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Estuarine, Coastal and Shelf Science 85 (2009) 651–660

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Estuarine, Coastal and Shelf Science

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Asymmetric tidal straining across an inlet: Lateral inversion andvariability over a tidal cycle

Chunyan Li a,c,*, Erick Swenson b, Eddie Weeks a, John R. White b

a Coastal Studies Institute, Department of Oceanography and Coastal Sciences, School of the coast and Environment, Louisiana State University, Baton Rouge, LA 70803, United Statesb Department of Oceanography and Coastal Sciences, School of the coast and Environment, Louisiana State University, Baton Rouge, LA 70803, United Statesc College of Marine Sciences, Shanghai Ocean University, 334 Jungong Road, Shanghai 200090, China

a r t i c l e i n f o

Article history:Received 19 December 2008Accepted 11 September 2009Available online 6 October 2009

Keywords:tidesestuariesestuarine dynamicsin situ measurementstidal strainingtidal pass

* Corresponding author at: Coastal Studies Institute,and Coastal Sciences, Louisiana State University, Baton R

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

0272-7714/$ – see front matter � 2009 Elsevier Ltd.doi:10.1016/j.ecss.2009.09.015

a b s t r a c t

Tidal straining is a phenomenon of temporal variations in stratification and mixing resulting from theinteraction of a longitudinal salinity gradient with the vertical shear of the horizontal tidal velocity. Asa result, the theory predicts stronger and weaker stratification during ebb/low tide and flood/high tide,respectively. In contrast to this well-known temporal asymmetry, in this study, we document in situmeasurements demonstrating a lateral asymmetry and lateral inversion of tidal straining at BaratariaPass, a narrow (w600 m wide) tidal inlet of Barataria Bay in southeastern Louisiana. During flood, theeastern side of the channel had strong stratification of 4 PSU salinity change over a 1.5 m thin layer whilethe western side had a 2 PSU change over a 12 m water column. This strong lateral difference decreasedas flood continued until near the end of the flood when it reached vertically well-mixed condition acrossthe channel. During ebb it was just the opposite such that the western side became stratified while theeastern end was well-mixed. This resulted to a small correlation coefficient of �0.05 for stratificationbetween the west and east sides, although the central channel and east side have a high correlationcoefficient of 0.88. The tidally averaged salinity was higher on the western end than the eastern endexcept in a narrow boundary layer close to the eastern shore. This is an apparent contradiction to whatthe Coriolis effect would produce in classical estuarine dynamics. Our hypothesis for the observeddifference arises from the influence of the river water coming out of the Mississippi River through theSouthwest Pass of the Birdfoot Delta. This water mass may have played a role in the observed,complicated lateral inversion of the tidal straining. This study underlines the complexity of estuarinedynamics proximal to large deltaic systems and we anticipate that these results will underscore the needfor a modeling study to further investigate this dynamic process.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

A classical estuary is a semi-enclosed body of water in whichsaltwater from the open ocean and freshwater from the land drainagemix with each other under tidal and wind forcing, producingmeasurable salinity gradient either in the horizontal or both in thehorizontal and vertical (Prichard, 1952; Cameron and Prichard, 1963;Hansen and Rattray, 1965; Dyer, 1997). The density distribution inmost estuaries is determined mainly by the salinity distribution andat the first order approximation, the density and salinity havea simple linear relationship r z r0(1þ 0.82s/1000), in which r0 is thefreshwater density and s is the salinity in practical salinity unit (PSU).

Department of Oceanographyouge, LA 70803, United States.

All rights reserved.

Because of bottom friction, tidal currents in the horizontal oftenhave a vertical shear such that the speed at the surface is faster thanthat near the bottom. This vertical shear and horizontal salinity(density) gradient work together to produce an asymmetricphenomenon called ‘‘tidal straining’’ (Simpson et al., 1990, 2005;Rippeth et al., 2001). Ideally, tidal straining refers to two differentsituations during different tidal phases. The first is that during theflood tide when the more saline ocean water is coming into theestuary with a faster advancement at the surface, the water columnwithin the estuary tends to become vertically well-mixed as theheavier saltwater on the surface promotes vertical mixing to reacha more stable state. The second is that during the ebb tide when thefresher estuarine water is going out of the estuary with a fasteradvancement at the surface, the water within the estuary tends tobecome vertically stratified as the lighter fresher water on thesurface and heavier and more saline water at the bottom forma more stable water column, thereby suppressing vertical mixing.

