PIV measurements in the bottom boundary layer of the coastal oceanW.A.M. Nimmo Smith, P. Atsavapranee, J. Katz, T.R. Osborn

Abstract Turbulence measurements were recently per-formed in the bottom boundary layer of the coastal oceanusing a submersible PIV system. The system consisted oftwo 2 K·2 K digital cameras, operating simultaneously.Optical fibers were used to transmit light from a surfacemounted pulsed dye laser to the sample areas. The systemwas mounted on a seabed platform that allowed the sampleareas to be aligned to the current, and measurements to bemade up to 10 m above the bed. Sample profiles and timeseries of mean velocity as well as structure functions arepresented. A method to calculate the Reynolds shear stressthat is not contaminated by surface wave motion and in-strument misalignment is also described.

1Background and motivationIn the coastal ocean, the momentum and energy balancesare influenced by many parameters, among which thebottom shear stress and the dissipation rate are of greatsignificance. The bottom shear stress affects the circulationdirectly and generates turbulence. The dissipation rate is acontrolling mechanism for the entire turbulent energybudget. Thus, modeling of ocean flows, sediment trans-port, pollutant dispersal, and biological processes rely onknowledge of the turbulence characteristics near the oceanbottom. Considerable effort has already been invested inturbulence measurements near the ocean floor, some in-volving direct measurements, others relying on an as-sumed velocity profile or turbulence characteristics. Forexample, a least-squares fit to a measured mean velocity

profile can be used to estimate the friction velocity and thebottom roughness length scale, assuming that a logarith-mic, constant stress layer exists (Grant et al. 1984; Huntleyand Hazen 1988). Another approach is based on assuminga balance between turbulent kinetic energy production anddissipation as well as a fit of the Kolmogorov –5/3 spectralslope in the inertial range of the vertical velocity spectrum(Grant et al. 1984; Johnson et al. 1994). One may alsoestimate the dissipation from a fit of the universal spec-trum in the dissipation range (Dewey and Crawford 1988).

Turbulent stress measurements have been performedusing several devices. Doppler shift based methods includethe acoustic Doppler current profiler, ADCP (Lhermitteand Lemmin 1994; Lohrmann et al. 1990; Lu and Leuck1999; van Haren et al. 1994) and the acoustic Dopplervelocimeter, ADV (George 1996; Kraus et al. 1994; Vo-ulgaris and Trowbridge 1998). The latter has a higherspatial resolution and can measure all three velocitycomponents, but it cannot scan the boundary layer. TheBASS system (benthic acoustic stress sensor) is based onmeasuring the acoustic travel time (Gross et al. 1994;Johnson et al. 1994; Trowbridge and Agrawal 1995;Trowbridge et al. 1996; Williams et al. 1996, 1987). Elec-tromagnetic velocity and vorticity sensors for measuringfine-scale fluctuations have been developed and deployedby Sandford et al. (1999), and Sandford and Lien (1999).An electromagnetic current meter has been used byWinkel et al. (1996) and laser Doppler velocimetry (LDV)has been utilized by Agrawal and Aubrey (1992), Trow-bridge and Agrawal (1995), and Agrawal (1996). The dataobtained using these sensors and assumed velocity dis-tributions constitute the current state of knowledge on thebottom stresses.

However, since these are point measurement tech-niques that generate time series of data, one encountersdifficulties in separating the unsteady flows associatedwith turbulence from the wave-induced motion. Since theshear stress is a correlation between streamwise and ver-tical velocity components, the alignment of the instrumentrelative to the mean flow in an environment with waves isalso a related difficulty. Consequently, Trowbridge (1998)incorporates simultaneous measurements using two sen-sors spaced about 63 cm apart and determines the stressfrom the covariance of the difference between the mea-sured velocities. His underlying assumption is that thespacing is larger than the characteristic length scale of theturbulence but smaller than the length scale of the wave. Indoing so he also overcomes uncertainties related to thealignment of the instrument as long as the error in angle is

