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 model's turbulence closure scheme and wind forcing.In the absence of wind forcing the modeled fiver 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. control the fate of fivefine waters and related materials afterPaper number 95JC03024. 0148-0227/96/95JC-0302455.00 their release in the coastal ocean. Our main objective is to describe the generation and evolution of a fiver plume on the continental shelf and determine the important factors that govern its offshore expansion and, consequently, the removal mechanism of fiver-borne materials.The frontal structure of a fiver plume has been discussed by several investigators. Earlier studies, such as those by Kao et al. [1977], Kao [1981], Ikeda [1984], and Csanady [1984], recognized the importance of nonlinearity, Coriolis, and friction in the development of the buoyant plume. McClimans [1986] identifi•ed the following three major processes that characterize the dynamics of the seaward expansion of the river flow: (1) acceleration, resulting from the balance between inertia and gravity (buoyancy) forces; (2) mixing, governed by turbulence due to bottom and interfacial friction; and (3) geostrophy, where the balance between Coriolis and the developed cross-shore pressure gradient (due to "freshening" of coastal waters) generates an alongshore coas...

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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.

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[1] The Loop Current (LC) is known to shed eddies at irregular intervals from 3 to 17 months. The causes of this irregularity have not, however, been adequately identified previously. We examine the effects of various types of external forcing on shedding with a model of the western North Atlantic Ocean (96°-55°W, 6°-50°N). We force the model with steady transport at 55°W, with winds, and include eddies in the Caribbean Sea. We examine their separate effects. With steady transport only, the model sheds rings at a dominant period of 9-10 months. Wind-induced transport fluctuations through the Greater Antilles Passages cause shedding at shorter intervals (%3-7 months). Caribbean eddies (anticyclones) cause shedding at longer periods (%14-16 months). Potential vorticity conservation indicates that Caribbean eddies tend to deter northward extension of the LC into the Gulf, which can lead to longer periods between eddy shedding. Fluctuating inflow at the Yucatan Channel that is associated with winds and/or Caribbean eddies can cause an LC eddy to temporarily ($1 month) detach from and then reattach back to the LC, a phenomenon often observed. Model results also suggest that southwest of Hispaniola, warm eddies are spun up by the local wind stress curl. This type of eddy drifts southwestward, then westward after merging with the Caribbean Current, and then northward as it progresses toward the Yucatan Channel; these eddies significantly affect the shedding behavior of warm-core rings. The timescale for spin up and drift from Hispaniola is about 100 days. Satellite data indicate the existence of these eddies in the real ocean.

[1] The flow through the Yucatan Channel and into the Gulf of Mexico is a major component of the Gulf Stream and the subtropical gyre circulation. Surprisingly, however, little is known about the forcing and physical parameters that affect the current structures in the Channel. This paper attempts to improve our understanding of the flow through the Channel with a detailed analysis of the currents obtained from a primitive-equation model that includes the Gulf and the entire Caribbean Sea and forced by 6-hourly wind from ECMWF. The analysis includes two parts: First, the overall statistics of the model results, including the Loop Current (LC) variability, the frequency of LC eddyshedding, and the means and standard deviations (SD) of transports and currents, are compared with observations. Secondly, an Empirical Orthogonal Function (EOF) analysis attempts to identify the physical parameters responsible for the dominant modal fluctuations in the Channel. The model LC sheds seven eddies in 4 years at irregular time intervals (6.6, 7.1, 5.3, 11.9, 4.2, 10.9 months). The model's upper (thickness $800 m) inflow into the Gulf of Mexico occupies two-thirds of the Channel on the western side, with a near-surface maximum (4-year) mean of around 1.5 m s À1 and SD % 0.4 m s À1 . Three (return) outflow regions are identified, one in the upper layer (thickness $600 m) on the eastern third of the Channel, with mean near the surface of about 0.2 m s À1 and SD % 0.14 m s À1 , and two deep outflow cores, along the western and eastern slopes of the Channel, with (Mean, SD) % (0.17, 0.05) and (0.09, 0.07) m s À1 , respectively. The total modeled Channel transport varies from 16 to 34 Sv (1 Sverdrup = 10 6 m 3 s À1 ) with a mean around 25 Sv. The above velocity and transport values agree quite well with observations by Maul et al. [1985], Ochoa et al. [2001], and Sheinbaum et al. [2002]. The deep return transport below 800 m was found to correlate with changes in the Loop Current extension area, in agreement with the observational analysis by Bunge et al. [2002]. The EOF mode#1 of the along-channel currents contains 50% of the total energy. It is surface-trapped, is 180°out of phase across the channel, and correlates well (correlation coefficient g % 0.8) with the cross-channel vacillations of the LC frontal position. The EOF mode#2 contains 18% of the energy, and its structure mimics that of the mean flow: dominated by two vertically more coherent regions that are 180°out of phase across the Channel. The mode is dominated by two periods, approximately 11 months and 2 months respectively, and correlates (g % 0.7) with the upper-channel inflow transport. The third and fourth modes, together, account for 18% of the total energy. Their combined time series correlates (g % 0.66) with the deep current over the sill, and is dominated by fluctuations with a period %205 days coincident with the dominant low-frequency fluctuations inherent in Maul et al. 's [1985] sill measurement. Thus the dominant mode of flow fluctuations in the Yucatan...

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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 decrease agrees with the TRW solution. The band is also located within the region where TRWs can be supported by the topographic slope and stratification used in the model and where wavenumber and frequency estimates are consistent with the TRW dispersion relation. The analysis indicates significant correlation between pairs of east-west stations, over distances of approximately 400 km. Contours of lag times suggest offshore (i.e., downslope) phase propagation, and thus the east-west band indicates nearly parabathic and upslope energy propagation. Ray tracing utilizing the TRW dispersion relation and with and without (for periods Ͼ43 days) ambient deep currents shows that TRW energy paths coincide with the above east-west high-energy band. It also explains that the band is a result of TRW refraction by an escarpment (with increased topographic gradient) across the central gulf north of the 3000-m isobath, and also by deep current and its cyclonic shear, and that ray convergence results in localized EKE maxima near 91ЊW and 94Њ-95ЊW. Escarpment and cyclonic current shear also shorten TRW wavelengths. Westward deep currents increase TRW group speeds, by about 2-3 km day Ϫ1 according to the model, and this and ray confinement by current shear may impose sufficient constraints to aid in inferring deep flows. Model results and ray paths suggest that the deep EKE east of about the 91ЊW originates from under the LC while farther west the EKE also originates from southwestward propagating LCEs. The near-bottom current fluctuations at these source regions derive their energy from short-period (Ͻ100 days) and short-wavelength (Ͻ200 km) near-surface fluctuations that propagate around the LC during its northward extrusion phase and also around LCEs as they migrate southwestward in the model.