Tearing instability of isolated compressible vortices

The present paper addresses the instability of a compressible vortex flow. We consider a family of so-called isolated vortices - the circular planar vortices that have zero circulation (net voracity). The term "isolation" implies the presence of a shield in the voracity field - a region of voracity of common sign surrounding the central domain where the voracity is oppositely signed. To model such a voracity field, a generalized Taylor-type profile for the swirl velocity in the radial direction is employed, which involves two parameters: intensity mu (proportional to the maximal velocity) and steepness beta (characterizing the scale of the shield zone). Vortices are assumed to be compressible and homentropic. The linear-stability analysis is carried out, which shows that isolated vortices can exhibit both stable and unstable behavior depending on the model parameters mu and beta. By numerical simulations of the non-linear stage, the unstable normal modes are shown to evolve towards tearing of the basic vortex with formation of smaller secondary vortical structures.