Journal of Marine Systems 75 (2009) 150–162

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Journal of Marine Systems

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Measurements of a small scale eddy at a tidal inlet using an unmannedautomated boat

Chunyan Li a,b,⁎, Eddie Weeks a

a Coastal Studies Institute, Department of Oceanography and Coastal Sciences, Louisiana State University, Baton Rouge, LA 70803, United Statesb College of Marine Sciences, Shanghai Ocean University, 334 Jungong Rd., Shanghai, 200090, China

a r t i c l e i n f o

⁎ Corresponding author. Coastal Studies Institute, Dgraphy and Coastal Sciences, Louisiana State Univer70803, United States. Tel.: +1 225 578 3619.

E-mail address: cli@lsu.edu (C. Li).

0924-7963/$ – see front matter © 2008 Elsevier B.V.doi:10.1016/j.jmarsys.2008.08.007

a b s t r a c t

Article history:Received 19 April 2008Revised 3 August 2008Accepted 21 August 2008Available online 13 September 2008

An unmanned automated boat equipped with an acoustic Doppler current profiler was used infield surveys at a tidal inlet, the Southwest Pass of Vermillion Bay, Louisiana on Sept 6 and Oct 6,2007. During the first survey, under calm weather conditions, a small scale eddy with adiameter of 300 m was discovered with strong upwelling and downwelling zones. A detailedanalysis of this small eddy shows that the eddy's velocity field is relatively uniform in thevertical and the eddy is formed by a flow convergence, tidal velocity shear induced relativevorticity, and the interaction between the horizontal flows and bathymetry. The majorupwelling area is where an uphill flow occurs while the major downwelling area is where adownhill flow occurs. The vorticity of this eddy is on the order of 0.013 s−1, which is two orders-of-magnitude larger than the planetary vorticity, and one-order-of magnitude larger than thatin a typical tidal inlet without eddies. The Coriolis effect is thus insignificant and the generationof the eddy cannot be affected by the earth rotation. Themaximum upwelling and downwellingvelocities exceed 0.3 m/s. This high vertical velocity in a tidal inlet does not appear to have beenreported before. The second survey, conducted under a thunder storm condition, did not reveala similar eddy at the same location during roughly the same tidal phase. Though themeasurements of 3-D flow structure under a thunder storm condition in a tidal channel doesnot appear to have been reported before, the second survey is of important value in providingsupport of the mechanism of the eddy formation during the first survey: the wind tends toproduce downwind flow in shallow water than in deep water, producing a velocity shearcounterproductive to the formation of the eddy. Therefore, the second survey under a thunderstorm condition did not showan eddy. A scaling analysis of the non-hydrostatic flow shows thatthe uphill and downhill flows introduce a non-hydrostatic flow component proportional to thesquare of the bottom slope which leads to the conclusion that the non-hydrostatic flowcomponent affects less than 10% of the vertical momentum balance.

© 2008 Elsevier B.V. All rights reserved.

Keywords:Small eddyTidal channelAutomated boatUpwelling and downwelling

1. Introduction

Eddies in the ocean are ubiquitous. They exist with variousspatial and temporal scales. Monk et al. (2000) provided acomprehensive review and introductory work of “spiral

epartment of Oceano-sity, Baton Rouge, LA

All rights reserved.

eddies” (Johannessen et al., 1996; DiGiacomo and Holt,2001), often observed from space such as by syntheticaperture radars (SARs) installed on satellites. The spiraleddies, mostly cyclonic, exist in the open ocean with a spatialscale of about 10–25 km and appear to be associated withshear instabilities. The Gulf of Mexico loop current eddies (e.g.Elliott, 1982; Auer, 1987) spin off the meandering warmcurrent provide another kind of eddies. The cyclonic “Hawai-ian eddies” (Seki et al., 2001), which have a scale of greaterthan 100 km, belong to a different category as their formationis related to currents behind an island. Eddies can also form in

151C. Li, E. Weeks / Journal of Marine Systems 75 (2009) 150–162

pairs (Feng et al., 2007). Deep water island wakes can havemultiple eddies (e.g. Wolanski et al., 1984; Pattiaratchi et al.,1987; Pawlak et al., 2003; Alaee et al., 2004; Dong et al., 2007).In coastal waters, coastline features, bathymetry, and dis-charges may influence the flow field and generate eddies, e.g.the eddy observed within the Louisiana Bight (Rouse andColeman, 1976), with a scale of ~50 km, using remote sensingdata and later confirmed by vessel-based current velocitymeasurements (Murray,1998). In shallow seas, coastal waters,especially within bays and estuaries, eddies can form by theinteraction of the geomorphology and hydrodynamics, e.g.,the headland eddies (e.g. Pingree and Maddock, 1977a,b;Pingree, 1978; Maddock and Pingree, 1978; Pingree andMaddock, 1979; Fang and Yang, 1985; Geyer and Signell,1990; Signell and Geyer, 1991; Geyer, 1993; Wolanski et al.,1996; Chant and Wilson, 1997). These eddies are transientphysical vortices, unlike the residual eddies obtained byaveraging the flow field over a tidal cycle (e.g. Li, 2006; Liet al., 2006; Li et al., 2008).

