Abstract
The Cauchy problem is solved for axisyimmetric vortex perturbations of an exponentially stratified incompressible ideal liquid. The behaviour of vorticity inside the region of its initial location, near the boundary of that region, and away from it in the “wave” zone is studied. A number of examples and analyzed with a specific initial distribution of vorticity, among which are examples of anomalous solution behaviour. It is shown that the initial jump of vorticity in a stratified liquid does not vanish, but oscillates at a frequency which depends on the direction. When passing to the limit of strongly singular initial distributions of the vortex filament and cylindrical vortex layer types, the solution increases with time.
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