Buoyant discharge on the inner continental shelf: A frontal model

A steady state, frontal model of the arrested topographic wave type (Csanady, 1978) is developed for application to buoyant coastal discharge of large-scale and weak stratification, typically found on the inner continental shelf. The across-shore momentum balance is geostrophic, while the alongshore momentum balance includes wind stress and bottom or interfacial friction. The dynamics thus has semi-geostrophic character. No mixing dynamics is present. The model has two major purposes: first, to serve as the vehicle for a process study requiring only moderate computing resources, and second, to inquire into the general consequences of extending the original single-layer model of Csanady (1978) into a two-layer, frontal model for application to buoyant coastal discharge. Analysis of the flow near the frontal bottom intersection shows that the bottom stresses on each side of the front must be equal and match as well the interfacial stress just above. Similar analysis near the surface front shows that static stability there requires the presence of only downwelling-favorable wind stress. This implies that a statically stable, steady state is not possible for upwelling-favorable winds. The model possesses an asymptotic downshelf state that is termed frictionally adjusted flow in which alongshore gradients and across-shore velocities vanish and bottom, interfacial, and wind stresses all are equal. The front then becomes trapped to the local isobaths. Numerical experiments showed that the model contains possible spatially growing instability because of the frontal boundary. Weaker baroclinic strength and diminished bottom slopes tended to increase flow stability. Stable flows were computed in their evolution from a prescribed upshelf state intended to simulate estuarine outflow of buoyant discharge and adjacent inflow of denser ambient shelf water. A turning region developed where the front moved first offshore then back nearer the coast. Experiments showed that the turning region was a joint product of the turning isobath geometry imposed near the estuary mouth and the estuarine inflow of shelf water. Comparisons of model results with recent observations of the Delaware Coastal Current showed general qualitative agreement, but highlight the lack of model mixing processes

The vertical structure and subtidal dynamics of the inner shelf off New Jersey

This paper seeks to exploit a recent data set obtained off the coast of New Jersey, USA in the summer of 1996. The two major objectives are to gain insight into mechanisms controlling the vertical structure, particularly the temperature and density, and into the subtidal frequency dynamics. The setting was strongly affected by three conditions: stratification was high, the bottom slope was comparable to the isopycnal slope, and buoyancy forcing from an upshelf freshwater source was, on average, of the same strength as wind forcing. Bottom mixed layer (bml) and surface mixed layer (sml) thicknesses increased offshore, opposite the sense predicted by standard formulations for stratified conditions. Maps of sml and bml thickness were coherent with maps of bml density, not with maps of vertical stratification. It appears that horizontal buoyancy flux from the Hudson coastal current sustains the stratified interior even very near shore. Well resolved vertical profiles at a mooring in 19 m water depth showed that above 1 m height off the bottom the Richardson number was very large, rendering vertical stress and eddy coefficients very small. In contrast at a deeper site offshore beyond the reach of freshwater intrusion a thick bml was present and vertical stresses and eddy coefficients were at expected levels. Moored instruments there revealed temporal variations in bml thickness which correlated with the strength and direction of the interior alongshelf current, but with the opposite sense found on the California shelf: thicker during upwelling and thinner during downwelling. The difference is well explained by the action of interior density changes at the bml edge produced by displacement of interior isopycnals. This action is significant when the ratio of isopycnal slope to bottom slope is of order one, as here. The subtidal dynamics featured high levels of bottom friction, despite the thin bml thicknesses nearshore. The large values of drag coefficient found are consistent with the large effective roughness heights induced by the orbital wave motion in this shallow water regime on an open coast. Bottom stress was comparable to wind stress both in mean values and in variations. No bottom stress reduction was evident, despite the sloping bottom and stratified interior. Volume transport in the bml rarely balanced the surface Ekman transport based on the alongshelf wind and rarely was consistent with bottom Ekman transport based on bottom stress. This implies that the flow field was seldom in a state of alongshelf invariance ( two-dimensional flow ). Despite the very shallow water depths, thermal wind balance was satisfied for the vertical shear of the alongshelf current

