Arnoldo Valle-Levinson

Effects of Bathymetry, Friction, and Rotation on Estuary-Ocean Exchange

An analytical model that includes pressure gradient, friction, and the earth’s rotation in both components of the flow is used to study the transverse structure of estuarine exchange flows and the nature of transverse circulation in estuaries of arbitrary bathymetry. Analytical results are obtained for generic bathymetry and also over real depth distributions and are compared with observations. This study extends previous efforts on the topic of transverse structure of density-induced exchange flows in three main aspects: 1) the analytical model explores any arbitrary bathymetry; 2) the results reflect transverse asymmetries, relative to a midchannel centerline, associated with the effects of the earth’s rotation; and 3) the transverse circulation produced by the analytical model is examined in detail. Analytical results over generic bathymetry show, in addition to the already reported dependence of exchange flow structure on the Ekman number, two new features. First, the transverse structure of along-estuary flows shows the earth’s rotation effects, even in relatively narrow systems, thus producing transverse asymmetries in these flows. The asymmetries disappear under strongly frictional (high Ekman number) conditions, thus illustrating the previously documented pattern of inflow in channels and outflows over shoals for typical estuaries. Second, transverse flows resemble a ‘‘sideways gravitational circulation’’ when frictional effects are apparent (Ekman number greater than ;0.1) responding to a transverse balance between pressure gradient and friction. These transverse flows reverse direction under very weak friction and reflect Coriolis deflection of along-estuary flows, that is, geostrophic dynamics. All examples of observed flows are satisfactorily explained by the dynamics included in the analytical model.

The effects of channels and shoals on exchange between the Chesapeake Bay and the adjacent ocean

The role of bathymetric changes in determining the transport of water and salt in the lower Chesapeake Bay (LCB) was investigated using high-resolution acoustic Doppler current profiler (ADCP) and conductivity-temperature-depth profiles. A cross-channel transect was repeated eight times during neap tides on October 6–7, 1993, which illustrated the lateral structure of the longitudinal and transverse flow fields and the intratidal variations in the flow structure across the LCB. Amplitude and phase of the M2 tidal component, as well as the mean flow velocity, were calculated using least squares fitting at every point of a uniform grid obtained from the ADCP data. The results differ from the classical two-layer pattern of estuarine circulation modified by Coriolis effects but are consistent with recent hydrographic observations. Semidiurnal flow was highest over the navigational channels, and lateral gradients were strongest in regions of sharp bathymetric changes. The phase lag of the semidiurnal flow also showed lateral and vertical gradients that represented advances at the bottom with respect to the surface and over the shoals in relation to the channels. The section of the water column measured indicated a mean outflow of 0.7×104 m3/s and a mean inflow of 1.3×104 m3/s. The apparent gain of water by the estuary during the period of observation can be explained by meteorologically forced net barotropic inflow. The depth-averaged mean longitudinal flow consisted of inflow in the navigational channels and outflow over the shoals. The mean transverse flow showed near-surface convergence over the channels. We propose a possible explanation for the observed flow and density structure as follows: the barotropic and baroclinic forcing interact with the bathymetry to extend the inflow from the bottom to the surface, thereby inducing a transverse circulation that yields near-surface convergence over the channels.

Lateral entrapment of sediment in tidal estuaries: An idealized model study

Two physical mechanisms leading to lateral accumulation of sediment in tidally dominated estuaries are investigated, involving Coriolis forcing and lateral density gradients. An idealized model is used that consists of the three?dimensional shallow water equations and sediment mass balance. Conditions are assumed to be uniform in the along?estuary direction. A semidiurnal tidal discharge and tidally averaged density gradients are prescribed. The erosional sediment flux at the bed depends both on the bed shear stress and on the amount of sediment available in mud reaches for resuspension. The distribution of mud reaches over the bed is selected such that sediment transport is in morphodynamic equilibrium, that is, tidally averaged erosion and deposition of sediment at the bed balance. Analytical solutions are obtained by using perturbation analysis. Results suggest that in most estuaries lateral density gradients induce more sediment transport than Coriolis forcing. When frictional forces are small (Ekman number E 0.02), the lateral density gradient mechanism dominates and entraps sediment in areas with fresher water. Results also show that the lateral sediment transport induced by the semidiurnal tidal flow is significant when frictional forces are small (E ? 0.02). Model predictions are in good agreement with observations from the James River estuary.

