A monopolar vortex encounters an isolated topographic feature on a beta-plane

J.H.G.M. van Geffen and P.A. Davies
Dynam. Atmosph. & Oceans 32, 1--26 (2000)

1. Introduction

Vortices are common phenomena under many geophysical circumstances. In the Earth's oceans, for example, Meddies, Gulf Stream eddies and anticyclones, Agulhas eddies, etc. have been observed (see e.g. Richardson 1993a,b; Bower et al., 1995; Kamenkovich et al., 1996; Bograd et al., 1997). These vortices move through the oceans due to a combination of the ambient flow and the latitudinal (y) variation of the Coriolis acceleration (the so-called beta-effect). On their way through the ocean, these eddies encounter topographic features at the ocean floor. It is known that such an encounter affects the eddy's trajectory. This can lead to large deformations of the eddy, or even to its destruction (e.g. Richardson 1993a,b; Shapiro et al. 1995), as a consequence of which the contents of the eddy may be released in the ocean. Though the background of the study presented here is a vortex that encounters a topography in oceans, similar processes can be of importance for the evolution of large-scale vortices in the atmosphere; for reviews see e.g. Bengtsson and Lighthill (1982) and Hopfinger and Van Heijst (1993).

Since oceanic vortices are thought to play an important role in the transport of water properties (such as salt, heat, momentum and pollutants), it is of importance to understand the basic mechanisms of what happens if a vortex encounters bottom topography. In that light, the present numerical study considers the effect of a circular mountain on the motion and evolution of a monopolar vortex, as a model for what could happen to an oceanic vortex. In Section 3.1 comparisons are made between the key controling parameters of the model and the oceanic eddies under consideration, in order to establish the relevance of the results to oceanic processes. The monopole in the simulations is cyclonic (anti-cyclonic) in the northern (southern) hemisphere and it moves to the north-west due to the beta-effect (see e.g. Van Heijst, 1994). Carnevale et al. (1991) have shown with laboratory and numerical experiments that in the northern hemisphere a cyclonic monopole, when placed on a hill, climbs to the top of the hill in an anti-cyclonic spiral. The reason for this is that the beta-effect is dynamically equivalent to a sloping bottom boundary, with north towards shallow fluid depth (Van Heijst, 1994); hence, for a hill the local topography-induced north-west is uphill and to the left.

In their experiments, Carnevale et al. (1991) used a monopole that was much smaller in lateral size than the topography and the monopole was released on the topography. In the present study, however, the monopole is initialised at a position to the south-east of the seamount. The radius of this mountain (R) is varied from the same size as to four times that of the monopole (a). The latter moves due to the beta-effect, represented by beta y in the Coriolis parameter f=f0+beta y, with y the local north coordinate. Carnevale et al. (1991) used two positive values of f0, representing a topography located at two latitudes in the northern hemisphere. In the case study numerical simulations discussed below, beta is kept constant at 0.3 (dimensionless units) and f0 is varied from -5 to +5, thus representing encounters taking place between far south and far north of the equator (for f0=0 the mountain is at the equator). Such extreme cases capture the essential features and ranges of the possible effects of a seamount on a vortex.

A range of numerical experiments in which a dipolar vortex (a modon) encounters a topography (ridge, hill, random or other) was presented by Carnevale et al. (1988). They observed in some cases effects of shedding of vorticity from the topography during the approach of the vortex similar to the effects discussed below. Carnevale et al. (1988) observed these effects, for instance, when the modon breaks up if it encounters a hill, in which case the positive vortex is seen to move uphill, where it can remain trapped; the negative vortex, meanwhile, moves away from the hill, together with positive vorticity generated by the flow across the hill. Modon breakup occurs on a hill with a horizontal scale similar to or somewhat less than that of the modon. In the present study, the monopole is of the same size as or smaller than the mountain.

The numerical model used is the same as that of Van Geffen and Davies (1999a,b): a one-layer two-dimensional barotropic model with rigid-lid approximation, with bottom topography suitably incorporated. Section 2.3 reviews the main assumptions and approximations of the model in relation with oceanic vortices such as those mentioned above.

Van Geffen and Davies (1999a,b) showed that when a monopole encounters a two-dimensional topographic ridge, the height and width of the ridge and the value of f0 (or, equivalently, the north-south position of the encounter) determine the evolution of the monopole: the vortex can cross the ridge, be trapped on the ridge and decay there, be destroyed on the ridge by strong vorticity gradients, or be rebounded by the ridge without reaching the foot of the ridge. The above studies have illustrated the practical difficulties in categorising flows corresponding to the many combinations of the free parameters of the problem. Accordingly, in the present study, the most profitable approach is considered to be that of the case study, for fixed values of some of the controlling parameters. The height of the cosine-shaped, circularly-symmetric seamount, for example, is kept fixed at hmax=0.4, relative to the fluid depth away from the topography, whereas its radius R is varied. Varied is also the value of f0 in the Coriolis parameter, as mentioned above. All other model parameters remain unchanged.

The remainder of the paper is organised as follows. The model and some computational aspects are given in the next section. Section 3 presents the results of the simulation and some concluding remarks are formulated in the final section.

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