On the Linkages Among Density, Flow, and Bathymetry ...arnoldo/ftp/papers/valle... · neap tides, while the July cruise occurred during spring tides. The bathymetry of the bay entrance

1437Q 2003 Estuarine Research Federation

Estuaries Vol. 26, No. 6, p. 1437–1449 December 2003

On the Linkages Among Density, Flow, and Bathymetry Gradients

at the Entrance to the Chesapeake Bay

ARNOLDO VALLE-LEVINSON1,*, WILLIAM C. BOICOURT2, and MICHAEL R. ROMAN2

1 Center for Coastal Physical Oceanography, Department of Ocean, Earth, and AtmosphericSciences, Crittenton Hall, Old Dominion University, Norfolk, Virginia 23529

2 Horn Point Laboratory, University of Maryland Center for Environmental Science, P. O. Box775, Cambridge, Maryland 21613

ABSTRACT: Linkages among density, flow, and bathymetry gradients were explored at the entrance to the ChesapeakeBay with underway measurements of density and flow profiles. Four tidal cycles were sampled along a transect thatcrossed the bay entrance during cruises in April–May of 1997 and in July of 1997. The April–May cruise coincided withneap tides, while the July cruise occurred during spring tides. The bathymetry of the bay entrance transect featured abroad Chesapeake Channel, 8 km wide and 17 m deep, and a narrow North Channel, 2 km wide and 14 m deep. Thetwo channels were separated by an area with typical depths of 7 m. Linkages among flows, bathymetry, and water densitywere best established over the North Channel during both cruises. Over this channel, greatest convergence rates alter-nated from the left (looking into the estuary) slope of the channel during ebb to the right slope during flood as a resultof the coupling between bathymetry and tidal flow through bottom friction. These convergences were linked to thestrongest transverse shears in the along-estuary tidal flow and to the appearance of salinity fronts, most markedly duringebb periods. In the wide channel, the Chesapeake Channel, frontogenesis mechanisms over the northern slope of thechannel were similar to those in the North Channel only in July, when buoyancy was relatively weak and tidal forcingwas relatively strong. In April–May, when buoyancy was relatively large and tidal forcing was relatively weak, the recur-rence of fronts over the same northern slope of the Chesapeake Channel was independent of the tidal phase. Thedistinct frontogenesis in the Chesapeake Channel during the increased buoyancy period was attributed to a strongpycnocline that insulated the surface tidal flow from the effects of bottom friction, which tends to decrease the strengthof the tidal flow over relatively shallow areas.

IntroductionStudies on the linkage between density gradients

and flow gradients have usually concentrated ontidal intrusion fronts and plume fronts (e.g., Gar-vine 1974; Luketina and Imberger 1989; Marmo-rino and Trump 1996; O’Donnell 1997; O’Donnellet al. 1998). A third type of fronts, the along-estu-ary or axial fronts (O’Donnell 1993), tends to belinked to bathymetric gradients. The formation ofaxial fronts has been explained only during floodtides (e.g., Nunes and Simpson 1985; Simpson andTurrell 1986; Huzzey and Brubaker 1988; Brownet al. 1991; Turrell et al. 1996) by invoking themechanism of differential advection of the along-estuary density field by the laterally sheared along-estuary flow. This mechanism is thought to allowthe development of surface transverse circulationfrom either bank of the estuary that causes axialconvergences along the middle of the channel orthalweg. The same mechanism has been used invarious studies (Sarabun 1980; Huzzey and Bubak-er 1988; Swift et al. 1996) to explain observations

* Corresponding author: tele: 757/683-5578; fax: 757/683-5550; e-mail: [email protected]

of late-flood axial convergence that actually ap-peared over the edge, not in the middle of thechannel. Most of the studies suggested that densitygradients are crucial for the development of trans-verse circulation associated with axial convergenc-es. These are reasonable explanations for conver-gences that appear during late flood stages, butcannot be used to explain along-estuary conver-gences during ebb stages as observed by Sarabun(1980), Ferrier and Anderson (1997), and Valle-Levinson et al. (2000).

The development of convergences over thechannel edges is also ubiquitous in the lower Ches-apeake Bay (e.g., Sletten et al. 1999), the JamesRiver (Valle-Levinson et al. 2000), and in coastallagoons with weak density gradients (Valle-Levin-son unpublished data). Supported by observationsin the James River and by results from an analyticmodel, Valle-Levinson et al. (2000) proposed thatthe location and timing of along-estuary conver-gences was primarily determined by the interactionbetween bathymetry and tidal flow. They postulat-ed that density gradients may contribute tostrengthen the convergences but not to formthem. The objectives of the present study are to

1438 A. Valle-Levinson et al.

Fig. 1. Map of the study area in the lower Chesapeake Bay showing the transect sampled as the white line between Cape Henryand Fishermans Island. The bathymetry is shown in shaded contours at intervals of 2.5 m and with labels for the Chesapeake andThimble Shoal Channels. The Chesapeake Bay Bridge Tunnel (CBBT) is represented by the black dotted line and E indicates theCBBT location for wind velocity and sea level measurements. A cross-section (looking into the estuary) of the transect sampled isshown in the upper panel.

extend the results of Valle-Levinson et al. (2000)by documenting the linkage of flow and densitygradients to bathymetry gradients during bothstages of the tidal cycle in the lower ChesapeakeBay, and proposing the dynamic underpinnings ofthese linkages.