C. Li et al. / Estuarine, Coastal and Shelf Science 85 (2009) 651–660652

This classical tidal straining problem is a temporal asymmetricphenomenon such that flood and ebb experience different condi-tions. Tidal straining has been a subject of studies since early 1990sfor problems in estuaries and coastal oceans in relatively simplesetups – narrow channels, or simple broad shelf (Simpson et al.,1990, 2005; Geyer et al., 2000; Rippeth et al., 2001; Chant andStoner, 2001; Stacey and Ralston, 2005). Many estuaries howevercan have additional factors that will make the problem much morecomplicated. For example, an estuary may not be elongated andthere may be multiple freshwater sources. In the case of Louisianacoast, the broad and shallow bays are irregular in shape with manyislands and shoals inside and multiple inlets formed betweenbarrier islands, typical of a deteriorating delta area.

The original objective of this study was to quantify the tidalflushing process and tide-induced transport of water, salt, andnutrients through in situ measurements and laboratory analysis ofwater samples collected in a complete tidal cycle at a major tidalinlet connecting the Barataria Bay and the Louisiana continentalshelf. To this end, a multi-disciplinary team was assembled forvarious components of the observations. A 26-ft catamaran wasused for repeated occupations of a 530 m cross channel transect atthe mouth of the Barataria Pass in a complete diurnal tidal cycle (w24 hours). A second boat was also used during the day (but not atnight) for additional flow velocity and bathymetry measurements.The data reveal an interesting phenomenon of lateral variation andeven inversion of stratification related to tidal straining, duringa tidal cycle. Therefore, in this paper, we focus on the descriptionand analysis of the new findings relating to tidal straining.

2. Study site and relevant studies

Barataria Bay is located in the southeastern Louisiana (Fig. 1). Ithas several tidal inlets connecting with the coastal ocean. BaratariaPass is between two barrier islands, the Grand Isle and Grand Terre

Fig. 1. Study area. (a) Southeast Louisiana and Mississippi–Alabama coast; (b) Barataria Passam Aug 1, 2008.

Island. It is a narrow constriction of only about 600 m in width. Thisis one of the main outlets of freshwater from the Barataria Basin.The Barataria Bay has a large variability in salinity from season toseason. For example, on April 8 of 2008, a hydrographic surveydone by the authors found that the salinity was 7–9 PSU, whileduring the July 31–Aug 1 survey discussed in this paper, themaximum surface salinity reached w 27 PSU and the bottomsalinity was close to 29 PSU. The low salinity in April was mainlydue to a strong spring flood in the Mississippi River. In fact, theBonnet Carre Spillway of the Mississippi River was opened forabout a month between April 11 and May 8, 2008, with an averageof 3200 m3/s after 11 years of the last freshwater diversion into theLake Pontchartrain to relieve the pressure of the downstream cityof New Orleans from possible flood (White et al., 2009).

Marmer (1948) measured tidal currents in the passes of theBarataria system over a 24 day period in 1947. Barataria Pass, QuatreBayou Pass and Pass Abel had similar current speeds of w0.60 ms�1,with Caminada Pass having higher current speeds of w0.80 ms�1.He concluded that of the total exchange 66% went through Bar-ataria Pass, 18% through Quatre Bayou Pass, 13% through CaminadaPass and 3% through Pass Abel. He also noted an excess of280 m3s�1 of ebb flux over flood flux which he attributed to thefreshwater inflow to the system. Swenson and Swarzenski (1995)estimated the average freshwater input to the Barataria system tobe about 200 m3s�1.

Snedden (2006) analyzed a 101 day record (December 20, 2002through April 3, 2003) from an upward looking ADCP deployed inBarataria Pass for the Louisiana Department of Natural Resources(Moffatt and Nichol, 2005). He concluded that 85% of the flowvariability in the pass was tidally induced with equal contributionsof the O1 and K1 constituents. An EOF analysis identified twomodes: (1) a barotropic mode which explained w90% of the totalvariance and (2) a vertically sheared flow (outflows at surfaceopposed by inflows at the bottom) which explained w8% of the

, ship track and intensive survey transect from a vessel-based study on 6 am July 31–6

C. Li et al. / Estuarine, Coastal and Shelf Science 85 (2009) 651–660 653

total variance. Mode 2 exhibited a strong coupling with diurnaltidal current amplitudes at the fortnightly timescales, with thegreatest velocity shear occurring during neap tides when the tidalcurrent amplitude is at its minimum.