Experiments in Fluids 33 (2002) 962–971

DOI 10.1007/s00348-002-0490-z

Accepted: 12 April 2002Published online: 27 September 2002� Springer-Verlag 2002

W.A.M. Nimmo Smith, P. Atsavapranee, J. KatzDepartment of Mechanical Engineering,The Johns Hopkins University, 200 Latrobe Hall,3400 N. Charles Street, Baltimore, MD 21218, USAE-mail: katz@titan.me.jhu.eduTel.: +1-410-5165470Fax: +1-410-5164316

T.R. OsbornDepartment of Earth and Planetary Science,The Johns Hopkins University, Baltimore, MD 21218, USA

Funded in part by ONR and in part by NSF. We are grateful to:Y. Ronzhes and S. King for their technical expertise in development ofthe equipment, the captain and crew of the RV Cape Henlopen,S. Mitchell, D.R. Baldwin, L. Luznik, W. Zhu, A. Fricova, andT. Kramer for their invaluable assistance during deployments.

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small. His analysis clearly illustrates the advantage inperforming simultaneous velocity measurements at mul-tiple points, which makes particle image velocimetry (PIV)a particularly attractive option for characterizing the flowand turbulence (including the Reynolds shear stresses) inthe coastal ocean. Unlike all other techniques, PIV pro-vides the instantaneous distribution of two velocity com-ponents over a sample area. Consequently, PIV enablesmeasurements of turbulent spatial spectra without as-sumptions involving Taylor’s hypothesis or homogeneity.Many repeated measurements can be used for obtainingthe turbulence statistics, however these, like all otheroceanic point measurement techniques in the coastalocean, are adversely affected by unsteady flows associatedwith surface waves. Methods to overcome this problem,based on the approach developed by Trowbridge (1998),will be addressed later in this paper.

In recent years we have developed and deployed sub-mersible PIV systems for velocity and turbulence mea-surements in the bottom boundary layer of the coastalocean (Bertuccioli et al. 1999; Doron et al. 2001). Theoriginal submersible system was based on a single 1 K·1 Kcamera that had a sample area of 20·20 cm2. The mea-surements were performed in the New York Bight at sixdifferent elevations ranging from 10 cm to about 1.4 mabove the sea floor. Unlike typical laboratory applicationsthat rely on artificial seeding with particles of knownproperties, natural seeding is sufficient for obtaining highquality PIV images in the ocean. Visibility measurementsperformed during the experiment indicate light transmis-sion of more than 80% (measured with the SeaCat, 25 cmpath-length transmissometer). In an earlier deployment offCape May, NJ, we also acquired data successfully when thetransmission was less than 50%. The data for each eleva-tion consists of 130 s of image pairs recorded at 1 Hz.Processing of this data provides a series of 130 2-D velocitydistributions within the sample area.

Subsequent processing provides distributions of meanvelocity and spatial spectra of energy and dissipation. Thedata extend well beyond the peak in the dissipationspectrum and demonstrate that the turbulence is clearlyanisotropic even in the dissipation range. The vector mapsare also patched together to generate extended velocitydistributions using Taylor’s hypothesis. Spectra calculatedfrom the extended data cover about three decades inwavenumber space. For the overlapping range, the ex-tended spectra show small differences from those deter-mined using the instantaneous distributions. Use ofTaylor’s hypothesis causes contamination of the extendedspectra with surface waves. However, the results still in-dicate that the turbulence is anisotropic also at lowwavenumbers, as expected in boundary layers. The verticalcomponent of velocity fluctuations at energy containingscales is significantly damped as the bottom is approached,while the horizontal component maintains a similar en-ergy level at all elevations. Different methods of estimatingthe turbulent energy dissipation are compared. Several ofthese methods are possible only with 2-D PIV data, in-cluding a ‘‘direct’’ method, which is based on measuredcomponents of the deformation tensor. Estimates based onassumptions of isotropy are typically larger than those

based on the ‘‘direct’’ method (using available velocitygradients and least number of assumptions), but the dif-ferences vary between 30% and 100%.