These widely studied eddies are, however, large scales.Here “large scale” means that the features can be observedfrom space using presently available high-resolution sensorson a routine basis. At the other end of the spectrum, in whichsmaller scale eddies formed in estuaries and coastal waters on100m scales cannot be readily observedwith existing satellitebased sensors on a routine basis, a gap of knowledge exists,particularly those pertinent to in situ observations of thesmaller eddies. This paper presents such a study of a smalleddy at an inlet of awide bay: Vermillion Bay of Louisiana.Wepresent a basic analysis on data obtained from an automatedunmanned boat equipped with an acoustic Doppler currentprofiler (ADCP). Just as discussed in numerous papers aboutthe biological characteristics of the large scale ocean eddies(e.g. Seki et al., 2001; Moore et al., 2007), we have also noticedthat the small scale eddy that we present here appear to havesignificantly higher biological activities. However, here weonly focus on the description of the physical phenomenon.The biological characteristics need to be investigated in futurestudies in collaborating with biologists. Before discussing theobservations and data, we will first describe the tool used inthis study: the unmanned automated boat.

2. Development of an unmanned automated boat (A-Boat)

Observational platforms have been evolving following theneed of oceanographers and the technological trend. Thefixed mooring platforms are now being supplemented withautonomous underwater vehicles (AUV). AUVs (which arebasically slow-moving unmanned submarines) are widelyused in offshore physical oceanographic and marine geologi-cal surveys (e.g., reviews in Schofield and Tivey, 2004;Schofield et al., 2004). The AUVs developed at MIT are aclass of underwater platforms which have been equippedwith acoustic Doppler current profilers (ADCPs from TeleDyneRD Instrument) or acoustic Doppler velocimeters (ADVs fromSonTek) (e.g. Curcio et al., 1998; Hoagland et al., 1999; Curtinet al., 2005). Acquisition of high resolution acoustic data(multi-beam bathymetry, side-scan swaths, and sub-bottomprofiles) in support of oil and gas activities in deep water ofthe northern Gulf of Mexico continental slope is now beingcarried out with AUVs. However, the high cost associated with

owning and operating an AUV, in addition to the challengesfaced in ultra shallow waters, such as those in the Louisianabays, precludes it as a viable option for most research groupsfocusing on shallow coastal water research. On the otherhand, automated surface crafts (ASC) are autonomous selfpropelling platforms (usually based on kayaks, catamarans,etc) only operating on the surface of water (e.g. Goudey et al.,1998). This makes the navigation easier using GPS andsignificantly reduces the associated operational costs. TheseASCs are used as educational tools, and precision surveyplatforms for profiling the water column and measuringhydrographic parameters and water depth.

The authors of this paper have been developing a similartype of ASC since March 2007 with some specific considera-tions of continuous operations. Three such unmannedautomated boats (A-Boats) have so far been made andrigorously tested. They are made of aluminum, plastic, andfiberglass, respectively. The newest A-Boat (made of fiber-glass) is equipped with a 600 or 1200 kHz ADCP and/or a3 MHzmini-ADP (there are twowells on the A-Boat for eitheror both instruments), an optional side-scan sonar, a highresolution GPS (~0.25 m accuracy by a special subscription toa designated area), and up to two real time web cameras. TheA-Boat has an onboard computer with a long-range (~10 km)wireless connection to another computer on land or on amother ship, an auto-pilot system, an electric compass, twoelectric motors that have been customer modified in-housefor better speed controls, two 12-V automobile batteries, anda 1-kW mini generator for charging the batteries. A softwarepackage written in Visual Basic computer language isdeveloped in-house by us. It can be programmed to runthrough a series of (unlimited number of) predefinedwaypoints continuously with high precision. Thesewaypointscan also be manually modified easily at any time during asurvey. The prototypes have been able to maintain the samedata collection transect over many replications accurately (toresolve tidal variations), a task that manned vessel cannotaccomplish with comparable precision and endurance. Theboat can achieve 5-knot maximum and 4-knot averagecruising speeds with at least 24 h endurance withoutrefueling. The fuel consumption is very economic: onlyabout 2 gal per day. The A-Boat is light weighted and can bepicked up by 1 person.

