circular plumes in lake pontchartrain estuary under wind straining

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Estuarine, Coastal and Shelf Science 80 (2008) 161–172

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Estuarine, Coastal and Shelf Science

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Circular plumes in Lake Pontchartrain estuary under wind straining

Chunyan Li a,f,*, Nan Walker a, Aixin Hou b, Ioannis Georgiou c, Harry Roberts a, Ed Laws b,J. Alex McCorquodale d, Eddie Weeks a, Xiaofeng Li e,f, Jessica Crochet a

a Department of Oceanography and Coastal Sciences, School of the Coast and Environment, Louisiana State University, Baton Rouge, LA 70803, United Statesb Department of Environmental Sciences, School of the Coast and Environment, Louisiana State University, Baton Rouge, LA 70803, United Statesc Department of Earth and Environmental Sciences, University of New Orleans, New Orleans, LA 70148, United Statesd Department of Civil and Environmental Engineering, University of New Orleans, New Orleans, LA 70148, United Statese NOAA E/RA3, 5200 Auth Road, Camp Springs, MD 20746, United Statesf 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 9 February 2008Accepted 21 July 2008Available online 5 August 2008

Keywords:saltwater intrusiontidal strainingestuarine circulation

* Corresponding author. Department of OceanogSchool of the Coast and Environment, Louisiana State70803, United States.

E-mail address: [email protected] (C. Li).

0272-7714/$ – see front matter � 2008 Elsevier Ltd.doi:10.1016/j.ecss.2008.07.020

a b s t r a c t

Circular shaped density plumes of low turbidity, low fecal indicator (Escherichia coli and enterococci)concentrations, and high salinity have been observed near the Industrial Canal in Lake Pontchartrain,north of the City of New Orleans. A conceptual model in polar coordinates and a numerical model aredeveloped, together with data analysis, to illustrate the dense plume. It is demonstrated that thenorthward expansion of the plume occurs under northerly winds. The northward expansion of theplume occurs under northerly winds that drive downwind flow at the surface and upwind radial flow atthe bottom. Northerly wind-induced straining, similar to tidal straining, promotes vertical stratification.As a result, the water becomes stratified near a thin bottom layer (<1 m), within which density currentsare facilitated. The stability of the stratified plume suppresses wind-induced turbulent mixing inside theplume. The bottom water outside of the plume is more effectively stirred by the wind, the result beingthat the suspended sediment concentration outside of the plume area is much higher than inside. Thiscontrast in mixing makes the plume visible from the surface by satellites even though the stratification isat the bottom. Laterally, wind stress produces a torque (vorticity) in areas of non-uniform depth such thatupwind flow is developed in deep water and downwind flow in shallow water. The continuityrequirement produces an upwind flow along the axis of the Industrial Canal (IC). The upwind flow isbalanced by the downwind flow over the shallower peripheral areas along the coast.

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1. Introduction

Estuarine plumes are often caused by buoyant fluvial freshwaterthat flows on top of more saline coastal ocean water beforecomplete vertical mixing occurs. A classical example is the Con-necticut River plume studied extensively starting in the mid 1970s(Garvine, 1974, 1977, 1984; Garvine and Monk, 1974). Buoyant riverplumes often form during periods of high river discharge. In theConnecticut River case, peak river discharge can exceed 2000 m3/sduring the spring. The plume exhibits itself as a large expansion ofsurface water lighter than the surrounding coastal seawater. Theplume occupies only the top couple of meters, over which thesalinity change can be 7–8 PSU or even larger. Van Maren andHoekstra (2004) recorded a w20 PSU top–bottom salinity differ-ence during flood tide in the Ba Lat River estuary in Vietnam.

raphy and Coastal Sciences,University, Baton Rouge, LA

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Similar masses of buoyant water or plumes are found outside ofmany rivers/estuaries, e.g. Chesapeake Bay (Johnson et al., 2001),Mobile Bay (Gelfenbaum, 1993), and the Hudson River (Johnsonet al., 2003).

Buoyant river plumes are mostly ephemeral – they are stronglysubject to the vertical and horizontal turbulent mixing anddispersion due to tidal and wind stirring (Chao and Boicourt, 1986;Chao, 1988a,b, 1990). Competition between the input of buoyancyand tidal and wind stirring determines the extent of water columnstratification, i.e. whether the water is stably stratified, partiallystratified, or vertically well-mixed. By a consideration of thepotential energy of the water column as a result of the densitydistribution and gravitational force, Simpson and Hunter (1974)developed a criterion for the identification of the frontal position –or the edge of a buoyant plume - formed by surface heating duringthe summer. The front is basically a boundary between the weakand strong tidal current areas in the northwestern Irish Sea. TheSimpson and Hunter theory predicts that the thermal frontalposition will occur along contours of constant h/U3, in which h andU are the water depth and the major tidal amplitude, respectively.

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Fig. 1. Study area – Lake Pontchartrain. The Pontchartrain Causeway Bridge is indi-cated by CW and the crossover locations are marked by S3–S7. IC, CM, and R representIndustrial Canal, Chef Menteur Pass, and the Rigolets. MRGO and GIWW are theMississippi River Gulf Outlet and Gulf Intracoastal Waterway, respectively. The colorcontours show the bathymetry of the lake (meters).

C. Li et al. / Estuarine, Coastal and Shelf Science 80 (2008) 161–172162

The theory is at least qualitatively verified by observations in theIrish Sea. When the buoyancy input is from river discharge ratherthan surface heating, the problem is necessarily more complicated.This is because river discharge is not uniformly distributed on thesurface along the axis of the channel. In contrast, surface heatingdue to solar radiation is relatively uniform over a large area. Byassuming a constant freshwater discharge induced density gradientindependent of depth and horizontal distance, the h/U3 criterion ismodified to be h5/U3 for the position of the front or the boundarybetween well-mixed and stratified regions (Bowman and Essaias,1981; Van Aken, 1986; Nunes and Lennon, 1987; Simpson et al.,1990). This indicates that the stability of the water column in regionsof buoyancy input from freshwater in estuarine circulation prob-lems is even more strongly dependent on the depth of the water.