3. Observations

The observations were conducted at the Baratraia Pass between6:30 AM July 31 and 6:10 AM, August 1, 2008, Central DaylightTime. Two small boats were used in the study. The first boat was26-ft long, equipped with a Teledyne RD Instruments 600 kHzacoustic Doppler current profiler (ADCP), a Seabird Electronicsthermosalinograph (SBE-45), and a differential GPS. A SeabirdElectronics Conductivity, Temperature, and Depth sensor (CTD, SBE19plus) integrated with a dissolved oxygen (DO) sensor (SBE 43),was also used for vertical profiles of water temperature, salinity,and DO. The measurements of vertical profiles of the threedimensional velocity components (u, v, w) were conducted almostcontinuously during the entire w 24 h period on the first boat. Thesecond boat was 22-ft long equipped with a Teledyne RD Instru-ments 1200 kHz ADCP. This second boat only covered the inside ofthe inlet for bathymetry and additional current velocity profilesduring the day. The ADCPs were sampling at 2 Hz frequency with0.5 m vertical bins. The focus was the 600 m wide tidal pass. Theboat was running along a 530 m long transect across the passrepeatedly several times during which three CTD casts were madeat each of the three CTD stations with their locations to be at(�89.9475�W, 29.2723�N), (�89.9484�W, 29.2712�N), and(�89.9495�W, 29.27 �N), respectively (Fig. 1). The boat would thengo to inside of the inlet, mapping the flow profiles, bathymetry, andsurface salinity and temperature continuously. It would then comeback to the transect within two hours to repeat the measurementsalong the line. This process was repeated continuously for 24 h. Theidea was to ‘‘weave’’ through the area with enough lines coveringthe area for the bathymetry and flow structures. As a result, theentire survey produced a track with repeated occupations along thecross-inlet transect plus the ‘‘spaghetti like’’ boat tracks (Fig. 1).A total of 10 CTD casts were made at stations 1, and 9 casts each atthe other two stations; thus 28 CTD casts in total.

Wind data from a weather station at the U.S. Coast Guardbuilding (29.267�N 89.957�W) at Grand Isle, Louisiana, owned andmaintained by the National Data Buoy Center are examined. Beforethe vessel-based observations the wind was relatively weak, alter-nating between southwest and northeast with an average magni-tude of less than 3 m/s. During the vessel-based survey, it switchedto south wind but with a small magnitude (<3 m/s) as well.

Daily total precipitation from the New Orleans InternationalAirport was obtained from the National Climatic Data Center anddaily 8 am Mississippi River discharge for Tarbert Landing (w15 kmsouth of the river control structure) was obtained from the U. S.Army Corps of Engineers. A small fraction of the Mississippi Riverwater is diverted through the Davis Pond freshwater diversionstructure into the northern portion of the Barataria Bay System nearNew Orleans. This structure, which has a design capacity of up to300 m3s�1, started operating in July, 2002. Value for the dailyaverage discharge (obtained from the U. S. Geologic Survey), in Julywas less than 150 m3/s. The precipitation in July was small while theMississippi River discharge was decreasing constantly in the 30 daysbefore the survey. As summarized in Inoue et al. (2008), the fresh-water input into the Barataria Bay system includes rainfall (minusprecipitation), runoff of rainfall over the surrounding drainagebasin, Mississippi River water diverted through man-made struc-tures, including those from the Naomi, West Pointe a la Hache, andDavis Pond Freshwater Diversions, and the Gulf IntracoastalWaterway connecting the Atchafalaya River. The discharge from the

Davis Pond was mostly below 200 m3/s in the month with an almoststeady increase in the last 10 days prior to the survey up to 220 m3/s.

3.1. ADCP data analysis and results

In order to obtain the tidal and mean velocity structures alongthe cross channel transect, we first limit the data to be withina 90 m band covering the 530 m transect – only those data pointswithin this band are selected for the analysis of the cross channelstructures. There are about 23% of data points concentrated in thisband, which is less than 5% of the total area of coverage (Fig. 1). Thevelocity magnitude for each component is w 1 m/s, with the eastcomponent slightly larger than the north component.

3.1.1. Coordinate transformThe transect has a 52.7 degree tilt from the east-west direction.

For convenience, we rotate the coordinate system so that the alongchannel and cross channel velocity components are along the new xand y axis. After rotating the coordinate system by 52.7 degreecounterclockwise, we transform the latitude and longitude of eachdata points to a local Cartesian coordinate with the origin defined tobe at near the western end of the transect at 29.269� N and�89.95�

W. The 90 m wide band is now shown in Fig. 2a. We then divide the530 m transect into 29 segments and group the data from eachsegment. Each segment has a length of about 18.3 m in the alongtransect direction. The depth distribution as a function of the alongchannel distance (x) is now shown in Fig. 2b. The elongatedsegments (18.3 m� 90 m) are used because the most variability isacross the channel, not along the channel, over the same lengthscale. The scattered points and solid line in Fig. 2b are the measuredand averaged depth, respectively, along the transect within the 90-m band. Fig. 2c,d show the along channel and cross channel velocitycomponents, respectively. The along channel velocity componenthas a strong and clear tidal signal, with a maximum magnitude ofabout 1.5 m/s; while the cross channel velocity component is muchsmaller, noisier, and with no clear tidal signal.