Field tests have demonstrated that the average offlinedistance from the planned route is 0.97 m (with the plastic A-Boat) or smaller (with the latest fiberglass A-Boat) under swiftlateral flow conditions (maximum flow velocity perpendicu-lar to the ship track ~1 m/s). In addition, multiple intensivetest runs have been conducted in the LSU's University Lake, anumber of tidal channels at Port Fourchon, Belle Pass, BayChampagne, and Vermillion Bay of Louisiana, with each testlasting between less than an hour to more than 24 h (day andnight continuously) for the hydrodynamics and hydrography,and multiple days for the sidecan sonar (during the daysonly). These tests demonstrate that the A-Boats are veryreliable, endurable, efficient, and accurate. It can go to muchshallower waters (almost any depth close to the bank) than amanned boat. In all the tests and surveys where the waterdepth is less than 1 m, for e.g. Bay Champagne, the A-Boat hasnever got stuck, even at the muddy bank. This makes it auseful tool in shallow deltaic or muddy coastal environments

152 C. Li, E. Weeks / Journal of Marine Systems 75 (2009) 150–162

like the Chenier Plain. Most importantly, it can follow aprogrammed route accurately (and repeatedly if needed) forsustained automated operation to obtain a high resolutionmap of bathymetry, flow conditions, and fishery dataobtained from echo sounder sonar, with a quality andquantity that a manned boat can never achieve. In addition,the A-Boat causes much less perturbation of the watercolumn and bottom sediments, making it a better choice forrecording backscatter and suspended sediment in shallowwaters.

3. Observations using the A-Boat

On Sep 6, 2007, a vessel-based survey of velocity profileswas conducted using a 22-ft catamaran and the 12-ftfiberglass A-Boat at the mouth of the Southwest Pass ofVermillion Bay, Louisiana (Fig. 1). The first objective was totest the A-Boat. The second objective was to measure thevelocity field through the narrow and deep (hN34 m) South-west Pass of the wide and generally shallow Vermillion Bay,with a particular interest of topographically induced upwel-ling and downwelling in estuaries. Maximum tidal range inthe area is on the order of 0.6 m. Tidal currents within thebays of the Louisiana coast are very weak and only the narrowinlets experience significant tidal currents which can be usedto estimate the flushing of the bays.

Fig. 1. Study area. Shown here are the location of the Vermillion Bay and the area ofright panel indicates the locations of the first two CTD casts on Oct 6, 2007 (see Ta

For this survey, the A-Boat was equipped with a 600 kHzacoustic Doppler current profiler (ADCP). The original planwas to use the A-Boat to cover the entire Southwest Pass witha polygon and then focus on areas of interest, which was to bedetermined. The A-Boatworked during almost the entire timeof the survey of 2 h and 10 min (Table 1) except with acommunication problem starting at about 1 h and 37min intothe survey, when an eddy like structure had just beenobserved. The structure was characterized with not only thechanging flow directions in a way suggesting a clockwiserotating feature but also surface signatures of upwelling anddownwelling. The upwelling areas were shown to haverelatively smooth surface while the downwelling areasappeared to have rough surfaces with foams and debrissimilar to areas of convergence fronts (e.g. Garvine, 1974;Garvine and Monk, 1974; O'Donnell, 1993). Within theapparent eddy feature, we observed plants floating on thesurface and several dolphins were seen constantly in the areapossibly hunting in the eddywithinwhich it might havemorebiological activities than its surroundings. Despite the mal-function of the communication system, the ADCP and GPSwere all working properly. We thus towed the A-Boat behindthe catamaran and continued the measurements. The eddywas less than 300 m in diameter, which appeared to be wellestablished and stable: there was no apparent change inposition and flowmagnitude during the observations. We ran

the ADCP surveys on Sep 6 and Oct 6, 2007. The numbers 1 and 2 in the lowerble 2 for time, depth, and coordinates).

Table 1ADCP surveys

Date Sep 6, 2007 Oct. 6, 2007ADCP used RDI 600 KHz, 2 Hz Ensembles,

0.5 m bin size, 1st bin=1.12 m(Same)

Start time (UTC) 19:23 19:57End time (UTC) 21:33 23:00Time for the eddy 27 min –

Total time 2 h 10 min 3 h 3 min

Table 2CTD casts

Cats # Time (UTC) Latitude (N) Longitude (W) Depth (m)

1 18:09 29° 36.704' 92° 00.361' 10.32 18:18 29° 36.299' 92° 00.458' 26.73 19:21 29° 34.945' 92° 02.275' 2.64 19:28 29° 34.945' 92° 02.275' 2.65 20:20 29° 35.215' 92° 02.394' 4.66 20:31 29° 35.078' 92° 02.288' 27.87 21:01 29° 35.223' 92° 02.111' 4.2

153C. Li, E. Weeks / Journal of Marine Systems 75 (2009) 150–162

across the eddy feature through its center a few times for atotal of 1600 s, allowing us to reconstruct the eddy structure.During this survey, the ADCP was sampling at 2 Hz frequencyand 0.5 m vertical intervals from 1.12 m below the surfacedown to near the bottom (Table 1). The observations weremade during strong ebb tide and currents were going fromthe bay toward the ocean.

