Lie-Yauw Oey

The Pressure Gradient Conundrum of Sigma Coordinate Ocean Models

Abstract Much has been written of the error in computing the horizontal pressure gradient associated with sigma coordinates in ocean or atmospheric numerical models. There also exists the concept of “hydrostatic inconsistency” whereby, for a given horizontal resolution, increasing the vertical resolution may not be numerically convergent. In this paper, it is shown that the differencing scheme cited here, though conventional, is not hydrostatically inconsistent; the sigma coordinate, pressure gradient error decreases with the square of the vertical and horizontal grid size. Furthermore, it is shown that the pressure gradient error is advectively eliminated after a long time integration. At the other extreme, it is shown that diagnostic calculations of the North Atlantic Ocean using rather coarse resolution, and where the temperature and salinity and the pressure gradient error are held constant, do not exhibit significant differences when compared to a calculation where horizontal pressure gradients are c...

The fate of river discharge on the continental shelf: 1. Modeling the river plume and the inner shelf coastal current

We study the development and evolution of buoyant river plumes on the continental shelf. Our calculations are based on three-dimensional numerical simulations, where the river runoff is introduced as a volume of zero salinity water in the continuity equation and mixing is provided by the models turbulence closure scheme and wind forcing. In the absence of wind forcing, the modeled river plumes typically consist of an offshore bulge and a coastal current in the direction of Kelvin wave propagation. We propose a plume classification scheme based on a bulk Richardson number, which expresses the relative magnitude of the buoyancy-induced stratification versus the available mixing. When the ratio of the discharge and shear velocities is greater (less) than 1, the plume is categorized as supercritical (subcritical); that is, the width of the bulge is greater (less) than the width of the coastal current. Supercritical plumes are often characterized by a meandering pattern along the coastal current, caused by a baroclinic instability process. For a given discharge, subcritical plumes are produced by large mixing and/or shallow water depths. In the presence of wind forcing, the favorable conditions for offshore removal of coastal low-salinity waters include high river runoff and strong upwelling-favorable wind stress. When the rivers are treated as individual sources of freshwater (“point source” behavior), the wind-driven flow may exhibit substantial spatial variability. Under the above removal conditions, strong offshore transport takes place in “jetlike” flow regions within the river plume, in contrast to the downwind acceleration of adjacent waters. When the rivers are treated as a long “line source” of freshwater, the plume region resembles a coastal low-salinity band, and the above removal conditions trigger offshore transport that is most pronounced at the “head” of the source.

A Three-Dimensional Simulation of the Hudson–Raritan Estuary. Part I: Description of the Model and Model Simulations

Abstract A time-dependent, three-dimensional, finite difference simulation of the Hudson‐Raritan estuary is presented. The calculation covers July–September 1980. The model estuary is forced by time-dependent observed winds, tidal elevation at open boundaries, and river and sewage discharges. Turbulence mixing coefficients in the estuary are calculated according to a second-moment, turbulence-closure submodel. Horizontal diffusivities are zero in the simulation and small-scale eddies produced by the interaction of unsteady, three-dimensional velocity and salinity fields with coastline and bottom bathymetry were resolved by the model. These eddies are important physical elements in shear dispersion processes in an estuary. Model results show unstably stratified water columns produced by advection of waters of different densities. These instabilities produce intense mixing with vertical eddy diffusivities reaching 2–3 times their neutral values. They occur most frequently at slack currents, during initial s...

Sigma Coordinate Pressure Gradient Errors and the Seamount Problem

In a recent paper by Mellor et al., it was found that, in two-dimensional ( x, z) applications with finite horizontal viscosity and zero diffusivity, the velocity error, associated with the evaluation of horizontal density or pressure gradients on a sigma coordinate grid, prognostically disappeared, leaving behind a small and physically insignificant distortion in the density field. The initial error is numerically consistent in that it decreases as the square of the grid increment size. In this paper, we label this error as a sigma error of the first kind. In three-dimensional applications, the authors have encountered an error that did not disappear and that has not been understood by us or, apparently, others. This is a vorticity error that is labeled a sigma error of the second kind and is a subject of this paper. Although it does not prognostically disappear, it seems to be tolerably small. To evaluate these numerical errors, the authors have adopted the seamount problem initiated by Beckman and Haidvogel. It represents a stringent test case, as evidenced by their paper, wherein the model is initialized with horizontal isopycnals, zero velocity, and no forcing; then, any velocities that develop must be considered errors. Two appendices are important adjuncts to the paper, the first providing theoretical confirmation and understanding of the numerical results, and the second delving into additional errors related to horizontal or isosigma diffusion. It is, however, shown that satisfactory numerical solutions are obtained with zero diffusivity.

Loop current, rings and related circulation in the gulf of Mexico : A review of numerical models and future challenges

Progress in numerical models of the Loop Current, rings, and related circulation during the past three decades is critically reviewed with emphasis on physical phenomena and processes.

