Richard W. Garvine

A dynamical system for classifying buoyant coastal discharges

Abstract Buoyant discharge into the coastal ocean occurs in a confusing variety of forms and scales. In this paper I offer a classification system for such discharges based on scaling analysis of the continuity and momentum equations. The approach is phenomenological, as the principal flow scales must be known a priori. The primary parameter that emerges is the Kelvin number K, the ratio of the buoyant structure width to the baroclinic Rossby radius. Two limiting cases, K small and K large, are readily understood from the scaling analysis. I arrange 12 examples of buoyant coastal discharge observations into a hierarchy in K. Those for the smallest K have the properties predicted by the small K limiting case: strong advection terms and Froude numbers of order unity, but small Coriolis effects. Those for the largest K correspond well to the large K limiting case: weak advection terms, small Froude numbers, but order one Coriolis terms. The classification system should be useful for interpreting both future observations and model results.

Estuary Plumes and Fronts in Shelf Waters: A Layer Model

Abstract A layer model that treats fronts as discontinuities is developed to study the steady state behavior of shallow estuary plumes on the continental shelf. The complete range of earth rotation effect is evaluated from small-scale or nonrotating plumes (Kelvin number equal zero) to large-scale, rotating plumes (Kelvin number equal order one). Supercritical flow is assumed in the outlet channel and the method of characteristics is used to compute the flow downstream. Nonrotating plumes have strong boundary fronts and concentrate their greatest layer depth and mass transport offshore near the front, but form no coastal current. Rotating plumes have boundary fronts that weaken soon after discharge, form a turning region where Coriolis action deflects the flow toward shore, and subsequently set up a coastal current. Soon after its formation this coastal current is bounded offshore by a strong front called the coastal front, across which the momentum balance changes from nearly inertial in the turning regi...

Wind influence on a coastal buoyant outflow

[1]xa0This paper investigates the interplay between river discharge and winds in forcing coastal buoyant outflows. During light winds a plume influenced by the Earths rotation will flow down shelf (in the direction of Kelvin wave propagation) as a slender buoyancy-driven coastal current. Downwelling favorable winds augment this down-shelf flow, narrow the plume, and mix the water column. Upwelling favorable winds drive currents that counter the buoyancy-driven flow, spread plume waters offshore, and rapidly mix buoyant waters. Two criteria are developed to assess the wind influence on a buoyant outflow. The wind strength index (Ws) determines whether a plumes along-shelf flow is in a wind-driven or buoyancy-driven state. Ws is the ratio of the wind-driven and buoyancy-driven along-shelf velocities. Wind influence on across-shelf plume structure is rated with a timescale (ttilt) for the isopycnal tilting caused by wind-driven Ekman circulation. These criteria are used to characterize wind influence on the Delaware Coastal Current and can be applied to other coastal buoyant outflows. The Delaware buoyant outflow is simulated for springtime high–river discharge conditions. Simulation results and Ws values reveal that the coastal current is buoyancy-driven most of the time (∣Ws∣ 1) several times during the high-discharge period. Strong upwelling events reverse the buoyant outflow; they constitute an important mechanism for transporting fresh water up shelf. Across-shelf plume structure is more sensitive to wind influence than the along-shelf flow. Values of ttilt indicate that moderate or strong winds persisting throughout a day can modify plume width significantly. Plume widening during upwelling events is accompanied by mixing that can erase the buoyant outflow.

Penetration of Buoyant Coastal Discharge onto the Continental Shelf: A Numerical Model Experiment

Abstract Plumes of buoyant water produced by inflow from rivers and estuaries are common on the continental shelf. Typically they turn anticyclonically to flow alongshelf as buoyancy-driven coastal currents. During this passage, mixing with ambient shelf water gradually erodes the plume buoyancy so that its alongshelf penetration is finite. This paper addresses the extent of this penetration and how it is determined by fundamental dimensionless flow parameters. A three-dimensional numerical model is applied to an idealized flow regime. Ambient shelf conditions include tidal motion, but neither wind stress nor ambient alongshelf current. The alongshelf extent of penetration is evaluated after the plume reaches a stationary condition downshelf. A total of 66 model experiments are conducted, including variations in buoyant source and ambient shelf properties. Five dimensionless parameters determine the alongshelf and across-shelf penetration, the latter the coastal current width. The most critical of these i...