Study AreaThe lower Chesapeake Bay is representative of

wide, partially mixed coastal plain estuaries with acharacteristic channel and shoals cross-sectionalbathymetry (Fig. 1). Physical oceanographic pro-cesses in the lower Chesapeake Bay are chiefly in-fluenced by bathymetry, wind, tidal, and buoyancyforcing. Despite the fact that the transect studiedhere is only approximately 2 km landward of thatpresented by Valle-Levinson et al. (1998), its ba-thymetry is decisively different. The portion of thebay studied here includes the confluence betweenthe Chesapeake Channel and the Thimble ShoalChannel. This junction depicts a broad bathymet-ric depression at least 8 km wide, with a maximumdepth of 17 m (Fig. 1). Immediately to the northof this juncture the bathymetry shoals rapidly to 6–

7 m within the 6-km wide Middle Ground. BetweenMiddle Ground and Fishermans Island lies theNorth Channel, with depths of 14 m that compareto those at the confluence of Chesapeake andThimble Shoal Channels and roughly double thetypical depth of Middle Ground.

Wind forcing in the lower Chesapeake Bay is sea-sonal and primarily from the northeast and south-west (Paraso and Valle-Levinson 1996). Northeast-erly winds prevail from late summer to early spring,while southwesterly winds dominate during thesummer. During any season, strong winds can oc-cur from either direction. The most energetic windevents are usually from the northeast or northwestduring late fall and winter, although southwesterlywinds can occasionally be very energetic.

Tidal forcing in the lower Chesapeake Bay is pre-dominantly semidiurnal (Browne and Fisher1988). The interaction among the three semidi-urnal tidal constituents (M2, N2, and S2) generatesfortnightly and monthly variability in the tidal cur-rents. Owing to the fact that the N2 constituentdominates over the S2 in the lower bay, there is amarked asymmetry between consecutive spring (or

Density, Flow, and Bathymetry Linkages 1439

neap) tides thus causing a primary and a second-ary spring (or neap) tide during one month. Dur-ing spring tides, the currents in the lower bay mayexceed 1 m s21.

Buoyancy forcing to the lower Chesapeake Bayis dominated by river discharge. River dischargepeaks during the months of March and April andis least during August and September. The meansurface salinity is lowest throughout the bay in theApril–May period and highest in September–No-vember, roughly 1 mo after the river discharge ex-tremes. The present study was conducted underneap and spring tides, relatively weak wind forcing,and during high and moderate buoyancy forcing.

Data Collection and ProcessingThe data collection consisted of repeating a 17-

km-long cross-estuary transect to capture the intra-tidal variability of the distribution of the flow anddensity fields across the entrance to the Chesa-peake Bay (Fig. 1). The cross-estuary transect wassampled throughout nearly four semidiurnal tidalcycles, first in the spring of 1997 and then in thesummer of 1997. The spring cruise was done April29–May 1, 1997, at neap tides. The summer cruisetook place July 20–22, 1997, during secondaryspring tides. These cruises were aboard the R/VCape Henlopen.

Each of the two cruises included records of un-derway current and density profiles, and of surfacetemperature and salinity values. This samplingstrategy allowed calculation of horizontal gradientsof density and flow, and determination of the ver-tical structure of properties where the gradientswere most intense. Velocity data were obtainedwith a 614.4 kHz Broad Band RD InstrumentsAcoustic Doppler Current Profiler (ADCP). TheADCP was mounted looking downward on a small(1.2 m long) catamaran and towed to the starboardside of the ship at speeds of approximately 2.5 ms21. Velocity profiles were recorded at intervals of5 s and averaged over 30 seconds, which gave ahorizontal spatial resolution of about 75 m. Thebin size for vertical resolution was 0.5 m and theclosest bin to the surface was located at a depth ofnearly 2 m. These settings yielded an accuracy of0.01 m s21 in the measured velocities. Compass cal-ibration and data correction were performed fol-lowing Joyce (1989) with navigation recordedthrough a Trimble Differential Global PositioningSystem.