The experience gained during the first series of exper-iments has led to the development of the system describedin this paper. As expected, it has become evident that asample area of 20·20 cm is not sufficient to cover all therelevant turbulent length scales. Enlargement of the sam-ple area without an increase in resolution is also not anoption because that would mean an undesirable compro-mise at small scales (the vector spacing is already six timesthe Kolmogorov scale). Evaluation of the data suggestedthat we should cover a range of length scales that exceed1 m, preferably close to 1.5 m. Consequently, we haveopted to develop a system that utilizes two 2 K·2 Kcameras, each with a sample area of 51·51 cm, operatingsimultaneously side by side. The system was successfullydeployed and we recorded data continuously over an en-tire tidal cycle, while scanning the boundary layer fromvery near the bottom up to 1.7 m above the bottom. Thesystem is described in the next section, while details of thedeployment are given in Sect. 3. Results, including samplemean velocity profiles and structure functions are pre-sented in Sect. 4.

2Description of the submersible PIV systemIn enhancing the original PIV system we have had severalobjectives: (i) Continuous data acquisition while profilingthe region of interest for at least an entire tidal cycle. Atleast 15 min of data at each elevation is a bare minimum inorder to obtain converged estimates of mean flow andturbulence parameters. (ii) The sample area must be largeenough to cover the wavenumber range that would be‘‘contaminated’’ by surface waves if one uses a time seriesof data and relies on Taylor’s hypothesis. Based on theresults in Doron et al. (2001), a wavenumber of 4.2 rad/m,i.e., a wavelength of 1.5 m, has been identified as a targetscale. However, the enlarged sample area should not causea reduced resolution in the high wavenumber range. (iii)The system should enable us to record data in two differentplanes simultaneously in order to obtain statistics on all thethree velocity components. When one of the light sheets isvertical and aligned with the flow direction, the secondsheet can be horizontal. Such a capability would providedata on eight of the nine components of the velocity de-formation tensor along the intersection line, which wouldgreatly reduce the assumptions associated with estimates ofdissipation. Stereo PIV is also an option, which wouldprovide 3-D velocity distributions within the sample area,but not the cross-stream gradients. (iv) Based on our pastexperience, a wide dynamic range for the cameras is anadvantage because of variations in background lighting,water transmissivity, and particle characteristics.

All of these features have been incorporated into thenew PIV system. Schematic descriptions of the submers-ible platform as it was deployed are presented in Fig. 1,and the components located on the ship are sketched inFig. 2. The system enables us to simultaneously operatetwo 2048·2048 pixels2, 4 frames/s, 12-bit digital cameras(manufactured by Silicon Mountain Design) with

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hardware-based image shifters to overcome directionalambiguity. When these cameras record double-exposureimages, the two overlapping frames are shifted on the CCDarray relative to each other by a prescribed number ofpixels. The magnitude (in pixels) of the shift can be ad-justed, using the computer controlling the camera, to belarger than all possible displacements in that direction.Consequently, all the particle traces appear to be movingin the same direction and the known fixed displacement issubtracted after processing the images.

The CCD has 14·14 lm pixels, making it quite sensitive(equivalent to 800 ASA film). The increased resolution andsensitivity of these cameras make it possible to increasethe sample size to 0.5·0.5 m2 without compromising thesmallest scales (0.6–0.8 cm). When these cameras werepurchased and deployed, the 2 K·2 K cross-correlationcameras (that are available today) were not available.However, the dynamic range and sensitivity of the presentimage-shifted auto-correlation cameras are still consider-able advantages in the ocean environment.

Each camera feeds data over 70 m of cable to a high-speed disk array with a capacity of 240 GB (six IDE disks,currently 40 GB each) that can acquire data at a sustainedmaximum acquisition speed of 60 MB/s (only 32 MB/s areneeded for the present system). When the experiment is

completed the data is compressed without loss of resolutionand then backed-up on another hard disk. Slower back-uptapes are also available. The storage capacity of this newsystem enables us to continuously acquire 16-bit images at0.5 Hz for more than 15 h (a maximum of 13 h was actuallyrecorded), i.e., we can cover an entire tidal cycle.

