Vortex Generation Through Balanced Adjustment

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Abstract
The problem of geostrophic adjustment, originally considered by C.G. Rossby, is solved in an axisymmetric geometry for a continuously stratified fluid, where the adjusted final state is in hydrostatic, gradient-wind balance. This problem is relevant to the generation of submesoscale coherent vortices in the ocean: diapycnal mixing events can create a local anomaly of less strongly stratified fluid, which then develops a balancing circulation through adjustment. An analytical solution is obtained for a few uniform-density layers, and this is compared with numerical solutions for continuous stratification. In both representations, two-dimensional solutions are compared with axisymmetric ones. Abstract The problem of geostrophic adjustment, originally considered by C.G. Rossby, is solved in an axisymmetric geometry for a continuously stratified fluid, where the adjusted final state is in hydrostatic, gradient-wind balance. This problem is relevant to the generation of submesoscale coherent vortices in the ocean: diapycnal mixing events can create a local anomaly of less strongly stratified fluid, which then develops a balancing circulation through adjustment. An analytical solution is obtained for a few uniform-density layers, and this is compared with numerical solutions for continuous stratification. In both representations, two-dimensional solutions are compared with axisymmetric ones.

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