The interaction of a pair of point potential vortices in uniform shear
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A simple point vortex model is formulated to investigate the deformation and translation of lens-like oceanic eddies, such as Mediterranean Salt Lenses, in large-scale shear. The idealized eddy is represented by a pair of quasigeostrophic ‘point potential vortices’ at different depths in a uniformly stratified fluid. The point vortices are assumed to be embedded in a flow with uniform vertical and horizontal shear, and they are advected by the background flow as they interact with one another. The model successfully reproduces many aspects of the behaviour of low-mode disturbances found in models with continuous (non-singular) representations. Depending upon the strengths of the vortices, their initial separation, and the intensity of the background shear, the vortex pair is either torn apart by the shear, or else remains coupled for all time, in which case the vortices execute a periodic motion while propagating with respect to the ambient fluid. Solutions representing steadily translating point vortex configurations are obtained for certain values of the model parameters. For a given vertical separation between the vortices and a specified background shear, there can exist up to three steadily translating solutions, each with a different horizontal separation between the vortices, and each aligned perpendicular to the background flow direction. The translation speed of these pairs is directly proportional to the difference in the strengths of the vortices. A detailed analysis of the character of the steadily translating solutions is made, and the linear stability properties of the solutions are investigated.