Analytical solutions for weakly compressible von Karman vortex streets

Abstract eng:
Vortex streets are a common feature of fluid flows at high Reynolds numbers and their study is now well developed for incom- pressible fluids. Much less is known, however, about compressible vortex streets. Recently Crowdy & Green presented analytical solutions describing a class of steady incompressible von Karman vortex streets with distributed vorticity. To construct these they adopted the hollow vortex model where each vortex is modelled as a finite-area constant pressure region with non-zero circulation. For weakly compressible flows steady hollow vortex solutions are well known to be candidates for the leading order solution in a perturbative Rayleigh-Jansen ex- pansion of a compressible flow. Here we give details of that expansion based on the vortex street solutions of Crowdy & Green. Physical properties of the compressible vortex streets are described. Our approach uses the lmai-Lamla method coupled with analytic function theory and conformal mapping.

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