The surface plume often occurs at the mouth of an estuary andextends to the coastal ocean. A related process, in most cases withmuch reduced vertical stratification compared to surface plumes, isthe classical estuarine circulation, in which relatively freshwaterflows in the same direction as the large-scale salinity gradient inthe surface layer and relatively salty water flows in the oppositedirection of the salinity gradient in the lower layer (Prichard, 1952;Hansen and Rattray, 1965). In contrast to the outgoing river plumes,this estuarine circulation occurs inside the estuary. Inside theestuary, the competition between stratification and mixing reflectsthe effects of tidal and wind stirrings, differential horizontaladvection of estuarine flows in the water column, and tidalstraining, which is associated with not only differential advectionbut also an alternation of flow directions (Simpson et al., 1990,2005). A special case of this is when tidal and wind stirrings areminimal and a bottom density current may form in the lower layer(e.g. Nunes and Lennon, 1987). Bottom density currents are a resultof gravitational circulation caused by sharp horizontal gradients indensity when vertical mixing is suppressed. Simple models havebeen developed to study the mechanisms driving density currents(e.g. Wåhlin and Cenedese (2006) and references therein).

While the estuarine surface plumes are visible and easy toidentify, the bottom density current and related plume edges orfronts are usually not visible from the surface. In this paper,however, we investigate the evolution, structure, and forcingmechanisms of extraordinary density induced plumes in LakePontchartrain, a shallow lake (average depth w4 m) just north ofNew Orleans, Louisiana. The plumes can be observed from space inthe visible bands with true color images as well as the ocean colorbands. Satellite measurements from the Moderate ResolutionImaging Spectroradiometer (MODIS) onboard satellites, Terra andAqua, and Oceansat-1 Ocean Color Monitor (OCM) data showconsistent features of the plume. We describe the satellite-observed features and in situ observations demonstrating strongbottom salinity fronts. A conceptual model is presented to facilitatediscussion of the effects of different wind regimes, based on whichwe interpret the satellite image patterns that demonstrate salt-water intrusions through a narrow man-made pass.

In Simpson et al. (1990), the potential energy of the watercolumn was considered in the context of stratification and mixingcaused by (1) estuarine circulation, (2) tidal straining, and (3) tidaland wind stirring. For the first mechanism – the estuarine circu-lation effect, Simpson et al. (1990) used the density-driven circu-lation component. It should be noted that the estuarine circulationcan be a combination of density-driven flow, fluvial discharge, andwind-driven flows. Wind-driven flows can produce a significantvertical shear of the horizontal velocity, causing opposing flows indifferent layers or across the channel (Wong, 1994). This wind-driven effect will therefore be similar to that of tidal straining suchthat wind from one direction may tend to stabilize the watercolumn while destabilizing it when coming from an oppositedirection. Observations in the York River Estuary (Scully et al.,

2005) have indicated straining caused by wind. We will thus usethe term ‘‘wind straining’’ for such effects, similar to ‘‘tidal strain-ing’’. In our study, we will use wind stress from different directionsto obtain flow fields that demonstrate the interaction of wind-driven flow and the bathymetry in a lake using polar coordinatesfor an idealized fan-shaped model. To complement the conceptualmodel, a numerical model is also presented to further demonstratethe effect of winds on plume development.

2. Study area and background information

2.1. General information

Lake Pontchartrain (Fig. 1) is an oval-shaped quasi-enclosed bodyof brackish water located north of the City of New Orleans. The mainaxis of the oval is in the east-west direction and spans 66 km, whilethe shorter north–south axis is about 40 km. The water is shallow inmost parts of the lake with an average depth of 3.7 m. It is deeperalong a roughly north–south direction aligned with the IndustrialCanal. The depth becomes increasingly shallower to the east andwest (Fig.1). Freshwater discharges into the lake directly through theTchefuncte and Tangipahoa Rivers. The Amite, Blind, and TickfawRivers provide additional freshwater flowing into the adjacent LakeMaurepas and enter the lake through Pass Manchac, on the westernedge. Freshwater also enters the lake via urban runoff along thesouthern shore and through the Rigolets from the Pearl River. Highersalinity waters from the coastal ocean enter the lake by tidal currentsand wind-driven flows through three narrow tidal passes, i.e. theRigolets, Chef Menteur, and a man-made canal – the Inner HarborNavigational Canal (IHNC) or Industrial Canal (IC) connected to theMississippi River Gulf Outlet (MRGO) and the Gulf IntracoastalWaterway (GIWW) (Fig. 1).

Unlike most estuaries, the lake has no ‘‘free’’ connection withthe open ocean. It is therefore not an estuary in the traditionalsense as defined by Cameron and Prichard (1963) or Dyer (1997).The lake’s circulation is mostly wind-driven. On the other hand,tidal currents through the narrow passages can be quite swift (2 m/s or even larger) during the peak flood phase of the tidal cycle. Asa result, saltwater can still enter the lake with a significant impact,depending on the wind regime. The lake is thus still classified as anestuary in many studies.

2.2. Saltwater intrusion

Past studies have shown a trend of increasing salinity in LakePontchartrain after the construction of the Mississippi River Gulf

Fig. 2. MODIS 250–500-m resolution RGB images (top to bottom) of the circularplumes in the Lake Pontchartrain observed on Nov. 29, 30, and Dec. 1, 2005, respec-tively. The causeway is shown by the white and yellow lines. The crossover stations S3through S7 are shown on the bottom image.

C. Li et al. / Estuarine, Coastal and Shelf Science 80 (2008) 161–172 163

Outlet (Sikora and Kjerfve, 1985; Carillo et al., 2001). More recentstudies have also demonstrated a trend of increase of surfacesalinity between Feb. 1997 and Feb. 2000 (Haralampides, 2000) andthe present surface salinity in the southern portion of the lake isaround 7–8 PSU according to surveys conducted by the authors ofthis paper between Sept. 2005 and Mar. 2007 after HurricaneKatrina (Aug. 2005).

