Vortex merger in rotating stratified flows

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Abstract
This paper describes the interaction of symmetric vortices in a three-dimensional quasi-geostrophic fluid. The initial vortices are taken to be uniform-potential-vorticity ellipsoids, of height 2h and width 2R, and with centres at (±d/2; 0, 0), embedded within a background flow having constant background rotational and buoyancy frequencies, f/2 and N respectively. This problem was previously studied by von Hardenburg etal. (2000), who determined the dimensionless critical merger distance d/R as a function of the height-to-width aspect ratio h/R (scaled by f/N). Their study, however, was limited to small to moderate values of h/R, as it was anticipated that merger at large h/R would reduce to that for two columnar two-dimensional vortices, i.e. d/R [approximate] 3.31. Here, it is shown that no such two-dimensional limit exists; merger is found to occur at any aspect ratio, with d [similar] h for h/R [dbl greater-than sign] 1.

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