One month later, on Oct 6, 2007, a second survey wasconducted using the same A-Boat and a 26-ft catamaran. Thistime the A-Boat worked during the entire survey for 3 h and3 min (Table 1). It was however under a thunder stormcondition in the middle of the survey and the flow field wasstrongly affected by the passing storm with gusty north andnortheast winds. At near the end of the survey, half of the A-Boat was filled with seawater caused by the storm and roughseas. The flow field was much more chaotic and noisier. It wasalso during a strong ebb tide. However, no eddy was observedthis time. Apparently, the strong northeasterly and northerlywinds from the thunder storm caused a relatively uniformflow which might have destroyed the eddy (see below). ASeabird SBE 19plus Conductivity, Temperature, and Depthprofiler (CTD) was used to measure the vertical structures ofsalinity and density. Seven CTD casts were made during thefirst third of the time prior to the maximum wind of thethunder storm (Table 2). The second survey is discussed inthis paper as a comparison to help the understanding of theflow features and the mechanism of eddy formation.

4. Analysis

The ADCP transducers record the ensemble water depth atthe same rate as that of the velocity profiles with an accuracyof about 0.1–1% of the total depth. The depth data thusrecorded can be interpolated if the ship track forms anenclosed or semi-enclosed area. The interpolation is accom-plished by a “triangulation” of the data points and bi-linearinterpolations using a software package TECPLOT. Fig. 2 showsthe original ship tracks for both surveys and the bathymetryby combining all data points. The bathymetry shows that theSouthwest Pass has a deep channel oriented in the east-westdirection (marked A in Fig. 2) and northeast–southwestdirection (marked B in Fig. 2) with the channel depthchanging from 15 m in the east to 34 m in the west. A smallchannel (marked C in Fig. 2) coming from the north is shownto have a depth of greater than 10m in its center. The width ofthe main channel is about 500 m while the width of thenorthern channel is only about 100 m. The first surveyincluded a polygon followed by a more intense repeatedcoverage shown by the crossing lines concentrated mainly atwest side of the bend of the main channel where water

coming out of the north channel meet the water in the mainchannel. It is also a place of significant depth change. Thefocused sampling of the first survey on the quasi-steady eddywas at this place. The second survey, being mostly under athunder storm condition, had quite chaotic flows super-imposed on the ebb currents. In the following we mainlyfocus on the data analysis from the first survey and examinethe eddy structure, while using data from the second surveyas comparisons.

4.1. Flow structure of the eddy

Fig. 3 shows the observed flow vectors at 1.62 m below thesurface. It is drawn in local (x, y) Cartesian coordinates. Theorigin of the (x, y) coordinates is at 29.58540°N, 92.03646°W.The contours show the interpolated water depth measuredfrom the ADCP transducers. From this diagram, it is apparentthat there is an eddy on the northwest corner of the sur-vey area. The maximum magnitude of the velocity is close to1 m/s. The diameter of the eddy is about 300 m and it iscentered in the north of the main channel outside of thewestern shoal of the North Channel at a depth of about 20 m.The edge of the eddy however extends to less than 5 mwater.The velocity vectors at deeper waters are similar, showing thesame clockwise circulation. The cause of the eddy is probablythat the westward flowing ebbing current from the mainchannel and the southeastward flowing ebbing currentfrom the North Channel meet and converge at 3–4 o'clockposition of the eddy, thereby producing a negative vorticity.This vorticity is further strengthened by the facts that (1) thestrong ebb current in the main channel impinges ontothe shallower water southwest of the North Channel and (2)the western shoal of the North Channel tends to have lessebbing momentum because of its shallow depth (Li, 2001,2003) which allows the northward flowing current at thatlocation to form easily. In other words, the tidal currents ofthe North Channel itself has a lateral velocity shear thatproduces a negative vorticity, which adds more negativevorticity to the eddy.

Fig. 4 shows the observed flow vectors averaged over thewater column for the 2nd survey conducted on Oct 6. Thenoisy data is much smoothed after the vertical averaging.The contours again show the interpolated water depthmeasured from the ADCP transducers. The absence of theeddy observed earlier is probably due to the thunder stormcondition during the survey, despite the fact that the tidalphase was similar to that of the first survey of Sep 6 (Fig. 5).When the survey on Oct 6 started, a thunder storm wasdeveloped nearby and there was gusty north and northeast

Fig. 2. Ship tracks from two surveys conducted on Sep 6 and Oct 6 of 2007; bathymetry contours obtained from the ADCP transducers; and 4 stations of CTD casts(the triangles). The letters A, B, and C indicate the eastern part of the channel, i.e. the east–west orientedmain channel, thewestern part of themain channel, i.e. thenortheast–southwest oriented main channel, and the North Channel, respectively. The thick line is the Sep 6 track while the thin line is the Oct 6 track. Thenumbers near the triangles indicate the CTD casts as defined in Table 2.