Beside the long term change in salinity, relatively saline waterenters the lake through the IC. Poirrier (1978) and Georgiou andMcCorquodale (2000) reported saltwater intrusion into the LakePontchartrain resulting in a salinity value of 15–20 PSU and a strongstratification at w1 m above the bottom. This salinity value isseveral times higher than the mean salinity of the lake. Sharpsalinity gradients were observed in the vertical and a bottom plumewas observed as a thin layer extending to w10 km away from theinlet (Georgiou and McCorquodale, 2000). Conceptually, the densesalty water that enters the lake via a swift current through thenarrow tidal passages slows down rapidly due to the radial diver-gence (Georgiou and McCorquodale, 2002) of the flow into the lake.The kinetic energy of the tidal current available for vertical mixingis therefore much smaller than is the case in estuaries (Simpson,1997; Rippeth et al., 2001; Baumert et al., 2005; Simpson et al.,2005). Consequently the saltwater intrusion can more easilysustain a strong vertical stratification that may contribute signifi-cantly to the production of a benthic ‘‘dead zone’’ in the lake(Poirrier, 1978) where oxygen is depleted. Wind stress is usuallyinsufficient to overturn the water column unless the wind speedexceeds 11 m/s when instability may develop (Georgiou andMcCorquodale, 2000). The saltwater intrusion may result in benthicmortality from low dissolved oxygen (hypoxia or even anoxia)developed or enhanced by the strong stratification. The saltwaterintrusion has been found to match the area of dead zones (hypoxiaand anoxia) (Schurtz and St. Pe’, 1984). Georgiou and McCorquodale(2002) conducted some numerical experiments and found thatnortherly and westerly winds favor the plume expansion. In thefollowing we will provide observations from satellites and in situmeasurements and examine the behavior and mechanisms of theplumes in more detail with both conceptual and numerical models.

3. Observations and hypothesis

Lake Pontchartrain was in the path of the infamous HurricaneKatrina, which struck the City of New Orleans on Aug. 29, 2005.Since then considerable effort has been made to study thedynamics of the lake and the effects of Katrina on water quality andthe concentrations of pathogens and chemical pollutants. As part ofthat effort, since Sept. 19, 2005 we have conducted numerous fieldobservations, including hydrographic and hydrodynamics surveysand the collection of water samples (Hou et al., 2006). During mostof the surveys, we measured hydrographic parameters in the watercolumn using a YSI CTD with multiple sensors and/or a SeabirdElectronics SBE 19 plus CTD profiler with a dissolved oxygen sensor.

3.1. Observation of a circular plume

On Nov. 29, 2005, a MODIS true color image (Fig. 2) showed anextraordinary feature suggesting a saltwater plume coming into theLake through the MRGO. The plume was oval/circular in shape witha scale of w15–17 km in diameter and a clear contrast in color withthe surrounding lake water – the plume water appeared to be muchclearer than the surrounding water (Fig. 2a). The plume came out ofthe IC as a narrow jet that subsequently expanded in a circularfashion. From Fig. 2a we can see that the plume would have beenmore symmetric if it had not been affected by the New OrleansLakefront Airport (indicated by NOLA on Fig. 1), which protrudesinto the lake and restricted spreading of the plume water toward

the east immediately after its entrance into the lake. As a result, eastof the Lakefront Airport, the plume was separated from the shore.In contrast, west of IC, the plume was in contact with the shoreline.The western edge of the plume had just passed the causeway (Figs.2a and 3). On Nov. 30, the plume further expanded toward thenorth and deformed into a mushroom-like feature. The south-western part of the plume was no longer in contact with theshoreline. The western end of the plume expanded further to thewest of the causeway (Figs. 2b and 3). On the following day, Dec. 1,

Lake Pontchartrain

Fig. 3. Plume evolution. Solid line denotes the edge of the plume on Nov. 29, thickdash line on Nov. 30, and thin dash line on Dec. 1, 2005.


the plume remained almost the same with some minor deforma-tion in shape and size (Figs. 2c and 3) as well as more diffusedboundaries. On the same day (Dec. 1) we collected water samplesand measured water temperature, salinity, and dissolved oxygen inthe water column at five of the seven crossover stations (S3–S7)along the concrete causeway bridge across the lake (Fig. 1). We alsocollected surface water samples to measure fecal indicator (i.e.Escherichia coli and enterococci) concentrations at stations S5–S7.Station S7 was closest (w5 km) to the southern shore of the lakeand just outside of the plume from the MODIS image. Stations S5and S6 were inside the plume. Stations S3 and S4 were outside andnorth of the plume.

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Fig. 4. Observed vertical profiles of salinity, temperature, dissolved oxygen, and density obtaon late afternoon of Dec. 1, 2005.

Fig. 4 shows the vertical profiles of the water salinity, temper-ature, dissolved oxygen, and density. Salinity at the northernmoststations (stations S3 and S4) was vertically uniform with a value ofaround 8 PSU (Fig. 4a). Both temperature and Dissolved Oxygen(DO) at these stations varied only slightly with depth (Fig. 4b and c).In general, DO concentrations were relatively high at all stationsthroughout the entire water column. The water columns at stationsS5–S7 were, however, distinctly stratified with respect to salinity.The salinity increased within less than 1 m of the bottom by about2, 4, and 1.5 PSU at stations S5–S7, respectively. The density profilesat all stations show similar patterns as salinity, a reflection of thefact that salinity is the controlling factor for water density underthese conditions (Fig. 4d).

On the MODIS image, station S7 appeared to be outside of theplume (Fig. 2c). The increase of salinity at station S7 indicates thatthe plume had expanded into a larger area underneath its apparentsurface signature by way of density current sinking and penetrationalong the bottom of the rather shallow lake. Alternatively, theapparently well-mixed area outside of the plume may haveadvected into the plume in the top layer of the water by windforcing (more discussion below). Station S7 can be seen to be nearthe edge but inside the plume on Nov. 29 (Fig. 2a). A northwardflow must have occurred to bring the water further to the north(Fig. 3). The distinctly clear water in the plume most likely reflectsa strongly stable water column, which suppresses vertical mixingthat could have potentially re-suspended bottom sediments. Theweak tidal motion in the lake leaves wind stirring as the only optionfor vertical mixing to de-stabilize the water column.