A two‐dimensional analytic tidal model for a narrow estuary of arbitrary lateral depth variation: The intratidal motion

An innovative method is introduced to solve a two-dimensional, depth-averaged analytic model for narrow estuaries or tidal channels with arbitrary lateral depth variations. The solution is valid if the lateral variation of the amplitude of tidal elevation (|Δa|) is small, i.e., |Δa| ≪ a, where a is the amplitude of the tidal elevation. This assumption is supported by a 60-day observation of elevation in the James River Estuary using pressure sensors at both sides of a cross section of the estuary. The error introduced by the solution is of the order of |Δa|/a, which has a maximum of ∼5% in the James River Estuary. The propagation of the tidal wave (elevation) is therefore essentially one-dimensional (along the estuary), regardless of the depth distribution, whereas tidal velocity has a strong transverse shear and is three-dimensional in general. Dozens of depth functions in six groups of various forms are used to calculate the solution. The tidal velocity is highly correlated with the bathymetry. The largest amplitude of the along-channel velocity is in the deepest water. The phase of the along-channel velocity in the shallow water leads that in deep water, causing a delay in time of flood or ebb in the deep water. The transverse velocity is generally small in the middle of a channel but reaches its maximum over the edges of bottom slopes. The depth function has a significant effect on the ellipticity and the sense of rotation of the tidal ellipses. By fitting the observed phase of semidiurnal tide in the James River Estuary to the phase of the momentum equation, we have obtained optimal values of the drag coefficient: 1.5 × 10−3 and 1.8 × 10−3 for the spring and neap tides, respectively. Then we apply these values of the drag coefficient and the model to the James River Estuary using the real bathymetry. Results show remarkable agreement between the observations and the model along the transects for both spring and neap tides. The cross-channel phase difference of the along-channel velocity between the channel and the shoal is found to be ∼1 hour, a value consistent with that from the model. The model-estimated lateral variation of elevation is 2.5% of the tidal amplitude, which is slightly smaller than the observed value.

Spatial Gradients in the Flow Over an Estuarine Channel

Acoustic Doppler current profiles were measured for a twelve-hour period on February 21, 1997 across Thimble Shoal channel, lower Chesapeake Bay, for the purpose of determining bathymetrically-induced spatial gradients in the flow and their implications for the lateral momentum balance in estuaries. A least-squares fit to semidiurnal and quarter-diurnal harmonics was used to separate the tidal and subtidal contributions to the observed flow. The period of observation was characterized by onshore winds and subtidal inflow everywhere along the transect sampled but strongest in the channel. Spatial gradients in both the tidal and subtidal horizontal flows showed that the greatest lateral shears and convergences were found where the bathymetric changes were sharpest, i.e., on the shoulders of the channel. The ratio of the quarter-diurnal to the semidiurnal tidal amplitudes was greatest over the channel shoulders, for both the along- and across-estuary flow components, and indicated the importance of non-linear effects there. The nonlinear term caused by across-estuary divergence was larger than the Coriolis term over the channel shoulders. The nonlinear contribution was comparable to the Coriolis acceleration in the subtidal and tidal lateral momentum balances. For the tidal balance, the local accelerations were also as important as the Coriolis accelerations. Equivalent results in the momentum balances were obtained with another data set of October 1993. Contrary to the customary assumption, the across-estuary momentum balance in this area was ageostrophic.