The impact of model configuration in studies of buoyant coastal discharge

Observations and model studies of large-scale buoyant plumes show three major types for the horizontal distribution of density. Type 1 represents the typical coastal freshwater plume of observations. The buoyant discharge turns right in the northern hemisphere (toward downshelf) under earth rotation at its source. Type 2 is common in many numerical model studies. Most of the buoyant water at the inlet turns left (upshelf) along the coast to form a continuously growing intrusion. Type 3 turns right but exhibits a massive anticyclonic bulge which grows with time; its coastal current is weak and carries a small fraction of the inlet fresh water or buoyancy flux. The great majority of observed coastal plumes and their appended coastal currents have been type 1, while models have most often produced type 2 or 3. To remedy this disparity, modelers have imposed an ambient shelf current in the downshelf (right hand) direction of sufficient strength to produce type 1 plumes. Field observations of the Delaware Coastal Current are presented. They show type 1 plumes occur even when the ambient shelf flow is upshelf. Imposing a downshelf ambient current is not, then, a generally applicable remedy to obtain a type 1 plume in model studies. A common element in the configuration of these models is use of the simple inlet, a rectangular breach in the coastal wall with uniform inflow water properties. An analytic treatment of the resulting flow near the coastal wall upshelf of the simple inlet predicts a steady intrusion of buoyant water that increases with depth of the coastal wall. Subsequent numerical experiments with this model configuration confirmed these predictions qualitatively. The simple inlet and the coastal wall are thus suspect. Three changes in model configuration yielded numerical model results that were type 1. The first was adoption of an idealized estuarine inlet in place of the simple inlet. The second was use of a greatly reduced coastal wall. The third was use of inlet channel angles less than normal. With all three of these alterations, upshelf intrusion was very weak, perhaps at a level that would be undetected in field observations. The flow was nearly steady state and no massive bulge was present, despite the absence of ambient shelf motion. Each of these three changes to configuration generated clear differences in the state of the buoyancy-driven coastal current well downshelf, despite use of the same bulk discharge properties such as total volume and freshwater fluxes. Using the results of observations, laboratory models, and numerical models, one may attempt to codify the natural and model settings or configurations that select which plume type occurs. Type 3 plumes seem the clearest to predict. They require weak or absent downshelf ambient current, nearly normal inlet channel angle, a steep coastal bottom slope, and water depths much greater than the typical depth of buoyant water. Type 2 plumes, in contrast, all appear to be shallow water phenomena. In addition they require weak or absent ambient downshelf current, inlet flow angles near normal, and a steep coastal bottom slope or vertical coastal wall. Type 1 plumes are the most common in field observations. They too are shallow water phenomena. Model configurations that favor them include absence of a significant coastal wall and use of more realistic inlet flow fields than the simple inlet

Buoyancy and wind forcing of a coastal current

Local winds and lateral buoyancy fluxes from estuaries constitute two major forcing mechanisms on the inner continental shelf of the Mid Atlantic Bight on the eastern seaboard of the U.S.A. We report observations of the resulting coastal current that suggest a linear superposition of the wind and buoyancy forced motions. This current, which we term the Delaware Coastal Current, has a mean flow of about 10 cm/s in the direction of Kelvin wave phase propagation. It opposes the generally upwelling favorable local winds there. The same winds, however, force important across-shelf flows that agree qualitatively with Ekman dynamics with Ekman numbers that are O(1). Velocity fluctuations at current meter mooring are consistent with the above dynamics, and explain the local hydrography well. Trajectories from drifters and derived velocity fields, too, reveal consistent flow patterns. We further find that Lagrangian and Eulerian integral time scales are similar, implying a linear flow field. We estimate dispersion coefficients for this buoyancy driven coastal current to be about 2000 and 200 m2/s in the along- and across-shelf direction, respectively. Our results disagree both qualitatively and quantitatively with those of a recent numerical model of the study area

Assessing the wind field over the continental shelf as a resource for electric power

