ

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

1/ 2

-1d spectrum and saturationare in good agreement from the peak to about 10 kp.

-Model is narrower on average byabout 10 degrees, with better agreementat the peak.

Ray Tracing over Simulated Wave Height and Direction+Local maxima generally correspond to opposing wavesand currents and ray convergence (and vice versa)+Flight track near Loop Current overlaps with a ray diverging area

*Ray tracing from surface currents and the peak wavelength and direction averaged over the flight track*Future measurements should target both focal and divergent areas to increasethe range of parameters

Focal(opposingWaves and currents)

Divergent(following waves and currents)

flight track

Modulation of the Surface Waves Statisticsdue to Wave-Current Interactions

• Wave slope

• Normalized Peak Saturation

• Peak directional spreading

• Kurtosis of the surface elevation

(measure of the incidence of large wave events)

Statistical Distributions Near Loop Current Edge

• Wave crests and troughs

• Crest length

Data Subsets

Wave Crests and Troughs

Crests Troughs

- 2nd order Tayfun distribution with parametricdependence on significant slope serves as upperbound even over areas with significant wave current interactions

Wave height

- Empirical Weibull distribution (Forristall 1978) serves as upperbound of the statistical distribution of large wave even in conditionswith strong wave-current interaction.

Crest Length Statistics

Romero and Melville (2011)

€

Lη o=

λη oi

A∑ : Length of crests exceeding elevation thresholds ηo per unit area

: individual crest length

: total area λ

€

λη oi

€

A

Crest-Length Statistics

• Length of crests exceeding elevation thresholds per unit area:

Second order Nonlinear distributionw/parametric dependence on The significant slope(Romero and Melville 2011)

Summary• Airborne observations of surface wave processes with significant wave-

current interaction.• Enhanced wave breaking near the Loop Current with opposing waves and

currents• Wave breaking is well correlated with the wave slope but not the

spreading.• Measured spectra exhibit power-law transition from k-5/2 to k-3.• The simulated wave heights are in good agreement with the observations.• Relative winds near the Loop Current increase the wave height by 15%• The simulated wave height modulation and wave steepness at the Loop

Current Edge are in good agreement with the observations.• Model directional spreading is generally narrower than the observations by

about 10 degrees.• Statistical distribution of wave crests and crest lengths are well described

by nonlinear predictions• The empirical Weibull distribution serves as upper bound of the wave

height statistics even in conditions with strong wave-current interactions

Deliverables

• Analysis of IR data from 2011 experiment to generate surface current fields for wave-current interactions with validation against available HF current data near the coast.

• Analysis and nonlinear predictions of wave statistics including the incidence of extreme waves and the lengths of crests exceeding wave height thresholds.

• Technical reports and papers for publication on the wave model, airborne measurements and wave-current interactions for the Gulf.

• Monthly and quarterly reports.

Prospects for 2014

• Improved numerical model that corrects the bias of the directional spreading being narrower than the observations ( anisotropic dissipation function)

• Extend the model for applied problems ( approximate nonlinear wave-wave interaction function; exact computations are too expensive)

• Collect airborne observations of wave current interactions over focal and divergent areas to increase the parameter space and fully test the model predictions and improve models of wave breaking

Thank You

Surface Elevation Statistics

Kurtosis vs. Wave Slope

Reaching Loop Current boundary2011/10/30 – Sea Surface Temperature SST

AVHRR NOAA-19October 30 2011 08:04 GMT

Flight track on 2011/10/30Enhanced breaking & SST front

Wave dir.