On the relative importance of the remote and local wind effects on the subtidal exchange at the entrance to the Chesapeake Bay

Water velocity data from acoustic Doppler current proe lers and electromagnetic current meters deployed at six separate locations across the entrance of the Chesapeake Bay from mid-April to early July of 1999 and from early September to mid-November of 1999 were used in conjunction with wind velocity and sea level records to describe the characteristics of the wind-induced subtidal volume exchange between the bay and the adjacent continental shelf. The current measurements were used to estimate volume e uxes associated with the local and remote wind-induced bay-shelf exchange over time scales of 2‐ 3 days. The results show that at these relatively short subtidal time scales (1) the net e ux integrated over the entrance to the estuary adequately describes the unidirectional (either ine ow or oute ow over the entire cross-section) barotropic volume e ux associated with the coastally forced remote wind effect, (2) during the e rst deployment there is always a bi-directional exchange pattern (ine ow and oute ow existing simultaneously over different parts of the cross-section) superimposed on the sectionally integrated unidirectional exchange, (3) the magnitude of the bi-directional transport associated with the local wind effect may be a signie cant fraction of the unidirectional transport associated with the remote wind effect, and (4) the relative importance of the local wind effect in producing estuary-shelf exchange changes appreciably with season, depending on the characteristic frequency of the wind events and the degree of stratie cation in the estuary.

Fortnightly variability in the transverse dynamics of a coastal plain estuary

Current velocity and water density profiles were obtained along two cross-estuary transects with the purpose of determining the fortnightly variability of the transverse dynamics in a partially stratified coastal plain estuary. The profiles were measured with a towed acoustic Doppler current profiler and a conductivity-temperature-depth recorder in the James River estuary, Virginia. The cross-estuary transects were sampled during the spring tides of October 26–27, 1996, and the ensuing neap tides of November 2–3, 1996. The transects were ∼4 km long, featured a bathymetry that consisted of a channel flanked by shoals, and were sampled repeatedly during two semidiurnal tidal cycles (25 hours) in order to separate semidiurnal, diurnal, and subtidal signals from the observations. This work concentrates on the subtidal transverse dynamics. The transverse baroclinic pressure gradients were larger during neap tides than during spring tides. During spring tides the advective accelerations were predominantly greater than the Coriolis accelerations, most markedly over the edges of the channel. Both effects combined with frictional influences to balance the pressure gradient in the transverse direction. During neap tides, advective accelerations were not as dominant over Coriolis accelerations as during spring tides. Also, during neap tides, Coriolis played a more relevant role, compared to spring tides, in combining with friction to balance the pressure gradient. This behavior was indicative of the momentum balance approaching gravitational circulation modified by the Earths rotation, weak friction, and nonlinear advection during neap tides. The balance became more influenced by nonlinear advection and friction and less influenced by the Earths rotation during spring tides. These results showed that transverse dynamics of a partially stratified estuary are far from being in geostrophic balance.

Spatial structure of hydrography and flow in a chilean fjord, Estuario Reloncaví

Underway current velocity profiles were combined with temperature and salinity profiles at fixed stations to describe tidal and subtidal flow patterns in the middle of the northernmost Chilean fjord, Estuario Reloncaví. This is the first study involving current velocity measurements in this fjord. Reloncaví fjord is 55 km long, 2 km wide, and on average is 170 m deep. Measurements concentrated around a marked bend of the coastline, where an 8-km along-fjord transect was sampled during a semidiurnal tidal cycle in March 2002 and a 2-km cross-fjord transect was occupied, also during a semidiurnal cycle, in May 2004. The fjord hydrography showed a relatively thin (<5 m deep), continuously stratified, buoyant layer with stratification values >4 kg m−3 per meter of depth. Below this thin layer, the water was relatively homogeneous. Semidiurnal tidal currents had low amplitudes (<10 cm s−1) that allowed the persistence of a surface front throughout the tidal cycle. The front oscillated with a period of ca. 2.5 h and showed excursions of 2 km. The front oscillations could have been produced by a lateral seiche that corresponds to the natural period of oscillation across the fjord. This front could have also caused large (2 h) phase lags in the semidiurnal tidal currents, from one end of the transect to the other, within the buoyant layer. Tidal phases were relatively uniform underneath this buoyant layer. Subtidal flows showed a 3-layer pattern consisting of a surface layer (8 m thick, of 5 cm s−1 surface outflow), an intermediate layer (70 m thick, of 3 cm s−1 net inflow), and a bottom layer (below 80 m depth, of 3 cm s−1 net outflow). The surface outflow and, to a certain extent, the inflow layer were related to the buoyant water interacting with the ambient oceanic water. The inflowing layer and the bottom outflow were attributed to nonlinear effects associated with a tidal wave that reflects at the fjords head. The weak subtidal currents followed the morphology of the bend and caused downwelling on the inside and upwelling on the outside part of the bend.