3.1.2. Harmonic analysisWe then apply the harmonic analysis (Li et al., 2000; Li, 2002) to

the along channel velocity component within each segment at eachdepth from the measurements. Since tide in this area is mainlydiurnal, and our survey only covers 24 h, we use only one tidalfrequency corresponding to a 24 h period in the harmonic analysis.Fig. 3a shows an example of the near surface and near bottom alongchannel velocity as functions of time within the 11th segment ofFig. 2a, and the fit from the harmonic analysis. The near surfacevelocity is larger than the near bottom velocity and lags the nearbottom flow by about one hour. This time lag is because of bottomfriction (e.g. Li, 2001, 2003).

3.1.3. Mean flowThe mean velocity is almost all negative with stronger magni-

tude on both ends of the transect (Fig. 3b). The mean flow is on theorder of 0–0.4 m/s. The smallest mean flow is in the center of thechannel. The negative net flow is an expected result as this shouldbe equal to the river discharge including that from the Davis PondDiversion unless a strong wind forcing modifies it. During the dayof the observations, the wind was weak throughout the 24 h period.

3.1.4. Velocity amplitudeThe diurnal tidal velocity amplitude (Fig. 3c) is mostly between

0.7 and 1.2 m/s with the minimum on both ends of the channel andmaximum in the center of the channel. The width of the maximumflow in the center channel is about 300 m, while within about100 m of the edges of the channel the velocity amplitude decreases

Fig. 2. (a) Sampling points within the 90 m wide band along the intensive sampling transect after rotation of the transect band and a coordinate transform changing latitude andlongitude to local Cartesian x–y coordinate; (b) depth distribution along transect within the band shown in (a) as a function of the rotated x coordinate along the transect; (c) alongchannel velocity at 1.32 m below the surface – the velocity component perpendicular to the transect; (d) cross channel velocity at 1.32 m – the velocity component parallel to thetransect.

C. Li et al. / Estuarine, Coastal and Shelf Science 85 (2009) 651–660654

toward the edges. Again, this is consistent with frictional tidalcurrents across a tidal channel (Li, 2001).

3.1.5. Standard errorThe RMS error of the harmonic fit to the data is between 0.13 and

0.30 m/s (Fig. 3d). It should be noted that in the center of the channelwithin a width of about 300 m where tidal amplitude is the largest,the RMS error is the least. On the edges of the channel, on the otherhand, the RMS error is much bigger. This bigger RMS error near theedges of the channel is apparently caused by the higher nonlinearflows there, especially transient eddies. The eddies around the barrierislands in the Louisiana coast have been both observed (Li and Weeks,2009) and simulated by a numerical model (FVCOM, Chen et al.,2003) as an ongoing study. During the survey, we also observed andmeasured a few such eddies at the edges of the channel around thebarrier island, where the standard deviation of the flow is large.

In short, the observations have indicated that the flow throughthe tidal pass is dominated by a frictional diurnal tide, with a sub-tidal net flow field consistent with the conventional estuary withfreshwater discharge and lateral depth variations (Wong, 1994).

3.2. Asymmetric tidal straining: Lateral inversion and variabilityover a tidal cycle

Throughout the 24 h observational period of continuous ADCPsurvey, we made 9–10 sets of CTD casts at the 3 stations (Fig. 1) with

each set of casts covering all the 3 stations once within 8–40 min,except the first set which covered station 1 twice (casts 2 and 3)within 14 min. Because casts 2 and 3 gave similar vertical profiles,we did not include cast 3 in Fig. 4a for clarity. Most of the casts areordered in time to cover stations 1, 2, and 3, in that order. The rest ofthe casts are ordered as stations 1, 3, and 2. This is because station 2is in the center of the channel and at times there was a need toavoid boat traffic which disrupted the order of the CTD casts.Fig. 4a,b,c show all the vertical profiles of salinity at stations 1, 2,and 3, respectively. The first set of casts at stations 1, 2, and 3 shownin Fig. 4 includes casts 2 (Fig. 4a), 4 (Fig. 4b), and 5 (Fig. 4c).

The vertical profiles at stations 1 and 2 for the first set of CTDcasts showed stratifications with a vertical salinity difference ofabout 4 PSU. Cast 2 at station 1 appeared to have a sharpest verticalgradient of salinity, particularly between 2 and 3.5 m within a thinlayer of less than 2 m. Cast 4 at station 2 had a strong verticalgradient above 3 m and a secondary maximum gradient between 8and 10 m.

The variations of some of the profiles at the mid-depth werecaused by water sampling procedures which required that the CTDbe stopped at a given depth for a few minutes during which the CTDmight move slightly up and down due to surface waves and boatmotion and the boat drift with the mostly swift current.

