A monopolar vortex encounters a north-south ridge or trough

J.H.G.M. van Geffen and P.A. Davies
Fluid Dynamics Research 26 157--179 (1999)

1. Introduction

Field observations (see e.g Richardson 1993a,b; Bower et al., 1995; Kamenkovich et al., 1996; Bograd et al., 1997 have shown the widespread existence of several kinds of oceanic vortices, such as, for example, Meddies, Gulf Stream eddies and anticyclones, and Agulhas eddies. These vortices are relatively abundant; Richardson (1993b) estimates that there are roughly 1000 discrete eddies in the North Atlantic. Many are created in frontal regions and they are thought to play an important role in the horizontal transport of quantities such as heat, momentum, salt and pollutants. The vortices move due to a combination of the latitudinal (y) variation of the Coriolis parameter f (the so-called beta-effect) and the general background oceanic flow. As such vortices move, they inevitably interact with submarine topographic features, and these interactions are known to influence the trajectories of the vortices (with the possibility that the vortex may be destroyed by the topographic encounter).

Van Geffen and Davies (1999) -- hereafter named VGD -- employed a simple one-layer two-dimensional (shallow water) model to study the basic features of vortex-topography interactions. They considered a cyclonic monopolar vortex encountering a smooth ridge with variable height, width and orientation on a pure beta-plane (i.e. with Coriolis parameter f=beta y) and showed, for example, that a north-south oriented ridge has a much larger impact on the monopole's evolution than an east-west oriented counterpart, under otherwise-identical conditions. VGD shows that the influence of the north-south ridge depends on the width and height of the ridge and reported that whereas the monopole can cross a low ridge with some disturbance to its trajectory, sufficiently high ridges cause topography-induced flow deformations that can lead to the disintegration of the vortex.

For cases of finite height topography where the monopole crosses the north-south ridge after significant topographic interaction, VGD concluded that such behaviour is determined crucially by whether the vortex has gathered sufficient positive potential vorticity on its (north)west side by moving north along the ascending (east) side of the ridge. A question that then naturally arises is whether the initial position of the monopole in the north-south direction (the y-coordinate) influences the monopole's evolution. The study described in the present paper investigates this point, for cases in which the width and orientation of the ridge are kept fixed but the height is varied; cases of negative heights (i.e. troughs) are included in this study. The other point left open by VGD is the influence of a non-zero f0 on the evolution of the monopole, where f0 is the constant part of the Coriolis parameter: f=f0+beta y. The present study shows that varying the initial y-position at f0 is dynamically equivalent to varying f0 at constant initial y-position.

Several workers have investigated theoretically the motion of vortices on a beta-plane. Of particular relevance here is the analytical study of Llewellyn-Smith (1997) on the evolution of non-isolated vortices (the monopole used in the present paper is non-isolated) on a beta-plane. Similar related studies have been performed by e.g. Sutyrin and Flierl (1994), Reznik and Dewar (1994) and Korotaev and Fedotov (1994). One of the results of these studies that the difference in magnitude of the vorticity gradient across the vortex and the background vorticity gradient due to the beta-effect determine the trajectory of the vortex. It is possible that these analytical approaches could be extended to incorporate the combined effect of a bottom topography and the disturbance in the overall background vorticity due to the beta-effect, though such an analytical treatment falls outside the scope of the present paper. Instead, the attention is focussed here on the results of numerical experiments of a set of interaction processes and the classification of the possible outcome of these interactions.

The remainder of this paper is organised as follows. The numerical model is outlined in Section 2 and the motion of a monopole on a beta-plane without topography is briefly addressed in Section 3. Sections 4 and 5 present the results of simulations in which the monopole encounters a north-south ridge and trough, respectively, and some concluding remarks are formulated in Section 6

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