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Finite speed propagation in the relaxation of vortex patches. (English) Zbl 1028.76004

Summary: A degenerate parabolic equation has been proposed by R. Robert and J. Sommeria [Phys. Rev. Lett. 69, 2276-2279 (1992)] to describe the relaxation towards a statistical equilibrium state for a two-dimensional incompressible perfect fluid with a vortex patch as initial vorticity. In this paper, flows obtained by numerical integration of Robert-Sommeria equation over a long-time interval are compared with those obtained for Navier-Stokes equations at high Reynolds number. A finite speed propagation for the extremal values of the vorticity is numerically shown to hold for Robert-Sommeria equation. A rigorous proof of this (fine) property is also provided.

MSC:

76B47 Vortex flows for incompressible inviscid fluids
35Q35 PDEs in connection with fluid mechanics
76M22 Spectral methods applied to problems in fluid mechanics
76M20 Finite difference methods applied to problems in fluid mechanics
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