As the system was originally designed, we opted to keepthe laser on the ship and transmit the light to the bottomvia optical fibers. The primary motivations were: (i) Adesire to operate for many hours continuously, eliminatingbatteries as an option; (ii) Reluctance to deploy large powersupplies fed by high-energy lines owing to logistics andsafety concerns; and (iii) Because of the image size, thedistance between the camera and the light sheet and con-cerns about water transmission, about 100 mJ/pulse shouldbe available for each laser sheet. Transmitting this energy/pulse through a fiber without damaging it, while leavingsome margin for variations in field-test conditions, andkeeping the fiber at a reasonable diameter (so that the beamcan be re-focused), eliminated Nd-YAG lasers as an option.As discussed in Bertuccioli et al. (1999), the short durationand high intensity of the Nd-YAG laser would have re-quired large fibers and an unacceptable compromise inenergy level. Consequently, we opted for a dual head, flashlamp, pumped dye laser that has a pulse duration of 2 ls,

Fig. 2. Schematic diagram of ship-board components of submersiblePIV system

Fig. 1. Schematic diagram of submersible PIV platform

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i.e., almost three orders of magnitude longer than the Nd-YAG, but still short enough for applications in water. Oursystem can generate 15 pulse-pairs/s with essentially un-limited in-pair delay. Using Rhodamine 6G as dye, thislaser can generate a maximum of 350 mJ/pulse at 594 nm.This energy is sufficient for pumping light through morethan one fiber. Consequently, as Fig 2 shows, we split thelaser beams and focus them onto two 400 lm diameteroptical fibers that transmit the light to the submergedprobes. The maximum output that we can transmit withoutdamaging the fibers (caused by slight misalignments) is120 mJ/pulse. This setup enables us to orient the twocameras and laser sheets independently. They can be po-sitioned to record images in the same plane, vertically orhorizontally, near each other or apart, but can also bealigned in different planes. Figure 1 shows the setup usedduring most of the recent deployment tests.

The submerged probes contain lenses for re-focusingand re-collimating the beam exiting from the fiber, and acylindrical lens for expanding the beam to a light sheet.The minimum thickness of the light sheet is limited by thediameter of the optical fiber, but the sheet also has to bethick enough to allow for out-of-plane displacement of theparticles between the two exposures since the flow is threedimensional. For the experiments described in this paper,the thickness of the laser sheets varied between 3 and4 mm over the sample areas. This width is much less thanthe vector spacing (about 8 mm), but still allows forvariations in the mean flow direction of ±20� (with atypical particle displacement of 20 pixels).

During the experiments described in this paper, thedistance between the camera and the light sheet was45 cm. Since the field of view was 51·51 cm we had to usewide-angle lenses (Nikon ASF-28 mm) and a circulardome as a front window to the waterproof camera hous-ings. To calibrate the system and correct for the resultingimage distortions we recorded images of a reference gridand created calibration maps that varied over the imageand between cameras (the latter only slightly).

The submersible system also contains a Sea-Bird Elec-tronics, SeaCat 19-03 CTD, optical transmission and dis-solved oxygen content sensors, a ParoScientific Digiquartz,Model 6100A, precision pressure transducer (for measur-ing surface waves), an Applied Geomechanics, Model 900abiaxial clinometer, and a KVH C100 digital compass.During the deployment reported in this paper, the plat-form was mounted on a hydraulic scissor-jack to enableacquisition of data at various elevations above the seafloor, up to a maximum elevation of 1.7 m. Using a mo-torized drive the platform can also be rotated to align thesample area with the mean flow direction. An on-boardvane that aligns itself to the flow and a video camera thatfocuses on this vane are used for indicating the flow di-rection. During the field tests we used a second submergedvideo camera to record images of the bottom topography.This platform has since then been replaced with a tele-scopic arm that has a substantially longer profiling range –from the bottom up to 10 m into the water column. Thislatter system has already been deployed successfully inMay and September 2001 (see Sect. 5).

3Details on the May 2000 deploymentsA series of experiments took place during the period, 9–20May 2000 at two sites on the east coast of the USA, one inthe vicinity of the Longterm Ecosystem Observatory (LEO-15), about 5 km off the New Jersey coast, the other insidethe wall of the harbor of refuge near the mouth of Dela-ware Bay. The system was deployed from the RV CapeHenlopen (one of the UNOLS ships managed by the Uni-versity of Delaware). The ship was held in a fixed positionusing a three point mooring system. The platform wasdeployed on the seabed at a depth of 12 m. A ship-boardADCP provided us with data on the mean velocity distri-bution in the water column for the entire duration of thetests. We also acquired water column profiles of temper-ature and salinity and collected samples of particles atdifferent elevations and from the seabed itself.