At the same time that the ADCP was beingtowed, water temperature and salinity profiles werebeing acquired with a Seabird SBE-19 Conductivity-Temperature-Depth (CTD) recorder mounted inan undulating towed body Scanfish MK II. TheScanfish was towed from the port side of the ship

and undulated at vertical rates of 0.5 m s21 within2 m from the surface and bottom. This yieldedminimum horizontal resolutions of 200 m and atypical vertical resolution of 0.25 m as the samplingfrequency of the CTD was 2 Hz. The separationbetween the ADCP and the undulating CTD wasapproximately 50 m at the surface and was takeninto account to correct the location of each mea-surement recorded by the CTD. Near-surface tem-perature and salinity values (at approximately 1 mdepth) were recorded with a Sea Bird SBE-1621thermosalinograph. The thermosalinograph re-corded one value every 10 s—i.e., it provided aspatial resolution of 25 m.

The towing speed of 2.5 m s21 allowed coverageof the 17-km transect in 2 h. By the end of eachcruise, the transect at the bay entrance was occu-pied 24 times. The current velocity data at each ofthe 24 transects were rotated by 118T to coincidewith a reference frame in which the direction per-pendicular to the entrance of the bay is denotedby x, positive toward the ocean, and y is positive inthe 118T direction (Fig. 1). The principal compo-nent of the flow (the component with largest var-iance) is u and the transverse component is v. Al-though the current orientation changes through-out the bay entrance transect, the u component(rotated 118T) accurately represents inflows andoutflows, and the v component reflects flow ap-proximately aligned with the transect. Different ro-tations of the axes did not affect the essence of theresults.

Instantaneous surface flow (u, v) and salinity Svalues were represented in the space-time domain(Fig. 2) in order to describe the intratidal varia-tions of these parameters, calculate transverse gra-dients of u, v, and S, and portray the evolution ofgradients throughout the four tidal cycles sampledand identify the regions of enhanced gradientsalong the transect. The space dimension y was as-signed as the distance from the southernmost endof the transect off Cape Henry. The time dimen-sion t was the number of hours elapsed after mid-night of the day when the experiment com-menced. Once u, v, and S were cast in the space-time domain, they were then interpolated onto auniform grid with Dy of 200 m and Dt of 1 h. In-terpolation was carried out through the construc-tion of Delaunay triangulations with the InteractiveData Language (IDL) software. Selected verticalsections of u, v, and S, for each of the two cruiseswere used to represent the vertical distribution ofproperties in the area of enhanced gradients.

Wind velocity and sea level were recorded at theChesapeake Bay Bridge-Tunnel by the NationalOceanic and Atmospheric Administration’s Na-tional Ocean Service and river discharge data were


Fig. 2. Instantaneous surface velocities (in the distance-timedomain) across the entrance to the Chesapeake Bay at the timesof observation during the cruise on April 29–May 1, 1997. Floodflow points upward. The bathymetry of the transect is presentedin the lower panel, looking into the estuary.

provided by the United States Geological Survey.The following section presents the wind, sea level,and river discharge conditions that affected the pe-riods of observation, followed by the description ofthe intratidal flow and salinity variations, and thelink of their respective transverse gradients to ba-thymetry. The linkages were documented with a setof velocity profiles measured across one section atthe Chesapeake Bay entrance in the spring andsummer of 1997. The dynamical underpinnings ofthe linkages were explained through examinationof the transverse variations of the along-estuarymomentum balance, i.e., through a simplified ver-sion of the relative vorticity equation.

ResultsDuring the period of observation of April 29–

May 1 wind forcing was, for the most part, relativelyweak (Fig. 3). The experiment began near the con-clusion (the last 4 h) of a northeasterly wind pulseof typical magnitudes of 10 m s21. During the restof the experiment, winds were dominated by a

southerly component that increased as the exper-iment progressed. By the end of the experimentthe winds were southwesterly at almost 10 m s21.These southwesterly winds may have produced up-welling off Cape Henry as reflected by a markedincrease in surface salinity and decrease in surfacetemperature. During July 22–24, winds were weak-er than in the April–May cruise (Fig. 3) and causedminor effects on u, v, and S. In the April–Maycruise, the subtidal sea level showed a decreasingtrend, while in the July cruise it tended to increase.The total river discharge into the bay was largerduring April–May than during July (Fig. 3c). Thiswas reflected in the different range of salinity var-iations observed in both cruises as described next.