To assess the wind power resources of a large continental shelf area, we analyze the 18-year hourly wind records from meteorological stations in the US Middle Atlantic Bight (MAB), comparing areas of coast, estuary, and open shelf. We calculate winds at turbine hub height for the sea breeze compared with synoptic winds and, for each type of site, we compare the seasonal and daily phase match to electrical load. To improve large-scale ocean power resource calculations, we derive an iterative algorithm to determine the surface roughness coefficient (z0). Our method calculates z0 for specific times and locations over the ocean, rather than the prior practice of using a generic z0 that is constant across time and space. Due to lower surface roughness of the ocean, wind speeds are notably higher at hub height, so that in the MAB we find that a representative open shelf site has three times the power content of a nearby land site. Regarding phase match to daily electric load, we find the sea breeze adjacent to the coast is a very good match to this region\u27s electric power load profile. However, the open shelf wind speeds are so much higher (10.9 m s–1 versus 5.7 m s–1 for the comparison period) that the near-coast phase advantage is obviated. We also find more consistent wind power production offshore, with single sites producing at least some power 88 to 92% of the time. By modeling electrically interconnected sites, power production improves to 96.3% with as few as three interconnected wind sites and to 99.3% with 5 interconnected sites

An estuarine box model of freshwater delivery to the coastal ocean for use in climate models

Present day climate models employ a coarse horizontal grid that is unable to fully resolve estuaries or continental shelves. The importation of fresh water from rivers is critical to the state of deep ocean stratification, but currently the processing of that fresh water as it passes from the river through the estuary and adjacent shelf is not represented in the coastal boundary conditions of climate models. An efficient way to represent this input of fresh water to the deep ocean would be to treat the estuary and shelf domains as two coupled box models with river water input to the estuarine box and mixed fresh water and coastal water output from the shelf box to the deep ocean.We develop and test the estuary box model here. The potential energy anomaly ϕ is found from the five competing rates of change induced by freshwater inflow, mixed water outflow to the shelf, tidal mixing, surface heat flux, and wind-induced mixing. When application of the box model is made to the Delaware estuary, the wind mixing term contributes little. A 15-year time series of ϕ compares surprisingly well with the calculations of a three-dimensional numerical model applied to the Delaware estuary. The results encourage the future development of a shelf box model as the next step in constructing needed boundary conditions for input of fresh water to the deep ocean component of coupled climate models

Observations of coastal upwelling off Uruguay downshelf of the Plata estuary, South America

We analyze hydrographic and current observations of an upwelling center off eastern South America on the Uruguayan coast (∼35S) and downshelf from the Rio de la Plata estuary. Our observations show that the buoyancy-driven subtidal alongshore circulation is modulated by winds. During the winter, strong upwelling-favorable local winds forced the Rio de la Plata buoyant plume poleward. In the summer, the plume detached from the coast with warm and saline subtropical waters intruding from the north. These waters bounded the upwelling of cold waters in the nearshore area off Uruguay. A shallow submarine canyon cutting obliquely across the shelf facilitates the advection of cold waters into the coastal upwelling domain. An upwelling jet was detected off Uruguay for summer conditions, while for winter the plume configuration generated strong horizontal shear of along-shelf currents. Cross-shelf circulation was dependent on the coastal stratification. Under low stratification (summer) a two-layer circulation developed, with thick surface and bottom mixed layers flowing in opposite directions. High stratification levels (winter) modified this pattern by allowing circulation along a thick stratified interior. The existence of upwelling was linked to the history of wind events and shelf stratification. During the winter, downwelling winds frequently restore the plume, so the upwelling efficiency is very low. In the summer, downwelling events are less frequent and intense, so that the cumulative effect of upwelling events act to export the Plata freshwaters offshore. The reduction of inner-shelf stratification increases the likelihood of a full upwelling to the surface. Analysis of the wind-induced Ekman transport suggests that the Uruguay upwelling system reflects a seasonal wind pattern modulated by significant interannual variability