154 C. Li, E. Weeks / Journal of Marine Systems 75 (2009) 150–162

winds. The strong winds must have contributed to thedestruction of the eddy, since the eddy observed on Sep 6was apparently caused by the interaction of the tidal currentsand bathymetry. The north and northeast winds from thethunder storm can generate a positive vorticity as the waterdepth at A is shallower than at B (Fig. 4) and because winddriven flow in shallow water often has a stronger flow in thedownwind direction than in deeper water or it may even havea reversed flow if the basin is closed (Fischer, 1976; Engelund,1986). In the present case, the basin is open to the ocean, theflow in the deeper water is smaller than that in the shallowwater (compare flows at A and B in Fig. 4). This makes apositive vorticity, which is not in favor of supporting theclockwise eddy with negative vorticity observed earlier.

4.2. Interpolated data: eddy, upwelling, and downwelling

To better visualize the spatial structure of the flow fieldand calculate the gradients of velocity and depth, theirregularly spaced raw data are interpolated onto evenlyspaced rectangular grids. Figs. 6 and 7 show such linearlyinterpolated velocity vectors from the Sep survey. They shownot only the eddy structure, but also the upwelling (red) anddownwelling (blue) zones, indicated by the arrows and lettersU and D, respectively. The velocity seems to be quite uniformalong the vertical down to 8 to 9 m below the surface. At thedepth of 10 m and beyond, the flow structure starts to deformas more points are below the bottom and the area of datashrinks (Fig. 7).

The magnitude of the vertical velocity can be as high as~0.3m/s (Table 3). Themain upwelling zones are located, nearthe center of the eddy, roughly centered at the coordinates(−40, 125), (0, 125), and (60, 10), which may vary in position

and strength, depending on the depth. There is a quitepersistent, wide, and curved zone of downwelling on the righthand side of each panel of Figs. 6 and 7. This zone is roughlyoriented in the northeast – southwest direction and isapparently a strong flow convergence zone.

Since the flow is quite consistent at different verticalpositions, we vertically average the velocity. The ADCP canprovide useful data within most of the water columnexcluding the top layer (0–1.12 m in this case) and the nearbottom (~10–15% of the water column) due to side-lobeeffect. The top and bottom layer velocities are obtained bylinear extrapolations. The depth-averaged flows are thencalculated by

u ¼ 1h

Z 0

−hu dz; v ¼ 1

h

Z 0

−hv dz;w ¼ 1

h

Z 0

−hwdz: ð1Þ

In the following discussion, we mainly discuss thederivatives of depth and velocity and associated quantities —

vorticity, horizontal convergence and divergence, and topo-graphic upwelling and downwelling.

4.3. Derived quantities

4.3.1. VorticityThe derivatives of depth and velocity can be used to

evaluate the depth gradients, vorticity, and topographicupwelling and downwelling. Here the “topographic upwellingand downwelling” are the vertical velocities following thebottom slope. Before these calculations, the data are firstsmoothed (Reinsch, 1967). The derivatives are then calculatedusing a spline function (Ralston and Wilf, 1967; Yang et al.,2005).

Fig. 3. Velocity vectors obtained from the ADCP at 1.62 m below the surface on Sep 6, 2007. The depth contours, as all contour plots in the following figures, areobtained by triangulation of the raw data and interpolation of thewater depth obtained from the ADCP transducers using TECPLOT (software package, http://www.tecplot.com/). The double arrow line shows the length scale of the eddy.

155C. Li, E. Weeks / Journal of Marine Systems 75 (2009) 150–162

To evaluate the strength of the circulation or rotation ofthe eddy, we calculate the vertical component of relativevorticity as defined by

n ¼ AvAx

−AuAy

: ð2Þ

The vorticity thus calculated within the eddy is shown inFig. 8a. Except on thewestern side, themajority of the eddy has

a negative vorticity which is expected for clockwise rotations.The maximum vorticty is at the center of the eddy with amagnitude of ~0.01. This is about 100 times larger than theplanetary vorticity caused by the earth rotation. This vorticityvalue is also about 10 times larger than that observed in anarrow tidal channel, Sand Shoal Inlet, VA, where tidal rangeexceeds 3 m, with the maximum tidal currents N2 m/s (Li,2002). This large vorticity also appears to be much bigger thanmany other published results (e.g. Klymak and Gregg, 2001;Edwards et al., 2004). This result indicates that the formation ofthe eddy observed here is not related to Coriolis force or earthrotation. The Coriolis force has a negligible effect on the rotation

of the eddy. In a numerical experiment by Eliassen et al. (2001)studying the circulation in Saltfjorden, Saltstraumen, andSkjerstadfjorden of Norway, where the world's most vigoroustidal currents and vortices exist, a similar conclusionwasmadeby changing the sign of the Coriolis force, which showed noeffect on the vortices formed by topography. The vortices inSaltstraumen can have currents of up to 10 m/s with 10 mdiameter, which would produce an order 1 s−1 vorticity.