INTRATIDAL VARIABILITY OF SALINITY AND FLOW

Surface salinity ranged from 17 to 27 in theApril–May cruise and from 24 to 31 in the Julycruise (Fig. 4). Flow magnitudes approached 0.9 ms21 in the first cruise (around neap tides) and sur-passed 1 m s21 in the second cruise (secondaryspring tides). In both cruises, the lowest and high-est salinities were usually found off Cape Henryand Fishermans Island, respectively, as expectedfrom the effects of the earth’s rotation. One ex-ception occurred toward the end of the first cruise,when the highest salinity was found off Cape Hen-ry, at the southern portion of the entrance (Fig.4a). The high salinity developed with the onset offlood tidal flow, in contrast to previous flood flows.These high salinity values coincided with low watertemperatures at the surface (not shown) and a pe-riod of southwesterly winds (Fig. 3), indicative ofupwelling off Cape Henry.

In both cruises, the strongest tidal flows ap-peared over both the Chesapeake and North chan-nels and the weakest flows appeared over MiddleGround—i.e., over the shallow portion betweenthe channels (Fig. 4). The tidal flow over the chan-nels lagged behind the flow over Middle Ground.This distribution of the tidal amplitude and of thephase lags was consistent with those expected fromthe effects of bottom friction (e.g., Valle-Levinsonand Lwiza 1995; Li and Valle-Levinson 1999). Thetransverse variability of the tidal current ampli-tudes and phases defined regions of strongest gra-dients in the flow, which corresponded to the tran-sition between channels and shoals.

During both cruises, surface flow and salinity dis-played covariability that was almost 90 degrees outof phase, i.e., extreme salinity values correspondedto periods of slack tidal currents (Fig. 4). This var-iability suggested the dominance of the advectionof the along-estuary salinity gradient by the along-estuary tidal flow in determining the temporalchanges in salinity. In general, the lowest salinities


Fig. 3. Meteorological and river discharge conditions during the periods of observation. (a) and (b) indicate wind velocity (vectors)and subtidal sea level (thick line) for the periods April 29–May 1, and July 22–24, respectively. (c) indicates river discharge during1997 from the three most important rivers.

were restricted to the 8-km wide Chesapeake Chan-nel (Fig. 4). The edge of this channel seemed todelimit the buoyant plume of the bay and reflectedthe appearance of salinity fronts associated withthis plume. On the other hand, the highest salin-ities were confined to the North Channel duringthe first three tidal cycles of the first cruise (Fig.4a). During those three tidal cycles, the southernedge of the North Channel (the left edge lookinginto the estuary) seemed to limit a branch of highsalinity water appearing at the bay entrance. Dur-ing the second cruise, the highest salinity extendedover the entire northern half of the transect. Thiswas likely due to the combination of weaker buoy-ancy and stronger tidal currents during the Julycruise relative to the April–May cruise. The com-bination of strong tidal and weak buoyancy forcingin July should have allowed the intrusion of highsalinity water with every flood period. The linkageamong salinity, flow, and bathymetry gradients isexplored next through estimation of transversegradients with the data available.

FLOW AND SALINITY GRADIENTS

To explore linkages among flow, salinity, and ba-thymetry we calculated transverse gradients of flow(u, v) and salinity S. The transverse gradients wereobtained with a forward (in y) discretization

scheme. The gradients were represented by 1) ]v/]y, denoting divergence of lateral flow, ]u/]y, por-traying transverse shears of the along-estuary flow,and ]S/]y. The divergence of lateral flow ]v/]y maybe a reasonable proxy for horizontal divergence inthese systems because the divergence of the along-estuary flow ]u/]x tends to be smaller by one orderof magnitude (Valle-Levinson et al. 2000). For thisparticular data set, we cannot assess the influenceof ]u/]x on the total divergence, but we acknowl-edge that this is a source of uncertainty in the rep-resentation of divergences.

DivergencesThe distribution of ]v/]y in the lower Chesa-

peake Bay showed distinguishable patterns relatedto bathymetry changes. These patterns were mostmarked near the northern end of the transect, i.e.,in the North Channel (dark-blue filled contours ofFig. 5). Largest convergence rates lasted between2 and 3 hours and approached values of 1023 s21

over the slopes of the channel. Looking into theestuary, convergence patterns appeared over theleft edge of North Channel (dark-blue filled con-tours at 15 km) during ebb and over the right edgeof the channel (dark-blue filled contours at 17 km)during flood. This alternation persisted duringboth cruises although not as clearly on the right


Fig. 4. Surface velocity vectors and salinity (colored contours) interpolated to a uniform time-space grid during both cruises. Thewhite contours indicate salinity at intervals of 1. Closely spaced white dots represent the time and location of each observation. Thelower panels represent the bathymetry of the transect sampled. (a) indicates April 29–May 1, 1997, cruise, (b) indicates July 22–24,1997, cruise. Flood flow points upward.