Energetics in Delaware Bay: Comparison of two box models with observations

A corrected version of an unstratified box model of potential energy anomaly , initially developed by Garvine and Whitney (2006), and a new two-layer box model that allows for stratified and well-mixed conditions are applied to Delaware Bay. The models are applied for the Garvine and Whitney (2006) 1988-1994 study period and in Spring 2003; however, only model results of potential energy anomaly from the latter period are compared to in situ observations obtained outside the bay mouth. Unstratified model results for the two study periods reveal that the river discharge (Ω1) is the largest potential energy anomaly contributor. This term is closely followed (but with opposite sign) by the coastal current efflux term (Ω2). For the two-layer model the largest contributor is the dense inflow term (Ω6). The wind term (Ω5) is the second largest, followed by the tide (Ω3), river discharge (Ω1) and coastal current terms. In both models the solar heat flux term (Ω4) makes the smallest contribution to ϕ. The available one-month comparison of model results to observations renders statistically insignificant correlation coefficients for both models. We speculate dynamical differences between conditions at the estuary mouth and the instrument location on the nearby shelf contribute to the model-observation mismatch. Other statistics, such as the root mean square error indicate that the unstratified model performs better than the two-layer model for the observation period. The latter model is, however, able to depict the importance of tides and winds in the computation of potential energy anomaly and is able to detect the response of ϕ due to strong wind events. While there is no clear model choice for the Delaware Bay, the unstratified model may be entirely inappropriate for highly stratified estuaries

A large-amplitude meander of the shelfbreak front during summer south of New England : observations from the Shelfbreak PRIMER experiment

Author Posting. © American Geophysical Union, 2004. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 109 (2004): C03006, doi:10.1029/2002JC001468.In order to examine spatial and temporal variability of the shelfbreak front during peak stratification, repeated surveys using a towed undulating vehicle (SeaSoar) are used to describe the evolution of shelfbreak frontal structure during 26 July to 1 August 1996 south of New England. Spatial correlation (e-folding) scales for the upper 60 m of the water column were generally between 8 and 15 km for temperature, salinity, and velocity. Temporal correlation scales were about 1 day. The frontal variability was dominated by the passage of a westward propagating meander that had a wavelength of 40 km, a propagation speed of 0.11 m s−1, and an amplitude of 15 km (30 km from crest to trough). Along-front geostrophic velocities (referenced to a shipboard acoustic Doppler current profilers) were as large as 0.45 m s−1, although subject to significant along-front variations. The relative vorticity within the jet was large, with a maximum 0.6 of the local value of the Coriolis parameter. Seaward of the front, a small detached eddy consisting of shelf water was present with a diameter of approximately 15 km. Ageostrophic contributions to the velocity field are estimated to be as large as 0.3 m s−1 in regions of sharp curvature within the meander. These observations strongly suggest that during at least some time periods, shelfbreak exchange is nonlinear (large Rossby number) and dominated by features on a horizontal scale of order 10 km.This work was performed under grants N-00014-95-1-0575 and N-00014-98-1-0059. as part of the ONR Shelfbreak PRIMER Initiative. Some additional analysis and writing was done under ONR grants N-00014-00-1-0931 and N-00014-01-1-0247

Generation of internal waves by a supercritical stratified plume

The generation of internal waves by a propagating river plume is studied in the framework of a fully nonlinear nonhydrostatic numerical model. The vertical fluid stratification, parameters of tide, river discharge, and the bottom topography were taken close to those observed near the Columbia River mouth. It was found that in the beginning of the ebb tidal phase the river water intruding into the sea behaves as a surface jet stream. It collides with the stagnant shelf waters and sinks down in the area of the outer plume boundary, forming a head of the gravity current. In supercritical conditions which are normally realized at the first stage of the ebb tidal phase, internal waves are arrested in the head of the gravity current because their phase speed is smaller than the velocity of the plume. They are released and radiate from the plume when the speed of the decelerating front becomes smaller than the internal wave phase speed. This mechanism of the wave generation is sensitive to the stratification of the ambient shelf waters. It was found that dramatic decay of the buoyancy frequency profile from the surface to the bottom provides the most favorable conditions for the efficient disintegration of the head of the gravity current into a packet of internal waves and their fast separation from the plume. In the case when the fluid stratification on the shelf is close to monotonous, the disintegration of the head of the gravity current into a packet of solitary internal waves is not expected. Copyright 2009 by the American Geophysical Union