4.3.2. Depth averaged vertical velocityThemaximum upwelling and downwelling velocity values

at different depths are shown in Table 3. The magnituderanges from 0.15 m/s to 0.30 m/s for upwelling and 0.16 to0.26 m/s for downwelling. The depth averaged verticalvelocity is shown in Fig. 8b. The magnitude of the depthaveraged vertical velocity is about 0.15 m/s with most of thearea having values smaller than 0.1 m/s except three zonesin which strong upwelling and downwelling are present(Fig. 8b). The main upwelling is centered at (−40,120) with anarea of about 30 m×50 m. The main downwelling zone has awidth of about 30–60 m and a length of about 180 m. The

Fig. 4. Velocity vectors obtained from the ADCP at 1.62 m below the surface on Oct 6, 2007. For clarity, only 1 vector is plotted every 5 consecutive points. The depthcontours are obtained by triangulation of the raw data and interpolation of thewater depth obtained from the ADCP transducers. Note that there is no eddy and theflow on the shallow shoals of the northwest corner is southward.

156 C. Li, E. Weeks / Journal of Marine Systems 75 (2009) 150–162

second largest downwelling zone is on the lower left handside at the edge of the eddy.

4.3.3. Topographic upwelling and downwellingThe vertical velocity at the bottom due to the bottom slope

is determined by a kinematic relation as the following

wjz¼−h ¼ dzdt j

z¼−h

¼ −ujz¼−hAhAx

−vjz¼−hAhAy

: ð3Þ

Since the velocity at the bottom measured by the ADCP isnot reliable due to sidelobe effect, and because the flow is

Fig. 5. Predicted tide at Vermillion Bay and observation periods for Sep 6 andOct 7, 2007, respectively, i.e. the solid (dashed) curve is the predicted tidalelevation for Sep 6 (Oct 6). The solid (dashed) vertical lines are the start andend time of the Sep 6 (Oct 6) survey.

unidirectional in the vertical water column, we use thevertically averaged horizontal velocity to replace that at thebottom and define the “topographic vertical velocity” as

wtop ¼ −uAhAx

−vAhAy

ð4Þ

which is shown in Fig. 8c. If the vertical velocity is purelycaused by the bottom slope and if there is no verticalvariation, the topographic vertical velocity must equal to the

Fig. 6. Velocity vectors of the eddy and contours of the vertical velocity at (a) 2.62 m, (b) 3.62 m, (c) 4.62 m, (d) 5.62 m, (e) 6.62 m, and (f) 7.62 m from the surface from data of Sep 6, 2007. The red (blue) areas indicated by theblack (red) arrows and the letter U (D) are where strong upwelling (downwelling) occurred. The unit of the vertical velocity is cm/s, with the color map shown on the right hand side the panels (c) and (f).

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Fig. 7. (same as above) Velocity vectors of the eddy and contours of the vertical velocity at (a) 8.12 m, (b) 10.12 m, (c) 14.12 m, and (d) 18.12 m from the surface fromdata of Sep 6, 2007. The unit of the vertical velocity is cm/s, with the color map shown on the right hand side the panels (c) and (f).

Table 3Maximum and minimum vertical velocity (positive upward) in differentlayers

Depth (m) Max w (m/s) Min w (m/s)

1.12 0.160 −0.1931.62 0.196 −0.1622.12 0.154 −0.1822.62 0.200 −0.1713.12 0.193 −0.1833.62 0.182 −0.1904.12 0.221 −0.1974.62 0.228 −0.2075.12 0.315 −0.2585.62 0.222 −0.2316.12 0.242 −0.2656.62 0.231 −0.262

158 C. Li, E. Weeks / Journal of Marine Systems 75 (2009) 150–162

depth averaged vertical velocity. Figs. 8b and c show that thedepth averaged vertical velocity from Eq. (1) and thetopographic vertical velocity defined by Eq. (4) have similarupwelling and downwelling zones. The downwelling zonefrom Eq. (4) however has a smaller area and a smallermagnitude. The difference of the two (Fig. 8b vs. c) indicatesthat the flow is not 100% caused by the bottom slope. The factthat Fig. 8b and c are consistent supports the idea thatthe main upwelling and downwelling in the eddy are a resultof uphill and downhill flows. As can be seen from thebathymetry gradient (Fig. 8d), indeed, the locations ofupwelling and downwelling coincide with significant bottomslopes. Combining with the flow field of the eddy, the uphilland downhill flows are obvious.

