THE INTERACTION OF A PAIR OF POINT POTENTIAL VORTICES IN UNIFORM SHEAR

A simple point vortex model is formulated to investigate the deformati on and translation of lens-like oceanic eddies, such as Mediterranean Salt Lenses, in large-scale shear. The idealized eddy is represented b y a pair of quasigeostrophic 'point potential vortices' at different d epths in a uniformly stratified fluid. The point vortices are assumed to be embedded in a flow with uniform vertical and horizontal shear, a nd they are advected by the background flow as they interact with one another. The model successfully reproduces many aspects of the behavio ur of low-mode disturbances found in models with continuous (non-singu lar) representations. Depending upon the strengths of the vortices, th eir initial separation, and the intensity of the background shear, the vortex pair is either torn apart by the shear, or else remains couple d for all time, in which case the vortices execute a periodic motion w hile propagating with respect to the ambient fluid. Solutions represen ting steadily translating point vortex configurations are obtained for certain values of the model parameters. For a given vertical separati on between the vortices and a specified background shear, there can ex ist up to three steadily translating solutions, each with a different horizontal separation between the vortices, and each aligned perpendic ular to the background flow direction. The translation speed of these pairs is directly proportional to the difference in the strengths of t he vortices. A detailed analysis of the character of the steadily tran slating solutions is made, and the linear stability properties of the solutions are investigated.