Fig. 5. Surface velocity vectors and divergence rates (colored contours) interpolated to a uniform time-space grid during bothcruises. The colored contours denote values of divergence (1024 s21) at intervals of 1. Blue denotes convergences. The white contoursseparate positive (divergence) from negative (convergence) values. Flood flow points upward. Yellow rectangles highlight eventsdescribed in the text. (a) indicates April 29–May 1, 1997, cruise, (b) indicates July 22–24, 1997, cruise.


Fig. 6. Surface velocity vectors and transverse shears of the along-estuary tidal flow (shaded contours) interpolated to a uniformtime-space grid during both cruises. The shaded contours denote values of shears (1024 s21) at intervals of 1. The white contoursseparate positive from negative values. White-dashed rectangles highlight events described in the text. (a) indicates April 29–May 1,1997, cruise, (b) indicates July 20–22, 1997, cruise. Flood flow points upward.

Fig. 7. Surface velocity vectors and transverse gradients in salinity (shaded contours) interpolated to a uniform time-space gridduring both cruises. The shaded contours denote gradients (1023 m21) at intervals of 0.05. The white contours separate positive fromnegative gradients. White-dashed rectangles highlight events described in the text. (a) indicates April 29–May 1, 1997, cruise, (b)indicates July 20–22, 1997, cruise.


edge of the channel in the second cruise (Fig. 5b)because of lack of measurements across the entireNorth Channel. Such alternation was also consis-tent with that observed in the James River by Valle-Levinson et al. (2000). The alternation of conver-gences from the left edge to the right edge of thechannel is considered to be a robust feature attri-buted to the interaction of tidal flow with bathym-etry under the spatially different effects of bottomfriction. Bottom friction causes phase lags of thetidal currents from channels to shoals and conver-gent flows at the channel edges.

Another area of convergences appeared over thenorthern edge of the Chesapeake Channel (Fig.5), around 8 km. Convergences were not as strongas over North Channel during the April–Maycruise (Fig. 5a), but still they were apparent duringlate flood to early ebb periods of the July cruise(starting at 30 h, 42 h, and 54 h on Fig. 5b). Thiswas likely favored by weaker buoyancy and strongertidal forcing in the July cruise relative to the April–May cruise. In general, the area of convergencesover the northern edge of Chesapeake Channelwas closely linked to the outer edge of the Chesa-peake Bay outflow plume (Sletten et al. 1999). Theebb convergences observed around 2 km in theJuly cruise were likely an effect of the confluenceof Thimble Shoal and Chesapeake Channels.

Transverse ShearsThe areas of strongest convergence in Fig. 5

were linked to large transverse shears in the along-estuary flow ]u/]y (Fig. 6). The distributions of]u/]y during the first cruise showed very similaralternations over the North Channel (light-shadedcontours on Fig. 6a) as the pattern of convergenc-es (Fig. 5a). Large positive shears, close to 5 3 1024

s21, were clearly observed during ebb flows overthe left slope of the North channel (looking intothe estuary). This meant that the ebb flow in-creased rapidly from the shoal to the channel dueto less bottom friction in the channel. Analogouslinkages between ]u/]y and ]v/]y over NorthChannel were observed in the July cruise (Fig. 6b).

Consistently with the distribution of convergenc-es over the northern edge of the ChesapeakeChannel there was no apparent regular pattern oftransverse shears at this location during the firstcruise (km on Fig. 6a). In agreement with the con-vergences in this area, there was a regular patternof shears during the July cruise (Fig. 6b). In July,enhanced positive shears (light-shaded contours)appeared during flood at approximately 8.2 kmand at 30 h, 42 h, and 54 h, as the tidal currents(negative) decreased from the channel to theshoal. Increased negative shears (dark shaded con-tours) appeared during ebb at approximately 7.5

km and at 22 h, 34 h, 47 h, and 60 h as the tidalcurrents (positive) decreased from the channel tothe shoal. This distinct behavior over the Chesa-peake Channel from the first to the second cruisewas attributed, once more, to the weakened buoy-ancy and stronger tidal currents during the secondcruise that allowed a tighter frictional coupling be-tween tidal currents and bathymetry.

Transverse Salinity GradientsThe transverse salinity gradients were sometimes

related to the flow gradients. During the firstcruise, increased salinity gradients were found overthe left slope of North Channel (;15 km) duringthe second and third ebb cycles, i.e., at 35 and 50h (light-shaded contours on Fig. 7a). These twofrontal regions were closely related to large con-vergences and transverse shears (Figs. 5a and 6a).The interesting feature of these two fronts was thatsalinity increased in the channel, relative to the ad-jacent shoals, during ebb. This increase was con-trary to the decrease expected from the greateradvection of fresher waters, relative to the regionsoutside of the channel, by stronger ebb currents(e.g., Nunes and Simpson 1985; Huzzey and Bru-baker 1988). Below, we shall examine the verticalstructure of one of these fronts, the one at 50 h,and offer a possible reason for this increase of sa-linity in the channel during ebb. During the Julycruise, salinity increases also appeared in NorthChannel. This time, the increment appeared closeto the right edge of the channel and by the endof ebb (Fig. 7b). Furthermore, these increaseswere not related to enhanced flow gradients (seeFigs. 5b and 6b).