Plume waters (stations S5–S7) exhibited a different verticalstructure compared with those outside the plume. Surface andbottom plume waters were warmer than lake water by 0.5–1.0 �C(Fig. 4b) whereas, from 2 to 4 m water depth, water temperatureswere more similar to lake water, ranging from 15 to 15.3 �C. Since in

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ined from the crossover stations (S3 through S7) of the Pontchartrain Causeway Bridge


winter time water temperature increases from inland water tocoastal ocean, the relatively warm water near the bottom of thelake suggests advection of water into the region from the ocean,which is consistent with the intrusion of more saline water throughthe IC. The surface layer of warmer water at the plume stations ismostly likely due to surface heating during the day and demon-strates that solar energy was concentrated in the plume’s surfacelayers due to the strong stratification. The colder water with moreuniformly distributed temperature at stations S3 and S4 is probablya result of relatively stronger wind-induced vertical mixing thatdissipated the effect of surface heating. Although wind stress isrelatively uniform over the lake, vertical mixing on this occasionwas apparently limited to the region outside the plume wherestratification was weak. Mixing-induced re-suspension of sedimentoutside the plume is thus implicated as the cause of the dramaticdifference in turbidity between the plume and the rest of the lake.

Escherichia coli and enterococci counts were determined usingstandardized methods (Method 1103.1 (USEPA, 2002a) and Method1600 (USEPA, 2002b)). Water samples were processed within 6 hafter sampling and results reported as CFU/100 ml. Significantdifferences were observed in the E. coli and enterococci concen-trations among stations inside (station S5 and S6) and outside(station S7) the plume on Dec. 1, 2005. The mean values of E. coli atstations S5 and S6 were about an order-of-magnitude lower thanthat at station S7 (5 CFU/100 ml versus 46 CFU/100 ml). Enterococciwere not detectable (i.e. no colony was formed on all plates) atstations S5 and S6, and the mean value for station S7 was 8 CFU/100 ml. Since water samples were obtained only from the surface,the higher value of E. coli and enterococci at station S7 implies thatthe turbid water at this station was likely advected from outside theplume (the surface signature of the plume moved northward in 2days as illustrated by Fig. 3) even though its bottom water stillshowed stratification (Fig. 4).

3.2. Water mass of the plume

A first impression about the plume may be that the plume isformed entirely by water coming into the lake through the IC andthat this water must be ‘‘clearer’’ than the water originally in thelake. If that were the case, the plume would simply be injected intothe lake by some forcing mechanism, whether by local wind effect(wind stress) or remote wind effect (the low-frequency water levelchange in the coastal ocean outside of the lake or a combination ofthe two) (Garvine, 1985). We can now make a simple order-of-magnitude estimate of the time scale needed to fill the lake withthe volume of water defined by the diameter of the plume. Themaximum diameter of the plume is about 17 km. The area of theplume is thus p r2¼ 2.27�108 m2. The lake has a mean depth ofabout 3.7 m, and it is deeper (5–6 m, Fig. 1) in the area of the plume.The volume of water within the plume area is thus about V¼pr2� 5¼11.4�108 m3. The width (W) and mean depth (H) of themouth of the IC estimated from surveys conducted on Nov. 23, 2005and Mar. 27, 2006 are about 70 m (W), and 10 m (H), respectively.Assuming a uniform mean flow of 1 m/s, the time for filling thisvolume of water defined by the size of the plume is therefore T¼ V/(70�10�1)¼ 19 days! If we consider the oscillatory nature of thetidal currents, the 1 m/s constant mean flow is most likely an over-estimate even during persistent wind-driven flow conditions. It istherefore unlikely that the plume is formed entirely from wateroutside of the lake because the event lasted at most a few days andpossibly no more than 2–3 days: the first image of the plume wasobtained on Nov. 29. A clear-sky image obtained on Nov. 24 showedno signs of the plume. Between Nov. 24 and 29 cloud coverobscured the lake surface in satellite imagery. CTD profiles docu-mented the presence of a saltwater lens very close to the bottom,

which suggests that only a fraction of the water within the plumewas actually from the coastal ocean.

3.3. Wind conditions, hypothesis, and more observations

Wind data were obtained from a weather station located on thewestern side of Lake Pontchartrain (30�1805400 N, 90�1605000 W(LKPL1 on Fig. 1)), maintained by Louisiana University MarineConsortium (LUMCON). The wind was mostly from the south formore than 2 days prior to late evening of Nov. 28 with a magnitudeof about 8–9 m/s. It then changed to northerly and reacheda second maximum on mid-day Nov. 29 with a smaller magnitude.The northerly wind lasted until the end of Nov. 30 (Fig. 5b). On Dec.1, the wind (not shown) switched to southerly again with a weakerintensity (<5 m/s). Note that the circular plume was first observedon Nov. 29 and lasted until Dec. 1, when it started to dissipate asdiscussed in Section 3.2. During the evolution of the plume fromNov. 29 to Nov. 30, observable in the MODIS images, it expandednorthward against the wind (Fig. 3). Upwind flow has also beendocumented in numerical model results (Georgiou, 2002), consis-tent with the observed movement of the plume.

A relevant hypothesis can be made based on our understandingof wind-driven flows in estuaries with significant cross-channeldepth variations. Using simple conceptual models, Hamrick (1979)and Wong (1994) showed that the cross-channel variation in depthwould produce reversed flows, surface to bottom, regardless of thewind direction. In general, water would flow downwind in shal-lower water and upwind in deeper water (Wong, 1994; Winant,2004; Sanay and Valle-Levinson, 2005). When the water depth isconstant across the channel, the flow would become two-layered –with downwind flow on the surface and upwind flow at the bottom.This kind of wind-driven flow is demonstrated in the laboratoryexperiments described in Fischer (1976). In our case, the situation isa little different from that of a coastal plain estuary in that the watercoming from the IC diverges into a larger unrestricted area in thelake. A similar mechanism of the wind-driven flow, however, maystill work for this situation (to be discussed below). Our hypothesiscan then be stated that under northerly wind conditions there is anupwind, radial divergent, near-bottom flow into the lake from theIC, which causes a circular shaped feature to develop. The down-wind flow is near the surface and on the sides of the lake. This two-layered flow promotes stability of the water column since thesaltwater coming from the IC is denser. Vertical mixing wouldtherefore be less intense if not completely suppressed. In addition,the radial divergence of the flow effectively reduces the speed ofthe water, causing even less bottom-turbulence-induced verticalmixing. This stable condition in the water column contributes toa less turbid state compared to areas outside of the plume wherevertical mixing produces higher turbidity due to sediment re-suspension.