5. Discussion

5.1. Non-hydrostatic motion

The observations of the eddy reveal strong verticalvelocity which is apparently associated with the bottom

slope, as discussed in the previous section. The verticalvelocity may introduce a non-hydrostatic flow component. Asa first order estimate, here we examine the effect of the

Fig. 8.More derived quantities: (a) vertical component of the relative vorticity derived from the depth averaged flow (unit: 1/s); (b) depth averaged vertical velocity(unit: m/s); (c) “topographically induced vertical velocity” (unit: m/s) (see text for explanation); (d) depth gradient –∇h (a dimensionless vector).

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bottom slope on the vertical velocity induced non-hydrostaticflow. Since the focus is only on the uphill and downhill flowscaused by the depth variations, we only discuss the barotropicvertical momentum equation:

dwdt

¼ −1ρAp0

Azð5Þ

in which p' is the non-hydrostatic pressure componentcontributed by barotropic motion only. If we use U, W, L, H,δp', and T to denote the scales for horizontal velocity, verticalvelocity, horizontal length scale, vertical scale, pressure varia-tions, and time scale, respectively, we can non-dimensionalizeEq. (5) as the following:

WTd~w

d~t¼ −

δp0

ρHA~p0

A~z

ð6Þ

in which the tildes indicate non-dimensional variables definedby the ratios of the original variables and their correspondingscales. From the horizontal momentum balance, it is easy to

show that the pressure change is related to the horizontalvelocity scale by the following relationship:

δp0 ¼ ρU2: ð7Þ

If we further define the aspect ratio to be:

e ¼ H=L: ð8Þ

The continuity equation

AuAx

þ AwAz

¼ 0 ð9Þ

gives the following aspect ratio relation

WU

¼ HL¼ e ð10Þ

From Eqs. (7)–(10), Eq. (6) is reduced to:

e2d~w

d~t¼ −

d~p0

d~z: ð11Þ

Fig. 11. Vertical profiles of salinity from CTD casts. The numbers indicate thestations as defined in Table 2.

Fig. 9. Schematic drawing showing the generation of the eddy under ebbtidal currents.

160 C. Li, E. Weeks / Journal of Marine Systems 75 (2009) 150–162

This result demonstrates that the barotropic non-hydrostaticacceleration is proportional to the square of the aspect ratio.Here the aspect ratio is also the slope of the bottom if we take Has the change of depth over a horizontal distance of L. As shownin Fig. 8d, the slope of the bottom is mostly between 0.2 and 0.3in the area of the eddy (look at the scale of the vectors, or that forthe depth gradient ▽h). This means that the non-hydrostaticflows caused by the uphill and downhill flows can affect thevertical momentum balance by 0.04 to 0.09. As an example, in anumericalmodeling exercise, to capture the verticalmomentumbalance within an error of, e.g. 5%, a non-hydrostatic model hasto be used in this study area. But on the other hand, if a 10% erroris tolerable, a hydrostatic model is still marginally acceptable.

5.2. Stratification of water column

Although the above discussion is only for barotropic flows,the water column was stratified in the deep water during theOct survey, while the Sep survey did notmeasure the profiles ofsalinity and temperature. The discussion of the vertical profiles

Fig. 10. Schematic drawing showing how strong wind would not be in favorof the generation of the eddy.

of salinity and density is included in Appendix A. Assuming thatduring the Sep survey when the eddy was discovered, thestratification was similar, the vertical velocity may be affectedby the density profiles to some extent. This may be one of thereasons for the discrepancy between Fig. 8b and c. The overallpatternof Fig. 8b and c arehoweververy similar,which suggeststhat the motion might be predominantly barotropic.

6. Conclusions

6.1. Summary:Why there was an eddy on Sept 6 but not on Oct 6?

As discussed in Section 4.1 and suggested by the analysis,the most plausible mechanism that causes the eddy can beexplained with the help of Fig. 9. The strong ebb tidal current(C1) in the main channel at A (Fig. 9) is from the east to west.This current (C1) is running toward the shallow bank at nearE, producing a tendency of uphill and divergent flow (C5 andC6) at E due to inertia, resulting in a upwelling. The NorthChannel also has a strong ebb current (C3), which convergeswith the main current (C1) at D, producing a downwelling.Since tidal current is usually larger in the channel thanover the shoals across the same lateral transect (e.g. Li andValle-Levinson, 1999; Li, 2001, 2003), the current through theNorth Channel (C3) at C should be larger than that over theshoal at F (C4), if wind effect is negligible. The current C3 andC4 converge with C1 and merge into the main stream. Theuphill current over the shallow water at E from the maincurrent and the North Channel ebbing current combine toproduce a strong negative vorticity, thereby producing theeddy. On the other hand, as shown in Fig. 10, during a strongnortherly and northeasterly wind conditions (such as thatduring the Oct 6, 2007 thunder storm), although tidal currentthrough the main channel is not significantly affected, theflows through the North Channel and adjacent shallowerbanks are affected. As previous studies have shown, windtends to produce a downwind flow in shallow waters andsometimes even cause an upwind current in deep water(Fischer, 1976; Engelund, 1986; Li et al., 2008). Therefore,currents over the shallow banks of the North Channel (C6 and