Cast 5 at station 3, on the other hand, showed a much smallervertical gradient of about 2 PSU salinity change within the entirewater column of 12 m. Tide was flowing into the channel at the

Fig. 3. (1) Example velocity time series and harmonic analysis fit from the 12th segment at 1.32 m (the ‘‘þ’’) and 16.32 m (the ‘‘*’’) below the surface; (b) mean along channelvelocity at 1.32, 6.32, and 11.32 m depths below the surface as functions of the cross channel position; (c) diurnal tidal velocity amplitudes; (d) standard (or RMS) error of the diurnaltidal velocity. The plus, star, and triangles are for 1.32, 6.32, and 11.32 m, respectively.

C. Li et al. / Estuarine, Coastal and Shelf Science 85 (2009) 651–660 655

time of these 3 CTD casts. We therefore have a strong stratificationon the eastern end of the transect, a weaker stratification in thecentral channel, and a much weaker and linear salinity variation atthe western end of the transect. Since Barataria Bay receivesfreshwater discharge from Davis Pond Diversion of the MississippiRiver water, it is an estuarine system that has a net output offreshwater as verified by our current velocity measurements dis-cussed earlier (Fig. 3b). Thus during the flood tide, the tidalstraining (Simpson et al., 1990) in this estuarine system shouldmake the water column tend to be vertically well-mixed. Thisshould be similar across the 600 m narrow channel. If the mainsalinity gradient is in the along channel direction as in most estu-aries, Coriolis force would make the constant density contour ina cross-section to be elevated on the eastern end during both floodand ebb phases of the tide (e.g. Prichard, 1952).

What we have observed here, however, is that during the firstset of CTD casts, the western side of the channel was relatively well-mixed and the eastern side of the channel was stratified. The nextset of CTD casts are casts 6, 7, and 8 at stations 1, 2, and 3,respectively, made about 2.5 h later. The salinity profiles for thesecasts are similar to that of the first set, with a decrease of stratifi-cation at station 1 and an increase of salinity values on surface layerat stations 1 and 2 and a salinity increase at station 3 throughoutthe water column. The obvious decrease of salinity in the lowerlayer (below 4 m) at station 1 (comparing casts 6 and 2 in Fig. 4a)indicates a vertical mixing occurred, a result consistent with tidalstraining during flood tide.

The third set of CTD casts: casts 9, 10, and 11 about 2 h latershow that station 1 was now almost vertically well-mixed, whilestation 2 had a further increase of surface salinity and decrease ofstratification to a lesser extent, and station 3 remained virtuallyunchanged. It should be noted that the third set of CTD casts wereconducted at around the slack water tide at the end of the flood(Fig. 4a at Hour 6 and Fig. 5a for the third set of casts at Hour 6).Immediately after the slack water and maximum surface salinity,there was appeared to be a short-term event, shown by a rapid dropin surface salinity (Fig. 5, between the third and fourth sets of CTDcasts), indicating fresher water from inside of the bay, which,however, didn’t last long and didn’t fall onto the overall sinusoidalcurve of the tidal variation of the time series (Fig. 5).

The next set of casts: 12, 13, and 14 at stations 1, 3, and 2, in thatorder, demonstrate almost vertically well-mixed conditions at allstations (Fig. 4a,b,c). Apparently, when the measurements started,the stratification was very different from the west to the east end ofthe channel. The tidal straining gradually increased the surfacesalinity at the east end but did not bring the water column toa complete well-mixed condition at the end of the flood (close tothe times of the 3rd set of CTD casts, 9, 10, 11). The water columnhowever reached a vertically well-mixed condition a few hoursafter the end of ebb (the 4th sect of CTD casts, 12, 13, 14). Note thatthe first few hours of ebb current caused the eastern end to becomefresher much faster than the middle and western end of thechannel (compare Casts 12 with 13 and 14, station 1 was 2 PSUfresher than the other two stations). This is contrary to

Fig. 4. Vertical profiles of salinity measured from Station 1 (a), 2 (b), and 3 (c).

Fig. 5. Color-coded plot of surface salinity time series (a) at all locations and (b) alongthe 90 m wide and 530 m long transect. The colors of (a) indicate the positions alongthe transect: red is at the east end and blue is at the west end (the color bar shows thedistance from the west end in meters). In (b) only black dots and red crosses are usedto indicate the time series from the west and east, respectively.

C. Li et al. / Estuarine, Coastal and Shelf Science 85 (2009) 651–660656

a conventional estuary that would tend to make the western (noteastern) side to be fresher during both flood and ebb (e.g. Prichard,1952), as a result of Coriolis force.

