Rosier, Carole; Rosier, Lionel Finite speed propagation in the relaxation of vortex patches. (English) Zbl 1028.76004 Q. Appl. Math. 61, No. 2, 213-231 (2003). 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. Cited in 1 Document 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 Keywords:pseudo-spectral method; third-order Adams-Bashforth scheme; degenerate parabolic equation; statistical equilibrium; two-dimensional incompressible perfect fluid; vortex patch; Robert-Sommeria equation; long-time interval; Navier-Stokes equations; high Reynolds number; finite speed propagation PDFBibTeX XMLCite \textit{C. Rosier} and \textit{L. Rosier}, Q. Appl. Math. 61, No. 2, 213--231 (2003; Zbl 1028.76004) Full Text: DOI