We recorded three data sets, two at the first site and oneat the second. The exact position of the first site was39�27¢00¢¢N and 74�14¢15¢¢W, i.e., about 0.5 nautical milesto the south-east of Node B (39�27¢25¢¢N, 74�14¢45¢¢W),and about 1.25 nautical miles to the south-east of Node A(39�27¢41¢¢N, 74�15¢43¢¢W) of LEO-15. The seabed consistsof coarse sand ripples of approximately 50 cm wavelengthand 10 cm height. The currents in the region are generallymoderate, however the site is exposed to the oceanic swell.On the night of 15–16 May we recorded data at 0.5 Hz for9 h continuously. On the night of 16–17 May we recordeddata at 0.5 Hz for 13 h continuously. Thus, we obtainedPIV images that will enable us to study variations in flowstructure and turbulence during an entire tidal cycle.During these tests the cameras were configured as illus-trated in Fig. 1. Both were focused on the same verticalplane, had the same field of view (51 cm), and their centerswere located 1 m apart (see next section for reasons). Thedata was acquired at three different elevations, 9.5–60.5 cm, 64–115 cm, and 118.5–169.5 cm above the bot-tom. At each elevation we aligned the system to the meanflow direction (using the video images of the vane) andthen acquired data, typically for 30 min, i.e., 2·900,2 K·2 K, 12-bit PIV images. The elevation was thenchanged and the next image set was acquired. Since theflow direction changed with time and with elevation, wehad to re-align the platform for each data set. In a fewcases the flow direction changed significantly during therun and we had to stop it early. The extent of the vari-ability in magnitude and direction of the mean current atthis site during the two nights can be seen from the outputof the ship’s ADCP, shown in Fig. 3. The numbered crossesshow the timing at the beginning of the 30 data seriesobtained during this field test.

On the night of 19–20 May 2000 we acquired a thirddata set behind the wall of the harbor of refuge of DelawareBay. Here, the flow is characterized by strong tidal cur-rents (with surface velocities in excess of 1.5 m s–1) andlittle wave motion. The seabed consists of fairly smoothsandy mud, with none of the sediment ripples observed atthe LEO-15 site. This time the two sample planes wereperpendicular to each other and the data was acquired at3 Hz. We recorded five data sets at different times and

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elevations, each consisting of 1,000 image pairs. Com-bined, we recorded 500 GB of images.

As of today, we have analyzed all three of the data sets.In-house developed software described in Roth and Katz(2001), Roth et al. (1999) and Sridhar and Katz (1995) withsome modifications to the image enhancement procedureshave been used for computing the velocity. Constrained bythe particle concentration, we used 64·64 pixel interro-gation windows and 50% overlap between windows. Thus,each resulting vector map consists of a maximum of 63·63velocity vectors with a vector spacing of 0.8 cm. Increasingthe resolution to 32·32 pixel windows, which would gen-erate 127·127 velocity vectors/image (i.e., vector spacingof 0.4 cm) would be possible for only some of the images,and will be performed only selectively for some of the data.After computing the velocity, the image shift was sub-tracted and the magnitude and location of each vector wascorrected for image distortion. The resulting slightly ir-regular array was then interpolated to generate a regular,

equally spaced array. The data quality varies depending onthe particle concentration, size and spatial distribution ofthe particles, and the orientation of the laser sheet relativeto the instantaneous flow. Typically we obtained 60–80%of the vectors that satisfied the accuracy criteria of the dataanalysis software (based on correlation magnitude, 0.2,and difference from neighboring vectors, 4 pixels). In-stantaneous distributions that contained less than 60%correct vectors were not used during subsequent analyses.

