Numerical simulations of the baroclinic dynamics of density‐driven coupled fronts and eddies on a sloping bottom

Abstract

Abstract. Numerical simulations of the baroclinic dynamics of density-driven coupled fronts and eddies are described. The simulations are based on a two-layer intermediate length scale model which filters out barotropic instability and focuses on the subinertial baroclinic evolution of density-driven flows within the context of allowing finite-amplitude height variations in the lower layer. The baroclinic destabilization of a bottom-trapped coupled front on a sloping bottom is described. In the overlying fluid the instability takes the form of amplifying topographic Rossby waves. In the coupled front the perturbations to the downslope incropping are preferentially amplified compared to those on the upslope incropping. The perturbations to the downslope incropping develop into downslope propagating plumes which eventually evolve into relatively coherent along-slope propagating domes. We discuss the propagation characteristics of these domes. We also simulate the evolution of density-driven eddies or domes. The first eddy simulation we describe is for an initial eddy configuration which satisfies a zero topographic Rossby wave condition in the upper layer. We show that these traveling solutions remain remarkably coherent over a period of about 40 eddy circulation times or about 250 days for typical continental slope values. For a sufficiently large initial eddy height, upper layer fluid parcels can be transported in the along-slope direction by the baroclinic eddy. We also simulate the evolution of an initial eddy configuration which does not satisfy a zero topographic Rossby wave condition in the upper layer. A relatively intense cyclonic circulation develops in the overlying fluid over the traveling dome as does a topographic Rossby wave tail. However, even these solutions remain surprisingly coherent over many eddy circulation times.

On the baroclinic instability of axisymmetric rotating gravity currents with bottom slope

“…A number of numerical simulations (e.g. Jiang & Garwood 1995Swaters 1998a) have also shown that the spatial structure of the baroclinic instabilities associated with density-driven flows on a sloping bottom are strongly asymmetrical in the cross-slope direction. This is in contrast to instabilities of surface-driven currents (on an f-plane), where there is no external force acting to break the underlying cross-current symmetry.…”

“…Swaters (1998a) described numerical simulations of the model for coupled fronts and eddies, and documented the evolution of the downslope plumes into alongslope propagating eddies. The propagation characteristics of these eddies have been studied by Swaters & Flierl (1991) and Swaters (1998b).…”

Stability of meridionally-flowing grounded abyssal currents in the ocean

“…The result is that there is a spatial asymmetry (even on an f -plane) in the destabilization of these grounded abyssal currents. This asymmetry is clearly seen in numerical simulations (Swaters [4,8]). …”

“…For a parabolically shaped abyssal current with up slope and down slope groundings, this condition holds on the down slope flank but not on the up slope flank. This is why the instability preferentially amplifies on the down slope flank and the amplitude of the perturbations along the down slope grounding are much larger compared to those on the up slope grounding (see Swaters [4,7,8]). Physically, energy is required to move grounded abyssal fluid parcels located adjacent to the up slope grounding up the sloping bottom (against the force of gravity), while energy is released by the down slope movement of grounded abyssal fluid parcels located along the down slope grounding.…”

Meridional flow of grounded abyssal currents on a sloping bottom in spherical geometry

“…These currents form an important component in the deep "leg" of the meridional overturning circulation in the oceans. The mesoscale dynamics of these currents has been described in a series of papers [1][2][3][4][5][6][7][8][9][10][11]. All of these studies have implicitly assumed either an f or β-plane approximation in which the dynamics is modelled in a Cartesian coordinate system with the implicit assumption that the horizontal length scales are not too much larger than the internal deformation radius (on the order of about 10-100 km in the ocean).…”