A model simulation of circulation in the northeast Atlantic shelves and seas

A three-dimensional, primitive-equation simulation of the circulation in the northeast Atlantic shelves and seas, defined by 51°–76°N latitudes and 20°W–22°E longitudes, has been conducted for the period February-March 1988. The simulation was initialized from a 585-day quasi-equilibrium calculation and included realistic meteorological forcing, inflows/outflows across the open boundaries (inflow of the North Atlantic warm water in particular), tides, coastal and Baltic discharges, and relaxation to wintertime climatology for model depths > 500 m. The calculation is the first part of an overall effort to nest a high-resolution region for simulation of eddies and fronts in the Norwegian Coastal Current (NCC). This paper presents detailed simulation strategies and discusses results from the coarse-grid region to study the larger-scale model response induced by atmospheric forcing, so that its effects on flow dynamics in the nested grid can be better understood. The mean and variability of the simulated flow field are compared, whenever possible, with published observations. In particular, we examine in detail the simulated wind-induced response in the Skagerrak transport, which produces blocking and outbreak of the Skagerrak and North Sea waters. These transport variabilities can be expected to be important in the development of the NCC meanders and eddies further north.

Subtidal Variability of Estuarine Outflow, Plume, and Coastal Current: A Model Study

Abstract The time evolution of an estuary plume and its coastal front over a continental shelf is numerically calculated here using a three-dimensional model with eddy mixing based on the turbulence kinetic energy closure. The plume and front system is found to be unsteady with a natural period of about 5–10 days, during which the plume pulsates and intermittent coastal currents propagate down the coast.

The fate of river discharge on the continental shelf: 2. Transport of coastal low‐salinity waters under realistic wind and tidal forcing

A three-dimensional numerical simulation of shelf circulation is presented. We employ realistic forcing for the Southeast U.S. Continental Shelf during the spring season. We show that the strongest offshore transport of river-induced, coastal, low-salinity waters and associated materials occurs near the surface. The preferred mean pathway is in the northeastward direction, and it takes about 2 months to cross the entire shelf. Owing to the mean direction of surface transport and the topography of the South Atlantic Bight shelf, the preferred location for springtime removal is off Charleston, South Carolina, and presumably in the vicinity of the Charleston Bump. The transport and fate of the river-induced, coastal, low-salinity waters during the spring season are determined by (1) the stratification of nearshore waters, which is due to the high river runoff and causes the decoupling between “near-surface” and “near-bottom” layers; (2) the prevailing northeastward winds, which cause significant offshore transport within the shallow near-surface Ekman layer; and (3) the tidally induced bottom stirring (M2 tides). Comparison of model and data time series of currents shows very good agreement. Standard deviations of the model and data-computed empirical orthogonal functions are almost identical, while the respective variance-conserving spectra agree both in amplitude and phase.

Simulation of mesoscale variability in the Gulf of Mexico : Sensitivity studies, comparison with observations, and trapped wave propagation

Abstract A primitive equation Gulf of Mexico model was used to examine variability of the Loop Current (LC) and Loop Current eddies (LCE). Realistic results were obtained for a certain range of values of the horizontal mixing coefficient: eddy paths were west and southwestward; eddy propagation speeds from 3 to 5 km day−1; the ratio of minor to major eddy axes about 0.8; eddy shedding periods from 200 to 500 days; eddy lifetimes from 100 to 200 days; eddy sizes from 200 to 400 km; and eddy swirl transports, as fractions of the specified inflow of 30 Sv, were from 0.55 to 0.85. On the other hand, the maximum vertical deepening of the 20°C isotherm was 15% to 50% less than that observed, resulting in weaker near-surface currents of about 0.65 m s−1, in comparison to observed values of 0.88 to 1.7 m s−1. A strong correlation between eddy shedding and decreasing or reversing lower-layer (below 750 m) transport in the Yucatan Channel is found. In the western Gulf, current variability is produced by eddy arriva...

Deep Eddy Energy and Topographic Rossby Waves in the Gulf of Mexico

Abstract Observations suggest the hypothesis that deep eddy kinetic energy (EKE) in the Gulf of Mexico can be accounted for by topographic Rossby waves (TRWs). It is presumed that the TRWs are forced by Loop Current (LC) pulsation, Loop Current eddy (LCE) shedding, and perhaps also by LCE itself. Although the hypothesis is supported by model results, such as those presented in Oey, the existence of TRWs in the model and how they can be forced by larger-scale LC and LCEs with longer-period vacillations have not been clarified. In this paper, results from a 10-yr simulation of LC and LCEs, with double the resolution of that used by Oey, are analyzed to isolate the TRWs. It is shown that along an east-to-west band across the gulf, approximately over the 3000-m isobath, significant EKE that accounts for over one-half of the total spectrum is contained in the 20–100-day periods. Bottom energy intensification exists in this east–west band with vertical decay scales of about 600–300 m decreasing westward. The de...