4Results

4.1Distributions of mean velocityFigure 4 shows a characteristic 30 min time series, fromthe LEO-15 site, of the instantaneous mean streamwisevelocity obtained from the PIV data by averaging thevelocity over the entire sample area of one camera. The

Fig. 4. Thirty-minute time series of map-mean horizontal (U) andvertical (W) velocity sampled at 0.5 Hz at the LEO-15 site. Run 22 inFig. 3

Fig. 3. Near-bed current speed and direction at the LEO-15 site asmeasured by the ship-board ADCP. Crosses mark the start times for30 min PIV sampling periods at one of three elevations

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mean velocity is about 14 cm s–1, consistent with theADCP data in Fig. 3, with the orbital motion caused bysurface waves, traveling in groups, superimposed. It can beseen that the amplitude of the streamwise wave-inducedflow (generated by the predominantly 10 s period surfacegravity waves) is comparable to the mean velocity, and atthe extreme, the flow direction is actually reversed. Asexpected, near to the bed, the waves have much less of animpact on the vertical velocity. The vertical distributionsof mean horizontal velocity under these conditions areshown in Fig. 5. Here, the vector maps forming each meanprofile were conditionally sampled based on the phase ofthe wave-induced horizontal velocity. At no point is alogarithmic profile in evidence, consistent with laboratorytests in an oscillatory boundary layer (Jensen et al. 1989).

In comparison, Fig. 6 shows a time series of the datacollected at the Delaware Bay site, where the mean flow wasmuch stronger, with only relatively weak orbital wavemotion. In this 5 min, 3 Hz time series, the mean velocity is35 cm s–1, and the orbital wave motion has a maximumamplitude of about 7 cm s–1 and a period of about 9 s.

Smaller amplitude (about 4 cm s–1) and longer period(about 150 s) variations in the mean flow, or ‘‘beating’’, arealso visible in the horizontal velocity record. To a lesserextent, this trend can also be identified in the vertical ve-locity record. The corresponding vertical distribution ofmean horizontal velocity, and that of the adjacent 5 minperiods, is shown in Fig. 7. In contrast to Fig. 5, it can beseen that they have a very definite logarithmic profile. Thus,a log layer forms only when the mean flow is substantiallyfaster than the orbital motion. A log layer was also observedby Bertolucci (1999) under similar conditions of relativelyhigh mean flow and low orbital wave motion.

Unfortunately, we have found that the combination ofthe large field of view, the small distance between thecameras and the light sheets, and the thickness of thesheets (3–4 mm) has introduced significant bias into ourmeasurements, caused by the out-of-plane component ofthe fluid velocity. For example, considering a case wherethe out-of-plane motion is sufficient to displace particlesbetween exposures away from the camera by half thethickness of the light sheet (2 mm – any greater dis-placement would typically result in loss of one of theparticle pairs). This motion results in an apparent inward,radial displacement of the particles on the image plane,which increases linearly in magnitude from zero at thecenter of the image up to a maximum of 4.5 pixels at theedges. This contamination is minimized for each vectormap by first subtracting the map-mean velocity from eachvector. Then the radial component of velocity and theradial distance of each vector from the center of the mapare calculated. From these, the mean radial gradient of theradial velocity is estimated using a least-squares method,setting the radial velocity to zero at the center of the map.This mean gradient is then used to construct a map ofradial contamination that is subtracted from the originalvector map. This procedure removes the instantaneousmean out-of-plane velocity from the measurements, butcannot account for any non-uniformity of the out-of-planemotion caused by shear or turbulence.

4.2Estimating the Reynolds stressThe two 0.5·0.5 m2 samples are aligned horizontally inthe same plane with a gap of 0.5 m between them. To

Fig. 5. Conditionally sampled vertical distributions of mean hori-zontal velocity at different phases of the surface-wave inducedmotion. The data shown is from three consecutive 30 min periods,one at each of the three elevations above the bed. LEO-15 data

Fig. 6. Five-minute time series of map-mean horizontal (U) andvertical (W) velocity sampled at 3 Hz at the Delaware Bay site

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calculate the Reynolds shear stresses and overcoming theproblems introduced by unsteady flow caused by surfacewaves, we follow the procedures introduced by Trow-bridge (1998), taking advantage of the 2-D velocitydistribution provided by PIV. Briefly, the velocity isdecomposed to ui ¼ �uui þ ~uui þ u0i, where �uui is the timeaverage, ~uui is wave-induced motion, and u0i is theturbulence contribution. Defining Dui ¼ ui xi þ rið Þ�ui xið Þ, we calculate the covariance of the differencein velocity between two points, also known as thesecond-order velocity structure function, Dij ri; xið Þ,defined as