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 0( 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 mz/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.

Dynamical properties of a buoyancy-driven coastal current

The outflow of buoyant waters from major estuaries affects the dynamics of inner continental shelves profoundly as lateral density gradients force an alongshore current. Often the Coriolis force causes the outflow to remain trapped near the coast. We observed one such current, the Delaware Coastal Current, on the inner shelf near the Delaware Estuary on the eastern seaboard of the United States. The spatial variability along the shelf, however, suggests at least two dynamically distinct regions that we term source and plume regions. In the source region we find fronts, a current whose width scales well with the internal deformation radius, and a ratio of relative to planetary vorticity that reaches unity, that is, the Rossby number is O(1). As nonlinear inertial forces in the across-shelf momentum balance are weak, we suggest that such forces contribute to the along-shelf momentum balance only. Farther downstream in the plume region, we find much reduced lateral density gradients, a current much wider than the deformation radius, and relative vorticities that are much smaller than the planetary vorticity. From our observations we compute nondimensional dynamical parameters, with which we discuss our observations. The Burger, Rossby, and Ekman numbers for the Delaware Coastal Current suggest that most models of buoyancy-driven coastal currents do not apply to this coastal flow.

Dynamics of Small-Scale Oceanic Fronts

Abstract An integral model of the steady-state dynamics of a shallow, small-scale oceanic front is developed. Such fronts have been observed at the boundaries of river plumes discharging into coastal sea water. They share with larger scale oceanic fronts the features of persistence in time, despite sharp horizontal gradients in properties, and strong horizontal convergence at the surface front with consequent sinking. For a steady state to exist in a reference frame moving with the front, the model shows that interfacial friction and/or upward mass entrainment is required to balance the net pressure gradient produced by the sloping sea surface and frontal interface in the light water pool. Maintenance of this balance dictates that the Richardson number be of order unity; thus, friction and entrainment coefficients are kept low allowing sharp property gradients in the steady state. Strong surface convergence is also a prominent feature of the model dynamics. Comparisons are made with the observations of Ga...

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.

Subtidal frequency estuary-shelf interaction: Observations near Delaware Bay

Interaction between a large estuary and the adjacent inner continental shelf at subtidal frequencies occurs through a variety of physical processes. I use recent field observations to study these processes near the weakly stratified estuary of Delaware Bay on the east coast of the United States. The primary observations were shipboard hydrography and long time series of current, temperature, and conductivity. The observations revealed three distinct spatial regions for the coupled circulation between estuary and shelf: the estuary mouth, the inner shelf where the mean flow is landward, and a buoyancy-driven coastal current. The coastal current is the principal discovery of the work. It begins near the estuary mouth as lighter water from Delaware Bay exits the mouth on the right side when viewed to seaward. Initially, the current is about one internal Rossby radius in width, but it broadens as it flows seaward to reach a width of about 20 km off the coast of Delaware. Observed mean currents were 3–5 cm s−1 there. In all three regions temporal variability in current and salinity was induced by variations in alongshore wind and river discharge into the estuary, the latter occurring mainly at very long periods of several weeks and longer.

Large CO2 reductions via offshore wind power matched to inherent storage in energy end-uses

[1]xa0We develop methods for assessing offshore wind resources, using a model of the vertical structure of the planetary boundary layer (PBL) over water and a wind-electric technology analysis linking turbine and tower limitations to bathymetry and continental shelf geology. These methods are tested by matching the winds of the Middle-Atlantic Bight (MAB) to energy demand in the adjacent states (Massachusetts through North Carolina, U.S.A.). We find that the MAB wind resource can produce 330 GW average electrical power, a resource exceeding the regions current summed demand for 73 GW of electricity, 29 GW of light vehicle fuels (now gasoline), and 83 GW of building fuels (now distillate fuel oil and natural gas). Supplying these end-uses with MAB wind power would reduce by 68% the regions CO2 emissions, and reduce by 57% its greenhouse gas forcing. These percentages are in the range of the global reductions needed to stabilize climate.