Casts 15, 16, and 18 (Fig. 4) form the 5th set of CTD casts atstations 1, 3, and 2, respectively. These casts were made rightbefore the maximum ebb currents (Fig. 3a). Now station 1 hadbecome significantly saltier than the other two stations:compared to the previous cast at station 1 (cast 12), cast 15showed significantly higher salinity after a few hours of ebbcurrent. The next set of CTD casts 19, 20, and 21, at stations 1, 3,and 2, respectively (Fig. 4), right after the maximum ebb currents(Fig. 3a), showed a decrease of salinity by 3.5–6 PSU, reaching analmost laterally uniform condition in salinity distribution (Fig. 4).In addition, in the middle channel and on the western end, thereappeared to be some stratification started to form creatinga relatively fresher layer above 4–6 m on the surface (casts 20 and21, Fig. 4). The 7th set of CTD casts (22, 23, and 24) showed furtherdecrease of salinity across the channel and a further developmentof stratification especially at station 3. While the 8th set of CTDcasts (25, 26, and 27) during slack tide or weak flood showedsimilar surface salinity, which was 1.5 PSU higher than the 7th set,the stratification further developed at all stations with themaximum change occurred at stations 3 which had a 5 PSUsalinity increase between 4 and 12 m below the surface, indicating

a bottom saltwater intrusion. This is apparently due to the bottomfrictional effect so that tidal current leads the phase at bottom andturns earlier at bottom than the surface (Li and Valle-Levinson,1999; Li, 2001, 2003; Li et al., 2004) as verified by the ADCP data(Fig. 3a). These findings are essentially consistent with theconventional tidal straining, except that here a lateral variation isfound such that the eastern side has less stratification than thewestern side. The last set of CTD casts, 28, 29, and 30 at stations 1,2, and 3, respectively, showed a decrease of stratification at allstations, consistent with the conventional tidal straining theoryduring flood tide.

Fig. 5a is a color-coded plot of in situ surface salinity time seriesmeasured from the SBE-45 thermosalinograph. The colors indicatethe rotated x coordinate (along transect distance in meters fromthe west end of the transect). Fig. 5b shows the time series ofsurface salinity from the west 1/3 (black dot) and east 1/3 (redcross) of the transect. From both figures, we can see that the surfacesalinity during the period of measurements had a clear sinusoidaltidal variation to the first order of approximation, such that duringflood (Fig. 3a, 0–5 h) the surface salinity was increasing until theend of the flood and then dropped with ebb currents until the endof the ebb (w5–17 h). The surface salinity ranged between 18.5 and27.5 PSU during this time period. This first order temporal variation

C. Li et al. / Estuarine, Coastal and Shelf Science 85 (2009) 651–660 657

in salinity is consistent with the system being estuarine such thatinside the bay it is fresher than outside. Beyond this first ordervariation, however, is the complexity that cannot be explainedeasily by a classical estuarine theory. It is apparent that the westside of the channel was having higher surface salinity, with someexceptions (Fig. 6), than most of the east side during most of thetime period for the first 17 h (Fig. 5). The east–west salinitydifference can be as high as 2 PSU at any instance. This trendreversed however right after the minimum salinity (Fig. 5b). Itreversed back again briefly before it changed back once more afterthe 20th h for a couple of hours. It then reversed yet again to havehigher salinity at the west end near the end of the survey duringstrong flood, similar to the beginning of the survey (Fig. 5b). Inaddition, a couple of episodes of significant salinity drops are seenafter the end of the flood (after the 5th h) with a maximummagnitude of about 5–6 PSU.

Fig. 6 gives some examples of the surface salinity along the shiptracks at the first, second, seventeenth, and eighteenth hours,respectively. During the first two hours (during flood) of the surveythe southwest side of the survey area (or left hand side of thechannel if one faces toward the interior of the bay) was much saltierthan the northeast or right hand side. The boundaries between thesaltier and fresher waters are quite clear in Fig. 6a,b, implyinga sharp gradient and distinct separation of different watermasseswith different salinities. Note also the small scale variations indi-cating the non-uniform distribution and the entrainment offreshwater into saltier water and vice versa. The last two panels

Fig. 6. Surface salinity distribution from the surface flow through system during hours (a) 1,

(Fig. 6c,d) show the opposite situation when the northeast (righthand side facing upstream) had higher salinity, at hours 17 and 18,respectively. This situation was shorter in duration and thus theoverall mean is such that the salinity on the left hand side of thechannel is higher than that on the right hand side facing the interiorof the bay. Our calculations showed that the cross channel distri-bution of the temporal mean of the surface salinity is greater than24.3 PSU and decrease almost linearly to below 22 PSU with 450 m,and then sharply increase back to above 24 PSU within the last80 m on the eastern side.

4. Discussion

The average potential energy demand (APED) in the verticalwater layer of unit horizontal area for a complete vertical mixing isdetermined by (Simpson et al., 1990)

f ¼ 1h

Z z

�hðr� rÞgz dz (1)

in which h, z, r, r, g, and z are the static water depth, surfaceelevation, vertically averaged density, in situ density, gravitationalacceleration (9.8 m/s2), and vertical coordinate, respectively.

