Motion of a compressible vortex pair

Abstract eng:
Two equal and opposite point vortices translate uniformly. The desingularization of this configuration to vortex patches and hollow vortices leads to a translation velocity that depends on the size of the vortices. The hollow case was first considered by Pocklington. We extend the hollow solution to the case with compressibility by employing the Imai-Lamla version of the Rayleigh-Janzen expansion. We find the O(M 2 ) correction to the shape and velocity of the pair. The results are compared in the limit of small vortex size to the previous compressible calculations of Moore and Pullin and of Leppington.

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