In other words, it is hypothesized that northerly winds facilitatethe formation of the circular plume with the bottom water flowingtowards the north (against the wind) unless the wind speed is toolarge (e.g. much greater than 10 m/s as discussed in Georgiou andMcCorquodale (2000)) such that wind-induced mixing can destroythe stratification of the bottom density current. Considering the factthat more saline water enters through the IC, the salinity gradient istowards the south, and northerly winds will tend to strengthenstratification through the vertical shear of the horizontal velocity, inthe same way as tidal straining (Simpson et al., 1990). We thereforecall it ‘‘wind straining’’ or ‘‘wind-induced straining’’ as discuss inScully et al. (2005).

This hypothesis is supported by more observations. Table 1 listsall plume events observed by satellites between Aug. 2005 and June2006. Fig. 5 shows the corresponding wind vectors for selectedplume events in August and November of 2005, and Jan., April, May,

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Fig. 5. Wind vectors from selected events in 2005 and 2006. The thick vector on the right is the reference vector with 5 m/s scale. Time is in UTC. (a), (b), (c), (d), (e), and (f) are forAug., Nov., 2005, and Jan., April, May, and June of 2006, respectively. The vertical arrows attached to the x-axis indicate the times when satellite images were collected withsignatures of the plume.


and June of 2006. The vertical arrows attached to the x-axis in Fig. 5indicate the times when satellite images were collected withsignatures of the plume. Apparently, under moderate northerlywind (speed< 10 m/s), plumes may form, mostly in circular formwith unique optical characteristics and distinct color boundariescompared with the ambient lake water. Under southerly winds orduring transition from northerly to southerly winds, the circularplume may be deformed, reduced in size, and with reduced clarityof boundaries (Table 1). Fig. 6a and b is OCM and MODIS imagesfrom Aug. 22, 2005 and Jan 13, 2006, respectively, both duringnortherly winds (Fig. 5a and c). Fig. 6c is a MODIS image from Jan 31of 2006 when the wind was weak southerly but it had beensoutherly for 3 days and then northerly for 1 day prior to the time ofthe satellite image (Fig. 5c). The plume was irregular in shape andappeared to have diffuse boundaries. Fig. 7a is a MODIS image fromMay 15, 2006 during which the wind was northerly. Fig. 7b is

Table 1List of plumes observed from satellite images

Date Time (UTC) Instrument Number of Image

Aug. 22, 2005 18:03 OCM 3Nov. 29, 2005 16:23 MODIS 1Nov. 30, 2005 18:03/18:38 OCM/MODIS 3/1Dec. 1, 2005 19:21 MODIS 1Jan. 13, 2006 19:03 MODIS 1Jan. 25, 2006 16:16 MODIS 1Jan. 31, 2006 18:03/18:55 OCM/MODIS 3/1April 27, 2006 18:03 OCM 3May 15, 2006 16:30 MODIS 1May 17, 2006 18:03 OCM 3May 18, 2006 18:34 MODIS 1June 4, 2006 18:03 OCM 3June 6, 2006 18:03 OCM 3

a MODIS image from May 18, 2006, when the wind had justswitched to southerly. The plume shown in Fig. 7b appeared to bemuch more diffused. Fig. 7c is a MODIS image from June 4, 2006when wind was southerly. The plume boundary was not clearlyvisible in this case.

4. Conceptual model and results

4.1. Model and solution

To further test the above hypothesis and demonstrate the windstraining mechanism, we will modify the model of Wong (1994) sothat it is applicable to a lake with an inlet, through which waterexchange with the coastal ocean occurs. The setup of the model isshown in Fig. 8. A steady state is assumed for simplicity in illus-trating the mechanism. The dynamical balance of the model is

s Wind direction Plume feature

N Circular; clear boundaryN Circular; clear boundaryN Circular; clear boundaryS Circular; deformed; diffused boundaryN Circular; clear boundaryN Elongated oval; clear boundaryS Irregular shaped; reduced in size than Jan 25N Small oval; clear boundaryN Circular; clear boundaryN Circular; clear boundaryS Deformed; diffused boundaryN to S Wide band; diffused boundaryS Wide band; more diffused boundary

Fig. 6. MODIS and OCM satellite images. (a), (b), and (c) for from Aug. 22, 2005, Jan. 13,2006, and Jan. 31, 2006, respectively (Table 1). (a) is an OCM chlorophyll a estimate(blue is relatively low chlorophyll a) and (b) and (c) are MODIS RGB images.

Fig. 7. MODIS RGB satellite images. (a), (b), and (c) for from May 15, May 18, and June 4of 2006, respectively.


between the pressure gradient and vertical mixing (Prichard, 1952;Wong, 1994). The water column is hydrostatic. The governingequations in a polar coordinate system are expressed as:

0 ¼ �1r

vpvrþ AZ

v2uvz2 (1)

0 ¼ �1p

vpvzþ g (2)

in which r,p, u, AZ, r, z, and g are the water density, pressure, radialcomponent of the velocity, vertical eddy viscosity, radial distance,

vertical coordinate, and gravitational acceleration, respectively. Theboundary conditions include the surface wind stress condition, theno-slip condition at the bottom, and the total mass conservationacross the inlet (which should be equal to the net freshwaterdischarge for a steady state condition), i.e.

rAZvuvz

��Z¼0¼ sa cosðqÞ ¼ CDraW cosðqÞjWj

ujh¼ 0Z 4=2

�4=2

0B@Z h

0u dz

1CA rdq ¼ R

(3)

/ 2ϕ/ 2ϕ

a

b c

r θ

h0

τ

τwind

Fig. 8. Diagram for the fan-shaped conceptual model. (a) the plane view of the model.The angle of the fan is 4. A northerly wind is indicated by the downward arrows. (b)Schematic view of the cross-section along r¼ const. spanning an angle of 4. (c) Windvector and its geometric relation with the position vector r.