The rate of change of 4 over time ðd4=dtÞ has been used toindicate whether the water column is becoming more stable ormore uniform in the vertical in the studying of tidal straining (e.g.Simpson et al., 1990):

(b) 2, (c), 17, and (d) 18 (i.e. each of these four panels are from data within a 1 h period).

C. Li et al. / Estuarine, Coastal and Shelf Science 85 (2009) 651–660658

d4

dt¼�

v4

vt

�þ�

v4

vt

�þ�

v4

vt

�þ�

v4

vt

�(2)

Fig. 7. Potential energy demand for complete vertical mixing for all three stations overthe 24 h period with nine casts at each station.

ts es tide wind

in which the right hand side terms are the contributions from tidalstraining, estuarine circulation, tidal stirring, and wind stirring,respectively. It has been established that the last two terms alwayshave negative signs. The negative sign of these two terms indicatethat they always contribute to the destabilization of the watercolumn. The other two terms, i.e., the tidal straining and estuarinecirculation components, are often times calculated from known orhypothetical velocity profiles. A common practice is that a one-dimensional mass conservation equation is used to relate thehorizontal density change to the density gradient and the velocity:

vr

vtþ u

vr

vx¼ 0 (3)

which leads to vr=vt ¼ �uðvr=vxÞ, and therefore

v4

vt¼ g

h

Z z

�h

�vr

vt� vr

vt

�z dz (4)

becomes

v4

vt¼ g

hvr

vx

Z z

�hðu� uÞz dz (5)

if vr=vx is independent of the vertical position. The key issues thenare determining both vr=vx and the vertical profile of the horizontalvelocity. In Simpson et al. (1990), a simple vertical profile of thevelocity from Bowden and Fairbairn (1952) was used to obtain anexpression for the tidal straining and the flow field for estuarinecirculation from Officer (1976) to yield the contribution fromestuarine circulation. These results all require the assumption of 1-D mass conservation, i.e. equation (3), and a vertically independenthorizontal density gradient vr=vx.

However, using equation (1), with a time series of verticalprofiles of the density from CTD casts, none of the above assump-tions (Simpson et al., 1990) are needed for the calculation of 4 asa function of time and thus d4=dt as an integrated effect of all of thefactors: tidal straining, wind stirring, tidal stirring, and estuarinecirculation. The use of equations (3)–(5) is very limited in value asflow field is not depth-independent, nor one-dimensional in space,especially considering the convergence effect of a narrow channel.In our survey, we made 28 CTD casts with an average of 9 casts ateach station over a 24 h period. Fig. 7 shows 4(t) for each station.The beginning of the survey had relatively large 4 values at station1, with comparable values at station 2, and a small 4 value (less thanhalf of that of the other stations) at station 3. The 4 values started todrop continuously at stations 1 and 3, while that at station 2increased slightly before the trend of drop. At about Hour 11 of thesurvey, all three stations reached their minimum 4 values at aboutthe same level when the profiles of the salinity and density arealmost vertically uniform (Fig. 4). This occurred during roughly themaximum ebb current. The 4 values then start to increase at allstations, until reaching their respective maximum values at aroundHour 20 into the survey (Fig. 7). The maximum at station 1 thistime, however, is much smaller than that in the beginning of thesurvey, while the maximum at station 2 remain about the same asits first maximum, the maximum at station 3 has got its highestvalue, reaching 23, almost triple that at station 1. Toward the end ofthe survey, when the flood tide reached its maximum, the 4 valuesall dropped sharply at all stations.

Overall, the APED (4) has a similar trend among all stations. Thevariations of 4 at station 2 are closest to symmetric in time. The 4

values at stations 1 and 3 have an obvious contrast such that the

first maximum at station 1 during the beginning of the survey ismuch larger than that at station 3 while at about Hour 20 theopposite occurred such that the second maximum at station 1 ismuch smaller than that at station 3. The correlation of 4 betweenthe east side (station 1) and west side (station 3) is calculated to beonly �0.05, even though the correlation between the west andcenter of the channel is much higher (0.88). This out-of-phaseand asymmetric variation in magnitude between the eastern andwestern sides cannot be explained by a simple classical estuarinetheory. The alternation of the intensity of the stratification of theeastern and western ends of the channel over the diurnal tidal cycleis obviously not a result of the Coriolis force. The Coriolis forceshould tend to make the salinity higher on the eastern end and thestratification condition across the tidal channel should be similar,rather than the opposite.