Dij ri; xið Þ ¼ cov Dui;Duj

� �

¼ ui xi þ rið Þ � ui xið Þ½ � uj xi þ rið Þ � uj xið Þ� �

:

Assuming horizontal homogeneity,

ui xi þ rið Þuj xi þ rið Þ� �

¼ ui xið Þuj xið Þ� �

and

ui xið Þuj xi þ rið Þ� �

¼ ui xi þ rið Þuj xið Þ� �

;

then

cov Dui;Duj

� �¼ 2ui xið Þuj xið Þ � 2ui xi þ rið Þuj xið Þ:

Decomposing ui, and assuming that there is no corre-lation between ~uui and u0i, i.e., ~uuiu0i � 0 (discussion follows),one obtains

cov Dui;Duj

� �¼ 2 ~uui~uuj þ u0iu

0j

h i� 2 ~uui xi þ rið Þ~uuj xið Þh

þ u0i xi þ rið Þu0j xið Þi:

Fig. 8. Sample distribution of –cov [Du,Dw](r1) using data from twoaligned vertical light sheets at the LEO-15 site

Fig. 7. Vertical distribution of mean horizontal velocity measured atthe Delaware Bay site. The discontinuity in the profile is a result ofperforming measurements at different times and the ‘‘short’’ period ofmeasurements at each of the three elevations

Fig. 9. Distribution of cov[Du,Dv](r1) (left) and –cov[Du,Dw](r1)(right) using data obtained using horizontally and vertically orientedlight sheets respectively, at the Delaware Bay site

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In flows with integral scale, l, much smaller than thewavelength of surface waves, k, as long as r>k one ob-tains:

cov Dui;Duj

� �¼ 2 u0iu

0j

h i� 2 u0i xi þ rið Þu0j xið Þh i

:

The first term on the RHS is the Reynolds stress and thesecond term is the two-point correlation tensor, Rij(ri).Typically Rij(ri) decreases with increasing r and diminishesfor r is larger than the integral scale. Thus, for, l<r>k,cov Dui;Duj

� �¼ 2 u0iu

0j

h i, i.e., the stress is equal to half the

covariance of the velocity differences. Trowbridge (1998)shows that this method substantially reduces the wavecontamination caused by instrument alignment.

Using the PIV data and assuming horizontal homoge-neity, it is possible to calculate cov[Du,Dw](r1), where r1 isthe streamwise separation, using data obtained in a ver-tical plane and cov[Du,Dv](r1) using the horizontal sheetdata. The two 51·51 cm samples, aligned horizontally inthe same plane with a gap of 50 cm between them, enableus to calculate cov[Du,Dw](r1) up to a scale of r1=1.5 m bydirectly multiplying the difference in the appropriatecomponents of pairs of vectors. Up to 51 cm, the twovectors are located in the same map and for larger scales,the vectors are located between the two maps. Assuminghorizontal homogeneity, one can average data obtained atdifferent x (but the same z) as well as at different times. Asample distribution of cov[Du,Dw](r1), using data fromboth light sheets, is presented in Fig. 8. Initially the valuesof cov[Du,Dw] increase with r1, but then they asymptoti-cally converge to a constant value as r1 becomes compa-rable to the distance from the bottom (�1 m). Thecondition of r>k is also satisfied (k�100 m). Thus, theexpected trends indeed occur and u0w0=–0.2 cm2s–2.Sample distributions of cov[Du,Dv] and cov[Du,Dw] ob-tained using the data recorded with perpendicular planesare presented in Fig. 9. Here the range of r1 is limited toone sample area, but the values of the covariance clearlystart reaching asymptotic values. Thus, u0w0=–0.3 cm2s–2

and u0v0=0.05 cm2s–2.Using this approach, PIV data of a vertical plane can be

used for obtaining the vertical distribution of u0w0. In thefuture we intend to use stereo PIV to provide the verticaldistributions of all three shear stress components, u0w0,u0v0 and v0w0. Furthermore, our assumption followingTrowbridge (1998), that ~uuiu0i � 0, also requires attention.When the turbulence is generated by the wave-inducedmotion, the validity of this assumption, which is based onthe ratio of length scales being greater than 100:1, requiresvalidation based on the data. We intend to measure themagnitude of this variable under different flow conditions.