161C. Li, E. Weeks / Journal of Marine Systems 75 (2009) 150–162

C4) are larger than the current (C3) over the North Channel.The relatively strong current C6 has two effects: (1) it resiststhemain stream (C1) from the channel to run over the bank atE; and (2) it produces a positive vorticity at E to prevent aclockwise eddy to form at that location where the clockwiseeddy formed on Sep 6, 2007.

6.2. Concluding remarks

In short, this study presents some new results. First of all, asmall eddy (diameter ~300 m) in a tidal channel has beenmeasured and analyzed in 3-D in detail. The strong upwellingand downwelling of up to 0.3 m/s highlights the secondimportant observation in a tidal constriction. Large verticalvelocity is not commonly reported in a tidal channel. Thethird finding of this work is that the eddy has a vorticity of oneorder of magnitude higher than the maximum vorticity of atypical tidal inlet with strong currents and strong velocityshears. Coriolis force is negligible in this case: the planetaryvorticity is two orders of magnitude smaller than theobserved vorticity. Fourth, we have found that the verticalmotion is caused by the bottom slope. Large bottom slopeexists in many tidal channels and the strong vorticity andvertical motion must have a significant implication to themixing, dispersion, and biological community. Fifth, themeasurements of the flow structure under a thunder stormcondition provide some insight to the existence and disrup-tion of the eddy that has been reported by local fishermen foryears: when wind is strong, the eddy tends to be destroyedbecause the downwind flow in shallow water will decreasethe tidal shear across different water depth. With theseresults from the observations and analysis, we anticipate thatmore studies on small eddies and their impact on biologicalactivities in coastal and estuarine environment will follow.

Acknowledgement

We thank the captain Mr. Floyd DeMers for assisting in thefirst survey. We also thank the Weeks family for providinglodging, food, and dock facilities for the surveys at their vacationhouse. We thank Dr. Masamichi Inoue for his continuedenthusiastic support of the development of the automatedboat.Wewould like to thank the two anonymous reviewerswhoprovided useful suggestions which helped the improvement ofthemanuscript. This project has been supported under an awardNA06OAR4320264-06111039 to the Northern Gulf Institute byNOAA's Office of Ocean and Atmospheric Research, U.S. Depart-ment of Commerce and Shell (http://www.ngi.lsu.edu/), throughContract NNS05AA95C by Louisiana Board of Regents, andthrough Grant# OCE-0554674 by National Science Foundation.

Appendix A. Stratification

During the first survey, there was no observation ofhydrography or vertical structure of water temperature,salinity, and density. During the second survey, which hadsimilar tidal phase as the first survey (ebbing tide with waterflowing out of the bay), there were a total of seven casts usinga conductivity, temperature, and depth (CTD) sensor (theSeabird SBE 19 plus, which has a sampling frequency of 4 Hz,Fig. 11). The locations of the CTD casts are shown in Fig. 1

(casts 1 and 2) and Fig. 2 (casts 3 to 7) or Table 2. Casts 1 and 2were made in the deep channel southwest of the SouthwestPoint (Fig. 1) with depths of 10.3 and 26.7 m, respectively.Casts 3 and 4 were from the same location where water was2.6 m. Casts 5 and 7 were made in shallow water near theedge of the survey area. Cast 6 was made in the center of thechannel at 27.8 m of the study area.

The CTD data showed that water density was mainlydetermined by salinity and the effect of temperature wasnegligible. Therefore, we only focus on the discussion ofsalinity. The surface salinity was between 8.5 and 11 PSU,while the bottom salinity in the deep water was 14–15.5 PSU(Fig. 11). More specifically, the first two casts north of theADCP survey area showed signs of stratification.

Casts 1 and 2 showed relatively large gradients of salinitybetween 11.5 and 13.5 m with a difference of 2 PSU. Casts 3and 4, which were made at the same location, had a gradientof salinity almost comparable to the maximum gradient ofcast 2. This is probably a result of strong tidal straining (e.g.Simpson et al., 1990; Rippeth et al., 2001; Simpson et al.,2005) during ebb. In contrast, cast 5 showed almost perfectvertical uniform condition. Cast 6, which was made in thecenter of the channel also showed a significant stratificationstronger than that of cast 2. The sharpest gradient is between13 and 15 m with 4 PSU salinity change. This is twice of themaximum gradient shown by cast 2 (Fig. 3). Cast 7 showedsmall vertical change of salinity.

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