Table 2Parameters used for the conceptual model. Note: For all cases, Cd¼ 0.0025, AZ¼ 5/1000m2/s, water density r¼ 1025 kg/m3, air density ra¼ 1.25 kg/m3, vr=vr ¼ �9=10;000kg=m4, h1¼2 m, h0¼ 6 m, a¼ 6

Case# Figure W (m/s) R (m3/s) Depth function

1 9b �15 �200 Gaussian2 10a �10 �800 Gaussian3 10b þ10 �800 Gaussian4 11a �10 �200 Flat5 11b þ10 �800 Flat


in which R is the total volume transport directed into the lake. Forriver discharge directed from the lake into the inlet, R is negative.For convenience, the river discharge is taken as evenly distributedalong an arc of constant r. Note that we have expressed the windstress in the radial direction (Fig. 8c). We also write the radialdensity gradient and surface slope to be

vr

vr¼ l;

vz

vr¼ i (4)

The water depth is defined to be ‘‘Gaussian’’ or ‘‘bell-shaped’’ witha maximum in the center and varying across an arc with r¼ const.in the following form

hðqÞ ¼ h1 þ ðh0 � h1Þe�a�

q4

�2��q�� 4 (5)

in which q is the angle of the polar coordinate. 4 is the angle span ofthe flow area. This function defines a maximum depth alonga radial axis with decreasing depth toward both sides of the axis,a simplification preserving the main feature of the lake’s bathym-etry as shown in Fig. 1. The values for h0, h1, and a determine themaximum depth, minimum depth, and shape of the depth function,respectively. Note also that this function is defined with r¼ const.In theory, h0, h1, and a can be functions of r. In our computations,however, we only use constant values for simplicity.

The solution of (1) and (2) with the given conditions can beobtained with an approach similar to that used by Officer (1976)and Wong (1994). Basically, the solution represents the velocityfield under the influence of wind, river discharge and pressuregradient. It can be expressed as a combination of three terms whichare linearly dependent on the wind stress, surface slope, anddensity gradient in the radial direction, respectively. These threeterms are also dependent on the water depth function andinversely proportional to eddy viscosity. The relevant equation is

u ¼ sa cosðqÞrAZ

ðh� zÞ þ gi2AZ

�h2 � z2

�� gl

6rAZ

�h3 � z3

�(6)

At this point the problem is not solved yet because the surface slopeis unknown. The surface slope can be related to the wind stress,river discharge and density gradient in the radial direction by thefollowing equation by applying the mass conservation constraint

i ¼ 3AZ

2gI2

Rrþ 3l

8r

I3I2� 3sa

2gr

I1I2¼ alþ bRþ gsa (7)

in which the coefficients are defined as

a ¼ 38r

I3I2; b ¼ 3AZ

2gI2r; g ¼ � 3

2rgI1I2

(8)

and

I1 ¼Z 4=2

0h2dq; I2 ¼

Z 4=2

0h3dq; I3 ¼

Z 4=2

0h4dq (9)

therefore, the solution for the radial component of the velocity asa function of q and r is

u ¼ sa cosðqÞ"

h� zrAZ

þg�

h2 � z2�

2AZg

#þ R

bg�

h2 � z2�

2AZ

þ l

"g

2AZ

�h2 � z2

�a�

g�

h3 � z3�

6rAZ

#(10)

Most of the dependence of the radial velocity on q is implicitlyincluded within the depth function h¼ h(q). Note that b is a functionof r (Eq. (8))): the mechanism associated with the net flow Rgenerates a flow that is inversely proportional to the radial distance r.

4.2. Results

To calculate the solution of the conceptual model – Eq. (10), wehave specified the minimum and maximum depths along an arc inthe polar coordinate to be 2 and 6 m, respectively, in considerationof the lake’s bathymetry (Fig. 1). The parameters for differentcalculations are shown in Table 2. The bottom drag coefficient(CD¼ 0.0025) and vertical eddy viscosity (0.005 m2/s) are taken asconstants with standard values (e.g. Officer, 1976; Gill, 1982) forsimplicity without affecting the conclusions. The density gradient istaken to be a constant as well with a magnitude of �0.0009 kg/m4,which is equivalent to about 10 PSU difference in salinity within10 km, a reasonable value for the plume situation. Different verticaleddy viscosity values are used examining the sensitivity of thesolution but the results are qualitatively the same. The first case isunder a northerly wind with 15 m/s wind speed and 200 m3/s riverdischarge (R< 0). The computational grids are shown in Fig. 9a.Fig. 9b shows the radial velocity – positive being toward larger r.Obviously, the flow is downwind on the surface and upwind atdepth. The surface flow is stronger (w0.2 m/s), and bottom flow hasa smaller magnitude (�0.12 m/s). The core of the bottom flow isconcentrated near the central deep water, while the downwindflow is on the surface of both sides of the cross-section. Thissuggests that the northerly wind tends to promote water transport

Z

-6

-5

-4

-3

-2

-1

0

theta (degree)

Z

-6

-5

-4

-3

-2

-1

0 u0.120.080.040.00

-0.04-0.08-0.12-0.16-0.20

-40 -20 0 4020

a

b

Fig. 9. Computational grids along a vertical cross section with r¼ const. and velocityprofile under northerly wind. Positive (negative) values are outward (inward) flows inradial direction. Parameters of calculations can be found in Table 2.


in the lower layer along the deep axis toward the north, and a directimplication of that is the enhancement of saltwater intrusion fromthe bottom. Fresher water on the surface, especially the surfacewater outside of the plume, flows radially inward toward the inlet.This flow further enhances vertical stratification, making thevertical water column more stable. This promotes a more stablewater column similar to the effect of tidal straining during ebb tide(Simpson et al., 1990) because of the radial gradient in density. Thesecond case has a northerly wind of 10 m/s and a river discharge of800 m3/s with otherwise the same parameters and setup. The flowis now reduced in both layers but the trend is still the same witha core of bottom water flowing from the inlet to the interior of thelake and a surface flow downwind toward the inlet (Fig. 10a). Thethird case is under a southerly wind (Table 2). Again, the downwindflow is on the surface but now it is from the inlet toward the interior

u0.060.040.020.00

-0.02-0.04-0.06-0.08-0.10

u0.070.050.030.01

-0.01-0.03-0.05

a

b

Z

-6

-5

-4

-3

-2

-1

0

Z

-6

-5

-4

-3

-2

-1

0

theta (degree)

-40 -20 0 4020

Fig. 10. Velocity profile under northerly (a) and southerly (b) wind. Positive (negative)values are outward (inward) flows in radial direction. Parameters of calculations can befound in Table 2.

of the lake since the wind is from the south. The upwind flowoccurs at the lower layer (Fig. 10b). This promotes a less stablewater column similar to tidal straining during flood tide (Simpsonet al., 1990) because of the radial gradient in density.