Over the northern edge of Chesapeake Chan-nel there were no clear tidal alternations of salin-ity gradients during the first cruise. Nonetheless,strong gradients appeared concentrated between7 and 9 km (light- and dark-shaded contours onFig. 7a). This distance was equivalent to the inter-nal radius of deformation obtained from theproduct of the buoyancy frequency (N equalsÏ2(g/r)(]r/]z), where g is the acceleration dueto gravity, r is water’s density, and z is the verticalcoordinate, positive upward) times the water col-umn depth H, divided by the Coriolis parameterf. During the first cruise, N was typically 0.077 s21

over a depth of 9 m, which gave a radius of defor-mation of 8 km, in the middle of the location ofmarked frontal features (Fig. 7a). These frontswere related to the Chesapeake Bay outflow plumeand were probably isolated from bathymetric influ-ences because their timing was not related to thetidal flow interacting with bathymetry gradients asobserved over the North Channel. There were twoinstances, however, when large salinity gradients


Fig. 8. Vertical sections, looking into the estuary, of along-estuary (contours) and across-estuary (vectors) flow during ebbon May 1, 1997. Contour interval is 10 cm s21. The upper panelwas sampled from left to right and the lower panel from rightto left.

coincided with increased convergences. One was ata distance of 8 km and around 35 h, during ebb,and the other one at a distance of 9.3 km andaround 45 h, at the end of flood (Figs. 5a and 7a).In the latter instance, the salinity gradients and theconvergences were also related to increased trans-verse shears (Fig. 6a). This linkage developed overthe shallow Middle Ground and did not coincidewith a bathymetric gradient. During the secondhalf of the second cruise the coupling among gra-dients in bathymetry, tidal flow, and salinity wasmore evident than in the first cruise (Fig. 7b). En-larged gradients appeared by the end of flood overthe northern edge of Chesapeake Channel, at adistance of 8.5 km, and at 43 h and 54 h, whichwere linked to increased ]u/]y (Fig. 6b) and neg-ative ]v/]y (Fig. 5b). Similarly, increased salinitygradients in late ebb developed twice, at a distanceof 7.3 km and at 47–48 h and 59 h, concurrentlywith enlarged negative ]u/]y but under weak con-vergences. As mentioned above, buoyancy was lessand tidal forcing was stronger than during theApril–May cruise. The different forcings couldhave allowed the surface tidal flow, modified by thebathymetry, to modulate the position of the plume,at least during the second half of the cruise, whichwas when the modulation was apparent. This link-age produced by the tidal flow interacting with ba-thymetry and the salinity field was further exploredby examining the vertical structure of the flow andsalinity fields at two selected fronts that developedover North Channel, one during each cruise.

FRONTS OVER NORTH CHANNEL

The first front examined appeared at a distanceof 15 km and at 50 h soon after maximum ebbduring the first cruise (Figs. 5a, 6a, and 7a). Thevertical structure of u at the front over NorthChannel showed marked transverse shearsthroughout the water column (Fig. 8). The regionof strongest transverse shears, as denoted by theclosely spaced contours, migrated from the chan-nel’s slope toward the channel’s edge as distancefrom the surface increased. The small bump in themiddle of the channel, at 15 km, partitioned thetidal outflow below 5 m as indicated by the iso-tachs. Similar spatial variations could be noticedfor the transverse flow, which showed marked con-vergences associated with the region of strongtransverse shears (Fig. 8). It is noteworthy that thetransverse flows associated with the convergenceswere in the same direction throughout the watercolumn in contrast to the proposed helicoidaltransverse circulation resulting from axial conver-gences (Nunes and Simpson 1985), but in agree-ment with observations in the James River (Valle-Levinson et al. 2000). Secondary circulation devel-

oped within the first 5 km of the ChesapeakeChannel during late ebb (upper panel of Fig. 8)and early flood (lower panel of Fig. 8). This typeof flow has been attributed to curvature effectsaround a headland (e.g., Geyer 1993), i.e., aroundCape Henry in this case.

