In this article, thanks to a detailed study of the Green function of Rayleigh’s equation near an extremum of the velocity of a shear layer, we study the asymptotic behavior of solutions to the linearized incompressible Euler equations and the so called “vorticity depletion property” discovered by Bouchet and Morita (Phys. D 239(12), 948–966, 2010). We, in particular, use a localization property of the solutions of Rayleigh’s equation near extrema of the velocity.
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Funding
National Natural Science Foundation of China(12271032)
RIGHTS & PERMISSIONS
Peking University
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