5. Discussion and numerical model experiments

5.1. Velocity distribution and boundary effects

The velocity distribution is apparently related to the bathym-etry. This can be further demonstrated by specifying a constantdepth within the lake. Fig. 11 presents such a situation with bothnortherly and southerly winds. The velocity is almost evenlydistributed. The only lateral variation is due to the change of theangle between the wind vector and the radial direction r (Fig. 8c). InLake Pontchartrain, depth is greater near the IC and shallower alongthe edges of the lake. The maximum depth at the mouth of the IC inthe lake is about 25 m, represented by two isolated deep holes,according to surveys conducted by the authors on Nov. 23, 2005,Mar. 27, 2006, and Mar. 23, 2007. On average, the depth is greateralong an axis extending from the IC toward the interior of the lake.Regardless of the actual depth function, the two-layered flow (withdownwind flow on surface and return flow or upwind flow at thelower layer) is always evidenced in the model results.

In addition, the fan-model predicts a radial flow field witha velocity magnitude decreasing with radial distance from thecenter of the circle forming the fan. Therefore, the flow velocityvalues away from the center (large radius points) are smaller thanthose at near the center (small radius points). Thus the downwindadvection at the upwind location away from the IC should besmaller than that near the IC. The advection at the boundary willblur the boundary because the water outside of the plume is mixedtop to bottom (no stratification to suppress the mixing). Thisadvection is limited in speed: it takes time for the advection toadvance into the stratified plume. Conceptually, under idealizedsituations, this advection is a stratifying factor (wind strainingunder northerly winds) such that it makes the sedimentation fasterthan suspension. Therefore, inside the plume, the advection causedblurring at near the boundary will not sustain or at least notadvance rapidly. Furthermore, the wind straining inside the plume

0.095

0.075

0.055

0.035

0.015

-0.005

u0.016

-0.002

-0.020

-0.038

-0.056

-0.074

-0.092

-0.110a

b

Z

-6

-5

-4

-3

-2

-1

0

Z

-6

-5

-4

-3

-2

-1

0

theta (degree)

-40 -20 0 4020

Fig. 11. Velocity profile under northerly (a) and southerly (b) wind for a flat bottomlake. Positive (negative) values are outward (inward) flows in radial direction.Parameters of calculations can be found in Table 2.

14

15

1617

1614

15

13

90.4 90.2 90.0 89.830.0

30.2

30.4Windat 5 m/s

Industrial Canal0.1 m/s

North

Fig. 12. Model simulated currents and circular plume extend into Lake Pontchartrain.Shown here is the plan view of velocity distribution and plume extend; vectors aredepth-averaged currents (every third vector is shown), and solid lines are bottomsalinity in PSU.


keeps the water column stably stratified. The satellite observations(Figs. 2, 6 and 7) do show that the boundaries are indeed blurred tosome extent. In other words, the upwind boundary is not exactlysharply defined. The process should be a dynamical one: as theupwind (northern) boundary surface water is advected into theinterior of the plume, the ‘‘dirty’’ water will replace the cleanerwater at the speed of the advection (which is smaller than interior),but only near the boundary. But this process itself has a negativefeedback: i.e. the wind straining is a stabilizing factor for the watercolumn, and thus the suspension of bottom sediment will not keepup with the deposition, which will make the water ‘‘cleaner’’ againas the particle advects further into the plume area.

5.2. Surface plume vs bottom plume

Estuarine outflow plumes are buoyant – they are on the surface.They represent the extreme conditions of estuarine circulation suchthat the stratification caused by fluvial discharge cannot bedestroyed by tidal or wind mixing. When tidal or wind mixing hassufficient energy, the water column can be vertically mixed by theturbulent energy. The potential energy of the water column is thenincreased and the stable layers destroyed. In contrast, the LakePontchartrain plume is an inflow density plume, a result of saltwaterintrusion mainly from the bottom. Though tidal straining duringflood tide can potentially mix the water column, the radial diver-gence of the flow as it enters the lake rapidly diminishes the tidalcurrent away from the inlet (IC or IHNC), thus decreasing much ofthe turbulent energy. The result is that the water column quicklybecomes stratified, especially under the effect of wind straining. Ofcourse, wind also acts as a force for mixing. Wind-induced mixingcan occur when wind is much larger than 10 m/s. The tidal current isnot explicitly considered in the above discussion. However, theeffect of the tidal current is similar to that of river discharge R witha net input of water from the inlet into the lake. Whether with orwithout wind or tidal current, the river discharge R is negative. Thesecond term in Eq. (10) describes this contribution.

5.3. Remote and local wind effects

The conceptual model only includes local wind effects, i.e. theeffect caused by the wind stress. Remote wind effects (e.g. Garvine,1985) are not included. The remote wind effect, which is mainlya low-frequency sea level variation, may generate a strong net flowthat injects saltier coastal water into the lake. Prior to the northerlywind starting late Nov. 28 (Fig. 5b) before the plume appeared onthe MODIS image, the wind was mostly strong and southerly fortwo days. Under this condition, the conceptual model describesa northward flow on the surface and a southward flow along thebottom. This would not cause a saltwater intrusion unless therewas a net sea level slope from the coastal ocean to the lake. Sucha slope could drive a net flow into the lake (the correspondingdischarge R would become much larger so that the entire watercolumn would flow northward toward the interior of the lake). Thissaltwater intrusion would not initially be apparent in satelliteimagery because vertical mixing would be strong and suspendedsediment concentration would be high during periods of southerlywinds. However, the subsequent change in wind direction, fromsoutherly to northerly would produce a stratified situation due towind straining. Therefore, the formation of the saltwater intrusionalong the bottom and subsequent development of the low turbidityplume, revealed in satellite images, may require a large-scalesoutherly wind (producing a sea level gradient conducive to flowinto the lake through the IC) and a subsequent northerly wind toreveal its presence. The first episode of southerly winds wouldinitiate the movement of saltwater into the lake through the ICbecause of the remote wind effect, and the second episode of

northerly winds would enhance the stratification that keeps thesaltwater near the bottom, while wind straining would furtherincrease bottom saltwater intrusion into the lake. Strong stratifi-cation resulting from northerly wind straining would inhibitvertical mixing of bottom sediments upward producing relativelyclear water in comparison to the ambient well-mixed lake wateraround the intrusion such that the bottom plume becomesapparent at the surface. This is of course a speculation of whatwould happen when remote effect of wind is strong. The presentstudy does not have useful data to prove or disprove this argument.