The flow gradients observed at 50 h in theApril–May cruise were linked to a marked salinityfront at 15 km that extended throughout the watercolumn (Fig. 9). Two branches of high salinity wa-ter coincided with the outflow bifurcation over thelower half of the water column. The concurrenceof flow and salinity gradients indicated that the sa-linity front was produced by the greater advection,relative to the region outside of the channel, ofhigh salinity water from an upstream location. Thismechanism had not been reported as causative ofalong-estuary fronts. The mechanism of differen-tial advection of the density field by the tidal cur-rents (e.g., Nunes and Simpson 1985; Huzzey andBrubaker 1988) would have predicted flow diver-gence and low salinity in the channel, contrary toour observations. As seen from the surface salinityvariations throughout the 4 tidal cycles observedin the April–May cruise (Fig. 4a), relatively highersalinity persisted in the channel with respect to theadjacent shoal. This probably resulted from the lo-cation of the channel where Coriolis accelerationsfavor intrusion of high salinity water into the Ches-apeake Bay. The transverse structure of the alongestuary density gradient also should play a role inthe formation of these fronts. Our sampling didnot resolve along-estuary gradients so we could not


Fig. 9. Same as Fig. 8 but for salinity fields. Contour intervalis 1. Fig. 10. Vertical sections, looking into the estuary, of along-

estuary (contours) and across-estuary (vectors) flow during ebbon July 23, 1997. Contour interval is 10 cm s21. The upper panelwas sampled from left to right and the lower panel from rightto left.

Fig. 11. Same as Fig. 8 but for salinity fields. Contour inter-val is 1.

determine the relative importance of this mecha-nism.

The second front examined appeared at a dis-tance of 14.7 km and at 33 h of the July cruise,also during ebb tidal flow (Figs. 5b, 6b, and 7b).In this case, the region of strongest transverseshears of u over North Channel extended roughlystraight down from surface to bottom (Fig. 10).The southern edge of North Channel (between 13and 14 km) markedly dampened the outflow, anal-ogous to the northern edge of Chesapeake Chan-nel (between 8 and 9 km), and allowed the devel-opment of large transverse shears. Strong conver-gences of lateral flow also appeared over these re-gions, most appreciably in the North Channel. Alsonoteworthy was the secondary circulation aroundCape Henry, within 4 km inside the ChesapeakeChannel, that appeared only in late flood-early ebb(upper panel of Fig. 10). The salinity front linkedto the flow gradients over the North Channel wasnot as dramatic as the one in the April–May cruisebut still was apparent (Fig. 11). The front was pro-duced by the outflow of low salinity water, in con-trast to the first cruise, in the form of a buoyantwedge. Although the transverse shears and conver-gences were practically depth-independent (Fig.10) the salinity gradients showed appreciabledepth-dependence. This buoyant wedge was ex-plained by the differential advection of the densityfield by the tidal currents (Huzzey and Brubaker1988) as clearly seen through the comparison ofFigs. 10 and 11 over the region to the north of 10km. The differential advection mechanism wouldhave predicted divergence not convergence. Thisis perhaps owing to a stronger linkage betweentransverse shears and convergences in the forma-

tion of along-estuary fronts, rather than betweendensity field and convergences (Valle-Levinson etal. 2000). We also propose here that the dynamiclinkage between transverse shears and convergenc-es occurs through the vertical component of vor-ticity as explored next.

LINKAGES THROUGH VORTICITY

The vertical component of the vorticity relativeto a rotating frame ]v/]x 2 ]u/]y may be expand-ed through cross-differentiation of the horizontalmomentum equations:


Fig. 12. Values of ]v/]y, f 2 ]u/]y, and the local contribu-tion to the first term on the right-hand side of Eq. 5. The ad-vective contribution to the temporal changes of the absolutevorticity has been neglected. The lines represent the maximumvalue, at any given time, that appeared between 14.6 and 15 km.(a) indicates April 29–May 1, 1997, cruise, (b) indicates July 20–22, 1997, cruise.

] ]u ]u ]u ]u1 u 1 v 1 w 2 fv1]y ]t ]x ]y ]z

0]h g ]r5 2g 2 dz 1 Friction (1)E x2]x r ]x

2z

] ]v ]v ]v ]v1 u 1 v 1 w 1 fu1]x ]t ]x ]y ]z

0]h g ]r5 2g 2 dz 1 Friction (2)E y2]y r ]y

2z

where f is the Coriolis parameter (s21), h is surfaceelevation (m), r is water density (m s), g is theacceleration due to gravity (9.8 m s), and w is thevertical velocity component (m s21). Differentia-tion of Eq. 1 and Eq. 2 and subtraction yields, aftersome algebra:

dz ] f ]u ]v ]u ]v1 v 1 f 1 1 z 11 2 1 2dt ]y ]x ]y ]x ]y

0 0] g ]r ] g ]r5 2 dz 1 dzE E1 2 1 2]x r ]y ]y r ]x

2z 2z

] ]1 (Friction ) 2 (Friction ) (3)y x]x ]y

(e.g., Gill 1982, section 7.10; Pedlosky 1979, sec-tion 2.4 for the left-hand side of Eq. 3, where z isthe relative vorticity ]v/]x 2 ]u/]y). The differ-entials with respect to x may be neglected if thealong-estuary gradients are one or more orders ofmagnitude smaller than the across-estuary gradi-ents, which was likely the case here. Then, the ab-solute vorticity zA may be re-written as f 1 5 f 2z̃(]u/]y), and Eq. 3 becomes:

0dz ]v ] g ]r ]A 1 z 5 dz 2 (Friction ) (4)a E x1 2dt ]y ]y r ]x ]y2h

And solving for ]v/]y, which represents a proxy forthe divergence of the flow, yields:

0]v 1 ]z 1 ] g ]rA5 2 1 dzE1 2]y z ]t z ]y r ]xA A 2h

1 ]2 (Friction ) (5)xz ]yA

Note that the first term in the right-hand side ofEq. 5, which represents the local temporal changesof absolute vorticity, has been linearized (relativeto Eq. 4) as suggested by Mied et al. (2000). Near-surface observations of ]u/]y in the North Chan-nel (15 km) from two cruises in the lower Chesa-peake Bay were used to assess that term, which wasthe one that could be most reliably evaluated. The

second term in the right-hand side of Eq. 5 rep-resented the transverse variability of the along-es-tuary density gradient, and the third term depictedthe transverse variability in friction. In Fig. 12, wecompare the values of ]v/]y to those of zA (alone)and the first term on the right-hand side of Eq. 5.The values of ]v/]y were closely followed by thevalues of zA and by the local changes of the abso-lute vorticity. The similarity between ]v/]y and thechanges in absolute vorticity was maximized by aconstant offset of 4 3 1024 s21, which should haverepresented a bias in the estimates and the com-bined contribution of the transverse variability ofdensity gradients and friction to the convergencerates. Nonetheless, the first term on the right handside of Eq. 5 reproduced well the timing of theconvergences. This relationship indicated a tightcoupling between transverse shears and conver-gence rates as alternatively proposed by Mied et al.(2000, p. 8654) through the ‘‘tilting of planetaryvorticity.’’ The other two terms on the right hand


side of Eq. 5 should conceptually contribute to theconvergences, as pointed out by Nunes and Simp-son (1985) for the transverse variability in the den-sity field, and by Bowman and Iverson (1977) forthe transverse variability in mixing. The relativecontribution of these two mechanisms, as well asthat from the advection of vorticity, remains to beelucidated. The present analysis (Fig. 12) did in-dicate that the convergence rates were closelylinked to the transverse shears of the along-estuaryflows, through the absolute vorticity. The trans-verse shears, which were of similar magnitude tothat of the convergences, were linked to the areasof bathymetry changes, as demonstrated analyti-cally by Li and Valle-Levinson (1999).

Summary

The strongest flow convergences alternated overthe left and right slopes of the North Channel(looking into the estuary) during ebb and floodperiods, respectively. These gradients in flow andbathymetry were linked to strong transverse shearsin the along-estuary flow and to fronts in the salin-ity field. The linkage was best defined over the leftslope of the channel during ebb periods. Thetransverse shears of the along-estuary tidal flowwere produced by lateral differences in tidal cur-rent amplitude and phase triggered by transversebathymetry changes. Through the vorticity equa-tion, we propose that there are three mechanismsthat may explain convergences/divergence pat-terns: linkage through the transverse shears of thealong-estuary flow; linkage through lateral varia-tions of the along-estuary density gradient; andlinkage through lateral variations of frictional forc-es. The observations obtained in this study allowedevaluation of the first mechanism, which appearedto reproduce the timing and approximate magni-tude of the convergences. It is proposed to be acrucial mechanism that produced fronts in areasof strong coupling between tidal flows and bathym-etry. The other two mechanisms should influencethe magnitude of the convergences and requirefurther evaluation.

ACKNOWLEDGMENTS

This study was funded by the U.S. National Science Founda-tion as part of the Land-Margin Ecosystem Research in theChesapeake Bay. The study Trophic Interaction in Estuarine Sys-tems (ITES) was funded under NSF Award DEB19412133. AVLacknowledges funding from NSF Award 9529806 that allowedhim to participate in the LMER project. We appreciate the ded-ication of the crew of the R/V Cape Henlopen and the efforts indata collection and preliminary processing by Lorraine Brasseur(formerly Heilman) and Cathy Lascara. This is UMCES Contri-bution # 3629.

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Received for consideration, April 15, 2002Revised, December 6, 2002

Accepted for publication, January 13, 2003

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On the Linkages Among Density, Flow, and Bathymetry ...arnoldo/ftp/papers/valle... · neap tides, while the July cruise occurred during spring tides. The bathymetry of the bay entrance