5Latest deploymentsTwo further deployments of the submersible PIV systemhave been performed recently. The original samplingplatform was redesigned to allow measurements to bemade over an extended range, from the seabed up to 10 minto the water column. The new platform (see Fig. 10)comprised a telescopic hydraulic cylinder mounted verti-cally on a weighted tripod base. The PIV system andauxiliary components were in turn attached to the top ofthe cylinder via rigid framework and a hydraulically op-erated turntable. Two hydraulic hoses linked the platformto a ship-board hydraulic power supply that used envi-ronmentally friendly, food-grade hydraulic oil. A remotelycontrolled manifold at the top of the cylinder was used to

Fig. 10. Schematic diagram of the new, extended-range, samplingplatform

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switch operation between the hydraulic turntable motorand the cylinder, reducing the required number of lineslinking the platform to the surface.

The PIV components were also re-configured to mini-mize the effects of the out-of-plane motion (see Sect. 4):the light sheets were made thinner (2.5 mm), the separa-tion between the cameras and the sample areas was in-creased to about 1 m, and the sample areas were reducedin size (to about 35·35 cm). Together, these alterationsreduced the maximum apparent radial displacement at theedge of the images to about 0.5 pixels (a reduction of90%). To achieve the reduction in sample area togetherwith the increased camera to light-sheet separation, weused longer focal length lenses (Nikon ASF-85 mm) be-hind flat ports, which had the additional benefit of re-ducing the optical distortion within the images from about10% (with the wide-angle lenses and dome ports) to lessthan 2%.

This latest version of the PIV system was deployed inMay 2001 for testing, and in September 2001 for datacollection. For the 1–10 September experiments, we againdeployed the system near LEO-15, 5 nautical miles south-east of our previous sampling location at 39�23¢37¢¢N,74�9¢32¢¢W, in 21 m deep water. Here the water columnwas strongly stratified, with a sharp thermocline situatedabout 7 m above the seabed. Data were collected for20 min periods at a time, sampling at either 2 or 3.3 Hz. Atotal of 700 GB of image data were collected at variouselevations, up to 8 m above the seabed and under differingconditions of mean flow and wave-induced motion.

After the re-configuration of the PIV system, the typicalsample area coverage of vectors that satisfied the accuracycriteria of the data analysis software increased to 75–95%.Gaps within these distributions can now be more reliablyfilled by taking the average of surrounding good vectors.Two sample vector maps that have had missing vectorsfilled in (the original vector coverage in each was about90%) are shown in Fig. 11, superimposed on the corre-sponding instantaneous vorticity fields. The two velocitymaps are of the same sample area, but separated in time by0.6 s. It can be seen that the flow is dominated by largecoherent structures, consisting in turn of groups of smallervortices. These structures are persistent and are advectedby the mean current and the wave-induced motion. Thelarge structure in the first map can also be seen in thesecond, displaced about 6 cm in the streamwise directionby the mean flow. According to Adrian et al. (2000), thesestructures are sections through hairpin vortices.

6ConclusionsAn enhanced submersible PIV system has been developedto enable the collection of turbulence measurements in thebottom boundary layer of the coastal ocean. The systemwas deployed at two sites under contrasting environmentalconditions. The data collected provide vertical mean ve-locity profiles and the time evolution of the mean velocity.It is found that a log layer only forms when the meanvelocity is substantially higher than the surface wave-induced motion. Using the covariance of the difference

Fig. 11. Two sample instantaneous vector maps from the re-configured PIV system. Vectors are shown with the mean streamwiseand vertical velocities removed, and are superimposed on the

vorticity fields. The two maps are of the same sample area, butseparated in time by 0.6 s

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between velocity components, it is possible to estimate theReynolds stress without being affected by unsteady phe-nomena related to surface waves.

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