5.4. Effect of earth’s rotation

The effect of the Coriolis force is not included in the conceptualmodel. The reason is two-fold. First, the inclusion of the Coriolisforce will complicate the problem, and the fan-model cannot besolved easily using an analytic method. Second, the effect of theearth’s rotation is most likely a non-significant modification to theflow pattern. The models of Hamrick (1979) and Wong (1994) alsoignore the Coriolis force. Wong applied his conceptual model toDelaware Bay without the inclusion of Coriolis force, which is wideenough for the effect of the Coriolis force to be evident. More recentwork trying to modify Wong’s model by adding Coriolis force (e.g.Kasai et al., 2000; Valle-Levinson et al., 2003) has demonstratedthat the modification is mainly a slight shift of the position of thevelocity core, but the conceptual picture of the flow pattern doesnot change, i.e. the fresher water flows out of the estuary near thesurface while the saltier ocean water flows inward through themain channel. The Coriolis force only deforms the velocity structureto a certain extent, but the difference is not significant enough tochange the conclusions here. In a recent paper by Valle-Levinson(2008), the density-driven flow was discussed in terms of Kelvinand Ekman numbers and the conditions for laterally sheared andvertically sheared flows were analyzed with a straight channelwhen Coriolis force can be significant. It will be interesting to seehow will the lake situations be similar to or different from thatdiscussed in that paper, especially under the effect of windstraining. This, however, will require additional research beyondthe scope of this paper.

5.5. Numerical model experiments

Although the conceptual model has demonstrated the windstraining mechanism that facilitates the radial expansion of bottomintrusion of ocean water through the IC, the model is idealized. Tofurther demonstrate that the same mechanism operates in the LakePontchartrain under realistic bathymetry and boundary conditions,

151618

14

Distance from Industrial Canal (km)

Dep

th

b

elo

w su

rface (m

- M

SL

)

5 10 15-5

-4

-3

-2

-1

0

151618

14

14

-5

-4

-3

-2

-1

0Northerly wind at 5 m/s

Southerly wind at 5 m/s

a

b

Fig. 13. Cross-sectional view (left is south and right is north) of velocity and salinity structure along the northward direction of the plume into Lake Pontchartrain; vectors arevelocity (every other vector is shown in the horizontal direction), solid grey lines are salinity in PSU. (a) and (b) are results under northerly and southerly winds, respectively.


a Princeton Ocean Model (POM) is used here. The horizontalresolution of the model consists of 169�70 cells with variablemesh spacing from 40 to 50 m in the vicinity of the IC to approxi-mately 400 m in the center of the lake. The vertical grid spacing islogarithmic near the surface and near the bottom to have higherresolution in the surface and bottom boundary layers. The resolu-tion varies from a few centimeters in the boundaries to less than0.5 m in the mid-depth. The model is driven with tidal forcing atthe IC, Chef Menteur and Rigolets Passes, spatially and temporallyconstant wind stress, and tributary flows from the major rivers. Thesalinity boundary condition at the IC is linearly stratified withdepth, with surface and bottom values derived from field obser-vations by Georgiou (2002). The spin-up time for the model is 1 day,and the model is run for 7 days. Boundary conditions during thesimulation are held constant, except for tidal forcing.

The model predicts a typical depth-averaged flow pattern overthe domain consisting of two gyres rotating in the opposite direc-tions consistent with Signell and List (1997), and Haralampides(2000). Flow is downwind near the surface and in the shallowregions of the Lake (shoreline) and upwind in the deeper centralregions (Fig. 12). Although depth-averaged currents exhibit thedouble gyre pattern shown in Fig. 12, velocity variations in thevertical are non-uniform. Fig. 12 shows the circular plume undera northerly wind of 5 m/s. Fig. 13 shows the response of the velocityto wind forcing from the north and from the south, along the radialaxis of the analytical model presented earlier. As observed in thefield and by the analytical model, northerly winds produce down-wind flow near the surface (Fig. 13a). Near the bed, however, and tosatisfy continuity a return upwind flow is predicted by the model,which subsequently aids in the further expansion of the circularplume. Similarly, southerly winds produce downwind flow near thesurface and upwind flows near the bed (Fig. 13b). This results innear-bed currents that tend to suppress the expansion of the plumeinto the lake, as shown in Fig. 13b.

The model predicts the plume thickness to be of the order of1.5 m or greater near the IC, and 0.7–0.9 m near the advancing front

of the plume (Figs. 12 and 13a). Field data indicate that the thick-nesses range from 1 to 2 m near the IC and 0.3–0.6 m at the front ofthe plume, respectively. The predicted area and extent of the plumeby the model is very similar to field and satellite observations.

In summary, the expansion of the saltwater plume is in generalin the direction of the near-bed current, typically with an upwinddirection. Northerly winds favor the plume expansion to the north.For strong northerly winds, periodic mixing is observed near thesource during the ebb cycle, at times, disconnecting the densitycurrent from its source. On the other hand, southerly winds helpsuppress the northerly expansion of the plume but assist ina somewhat lateral expansion along the south shore to the east andwest.

Acknowledgments

The staff and students of the Earth Scan Laboratory are thankedfor developing and maintaining the MODIS products used in thisstudy. This project was funded by NSF Grant# OCE-0554674.Additional funds were provided by NASA URC-HBCU-02-0017-0002and NASA(2007) – Stennis-05, and NOAA NA06NPS4780197. Weappreciate the three anonymous reviewers whose constructivecomments and suggestions have helped the improvement of themanuscript.

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circular plumes in lake pontchartrain estuary under wind straining

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