This unexpected result implies that some other factor(s) must beimportant in modifying the stratification conditions. One of suchfactors is that the Mississippi River’s discharge through thesouthwest Pass and other outlets at the Birdfoot Delta bringsfreshwater onto the shelf including the Louisiana Bight, wherea mesoscale gyre often exist (Rouse and Coleman, 1976). Bothcoastal current and the Louisiana Bight gyre are strongly dependenton the wind condition. These physical processes will provideconduits to allow the freshwater, after mixing with the ambientsaltier shelf water, to enter into Baratarian Bay through BaratariaPass. This will make the Barataria Bay not a simple estuarine baywith a simple salinity gradient. Rather, depending on the circula-tion condition outside of the bay on the Louisiana Bay, there may beadditional dilution of salinity by the Mississippi River freshwater,entering the Barataria Bay through the tidal channels includingBarataria Pass. This will complicate the density gradient, baroclinicpressure gradient, and the stratification condition, such as thoseshown by the data of this study. How exactly does this work toproduce the type of asymmetric distribution and variation ofstratification and tidal straining may require an extensive fieldstudy that covers both the tidal pass and Louisiana Bight. Thecirculation pattern and water mass (salinity) distribution must beresolved in the bight to illustrate the dynamical processes andthereby determine the key mechanisms that can cause the lateralvariation and even inversion of the stratification conditions.

Alternatively, a high resolution numerical model may be used toillustrate this dynamical process. Recently, Wang and Justic(submitted) have applied the Finite Volume Coastal Ocean Model(FVCOM) to this study area and demonstrated the circulation

C. Li et al. / Estuarine, Coastal and Shelf Science 85 (2009) 651–660 659

features driven by wind, including the Louisiana Bight Gyre. Weanticipate that future model simulations will help shed light on thelateral distribution of stratification and tidal straining in the Loui-siana Bight influenced by the Mississippi River plumes.

5. Summary

In summary, the variation of the velocity is dominated bya frictional diurnal tide with the subtidal flow structure consistentwith an estuarine circulation pattern affected by a cross channeldepth variation (Wong, 1994). The difference that complements thetheory is that there is a much larger uncertainty over the banks,suggesting a stronger nonlinearity near the edges of the barrierislands on both sides of the channel. The subtidal transport of wateris out of the bay. The most significant finding of the study, however,is the lateral variation and inversion of the average potential energydemand which is a result of differential tidal straining across thetidal channel. This lateral asymmetry is in contrast to the temporalasymmetry that has been most studied (e.g. Simpson et al., 1990,2005; Geyer et al., 2000; Rippeth et al., 2001; Chant and Stoner,2001; Stacey and Ralston, 2005; Ralston and Stacey, 2007; Li andZhong, 2009). Related to that finding is the non-uniform distribu-tion of the surface salinity which had a larger mean value on thewestern end than much of the eastern end, contrary to the expectedsituation in an estuary where a larger mean surface salinity isproduced on the eastern (opposite) end due to stratification and theCoriolis force. In the beginning of the survey (during flood tide), theeastern side had more than twice as large of the APED as that ofthe western side; while toward the end of the survey (close to themaximum flood), the western side had an APED more than 6 timesof that of the eastern side. This lateral difference in APED suggeststhat there must be other factors influencing the stratification andaltering the tidal straining. One possible factor is that there may bea relatively fresher water plume entering the bay through thewestern side. This relatively fresh water (compared to the averageshelf water in the area) may come from the Southwest Pass of theMississippi River Birdfoot delta. This hypothesis, however, cannotbe verified unless a much larger scale observation is implemented.As is well-known, Louisiana shelf has the second largest recurringseasonal hypoxia zone or ‘‘dead zone’’, with dissolved oxygen lev-els< 2.0 mg O2 l�1. It has been demonstrated that the size andintensity of the zone during the last half century (Rabalais et al.,2007a,b) has been increasing, causing adverse environmental andeconomic consequences (Rabalais and Turner, 2001a). Extensiveand seasonally recurring hypoxia developed on the Louisiana–Texas shelf from the 1970s through the 1990s, coincided witha tripling of nitrate loading from the rivers between the 1950s and1990. The Mississippi River is the source and initial driver of thephysical structure, productivity, eutrophication and hypoxia of theLouisiana Texas shelf. The work presented here provides newfindings of the dynamical process influencing the exchange ofwater through tidal inlets that may be useful in helping theunderstanding of hypoxia related processes. It provides in situ datafor model validation and a validated model can in turn providea useful tool for an illustration of the mechanisms involved in theobserved characteristics of lateral variations.

Acknowledgments

Dr. John Simpson and an anonymous reviewer provided usefulreviews that helped the improvement of the paper. The researchwas supported by NSF (DEB-0833225), and two NOAA grants,NA06NPS4780197 for NGoMEX funded to LUMCON and LSU, andNA06OAR4320264-06111039 to the Northern Gulf Institute byNOAA’s Office of Ocean and Atmospheric Research, U.S. Department

of Commerce and Shell (http://www.ngi.lsu.edu/), and througha contract, NNS05AA95C, by Louisiana Board of Regents. We wouldlike to particularly thank Charlie Sibley, Chris Cleaver, DarrenDepew, Steve Jones, and Rodney Fredericks for the field work.

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