Observations of the wind-induced exchange at the entrance to Chesapeake Bay

Water density and velocity data from two ;75-day deployments across the entrance to the Chesapeake Bay were used in conjunction with wind velocity and sea level records to describe the transverse structure of wind-induced subtidal exchange. Acoustic Doppler current proe lers, electromagnetic current meters, and conductivity-temperature-depth recorders were deployed at the entrance to the bay from mid-April to early July of 1999 and from early September to mid-November of 1999. Three main scenarios of wind-induced exchange were identie ed: (1) Northeasterly (NE) winds consistently drove water from the coast toward the lower Chesapeake Bay as well as water from the upper bay to the lower bay, which was indicated by the surface elevation slopes across the lower bay and along the bay. This resulted in water piling up against the southwestern corner of the bay. The subtidal e ow over the southern portion of the bay entrance was directed to the left of the wind direction, likely the result of the ine uence of Coriolis and centripetal accelerations on the adjustment of the sea level gradients. Over the northern shallow half of the entrance, the subtidal e ows were nearly depth-independent and in the same direction as the wind. (2) Southwesterly (SW) winds caused opposite sea level gradients (relative to NE winds), which translated into near-surface oute ows throughout the entrance and near-bottom ine ows restricted to the channels. This windinduced circulation enhanced the two-way exchange between the estuary and the adjacent ocean. (3) Northwesterly winds produced the same exchange pattern as NE winds. Water piled up against the southwestern corner of the bay causing net oute ow in the deep, southern area and downwind e ow over the shallow areas. Northwesterly winds greater than 12 m/s caused the most efe cient e ushing of the bay, driving water out over the entire mouth of the estuary.

Convergence of lateral flow along a coastal plain estuary

A set of velocity profiles obtained in the James River estuary with an acoustic Doppler current profiler was used in combination with the results of an analytic tidal model to depict the appearance of surface lateral flow convergences (∂v/∂y) during both flood and ebb stages of the tidal cycle. The bathymetry of the estuary was characterized by a main channel and a secondary channel separated by relatively narrow shoals. Lateral surface flow convergences appeared over the edges of the channels and were produced by the phase lag of the flow in the channel relative to the shoals. Flood convergences developed in the late tidal stages and ebb convergences appeared soon after maximum currents. Most of these convergences caused fronts in the density field and flotsam lines that also appeared over the edges of the channel and that lasted <2 hours. The transverse flows associated with the convergences were mostly in the same direction throughout the water column. In fact, the vertically averaged flow produced the same convergence patterns as those near the surface. The analytic tidal model reproduced well the timing and location of the convergences as observed in the James River. Model results with different bathymetry emulated the results in other estuaries, e.g., axial convergence in an estuary with a channel in the middle. This work showed that the strength of lateral convergences along the estuary was proportional to the tidal amplitude and the channel steepness. It also suggested that the convergences were produced mainly by the tidal flow interacting with the channel-shoal bathymetry, i.e., that they did not require the presence of density gradients. However, the analytic model underestimated the magnitude of the convergences and did not account for vertical circulations associated with fronts. The formation of fronts resulted from the interaction of the tidal flow with the bathymetry and the density field.