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)

6. Concluding remarks

A two-dimensional numerical model has been used to study the effect of a north-south oriented ridge or trough on the evolution of a monopolar vortex that moves to the north-west due to the beta-effect. The principle objective of the study has been to investigate the effects of different initial north-south positions y0 of the monopole on the interaction with the topography, in order to extend a previous study (Van Geffen and Davies, 1999 -- here named VGD) in which such an interaction was studied for a fixed value of y0. The present study has shown that varying the initial y0-position of the monopole is dynamically equivalent to changing the value of f0, the reference constant value in the Coriolis parameter f=f0+beta y. (Note that the previous VGD study considered only f0=0, and that here only changes in y0 were considered since varying y0 at f0=0 produces the same effect dynamically as varying f0 at constant y0.)

A further objective has been to investigate the effect upon the vortex-topography interaction of the initial, undisturbed configuration of the potential vorticity field associated with the topography. Since positive (ridge) and negative (trough) topographies of otherwise-identical geometrical forms and dimensions have different potential vorticity configurations, differences are to be anticipated between the interactions of a given monopole with a ridge or trough. The focus of the study has been to determine the nature of these differences for different values of A, the amplitude of the topographic element, and y0, the initial north-south location of the monopole.

The study has shown that all of the above factors are able to influence directly the type of flow that results from the interaction of the self-propelled vortex and the topographical element. Tables I and II (contained within Sections 4 and 5, respectively) have summarised the various characteristic flow types observed with ridge and trough topographies, respectively, and have demonstrated, in particular, the differences between such identifiable flow types for the positive and negative A values. The model shows that for different initial positions y0 there are essentially four regimes for the fate of the monopole: it can be destroyed, trapped or rebounded by the topographic interaction, as well as being able to cross it. Furthermore, the fate of the monopole depends on the amplitude |A| of the tropography: the lower the value of |A|, the easier (i.e. for a wider range of y0-positions) can the monopole cross the obstruction.

Of particular relevance here has been the observation in VGD that for the same domain and the same initial conditions as the present study, a monopole initially located at a fixed reference position y0=-3 (f0=0) was evidently able to cross a given ridge only if it had gathered sufficient positive potential vorticity omegap at its northwest side. Though such a conclusion is trivially invalid for ridge and trough topographies having infinitessimal amplitudes A, the cases of finite height ridge topography considered in VGD and the particular value of y0=-3 investigated therein suggest strongly that such a distribution of omegap is associated with the passage over the ridge by the vortex. The present study, however, with varying values of y0 (or, equivalently, varying f0-values) has shown that the finding of VGD is incomplete in this regard and that the fate of the monopole is determined generally by the initial potential vorticity configuration above the topographic element. The sign of the potential vorticity is of importance because it determines the details of the potential vorticity distribution above the topography.

The present study has confirmed the findings of VGD that as the monopole propagates towards the topography, the principal effect of the motion of the monopole is the distortion caused to the initially-undisturbed vorticity contours by the generation of Rossby waves. As a result of subsequent interactions with this secondary vorticity, so-called beta-gyres (e.g. Sutyrin and Flierl, 1994) are generated (see Section 3); the monopole's trajectory far from the topography consists of small scale lateral deviations superimposed upon a straight line path. As the vortex encounters the topography, the topographically-generated potential vorticity field is advected by the velocity induced by the vortex itself. Since the contours of potential vorticity in the presence of a north-south ridge or trough are not simply aligned in the east-west direction, the topographic beta-gyres induced by the advection process become significantly different from the counterpart beta-gyres associated with the beta-plane motion in the absence of topography.

Moreover, as the results of the computations discussed in the present paper illustrate (see, for example, Figs. 2, 3, 6, 8, and 12), the shape of the initially-undisturbed potential vorticity contours with topography present depends on (i) the value of y0, and (ii) whether the topographic element is a ridge or a trough. Consequently, as the model results illustrate, the advection of the ambient potential vorticity field by the approaching monopole induces topographic beta-gyres of fundamentally different character for different values of y0 and for different polarities of A. The outcome of a vortex-topography interaction is thus determined by the topography-induced deformation of the background vorticity field due to the beta-effect. And this deformation is larger for initial positions more to the north or south and for higher ridges and deeper troughs.

Note on notation here
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