Abstract:We study the dynamics of the two dimensional Navier Stokes equations linearized around a strictly monotonic shear flow on T×R. The main task is to understand the associated Rayleigh and Orr-Sommerfeld equations, under the natural assumption that the linearized operator around the monotonic shear flow in the inviscid case has no discrete eigenvalues. We obtain precise control of solutions to the Orr-Sommerfeld equations in the high Reynolds number limit, using the perspective that the nonlocal term can be viewe… Show more
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