On the smallness condition in linear inviscid damping: monotonicity and resonance chains.

We consider the effects of mixing by smooth bilipschitz shear flows in the linearized Euler equations on. Here, we construct a model which is closely related to a small high frequency perturbation around Couette flow, which exhibits linear inviscid damping for L sufficiently small, but for which damping fails if L is large. In particular, similar to the instability results for convex profiles for a shear flow being bilipschitz is not sufficient for linear inviscid damping to hold. Instead of an eigenvalue-based argument the underlying mechanism here is shown to be based on a new cascade of resonances moving to higher and higher frequencies in y, which is distinct from the echo chain mechanism in the nonlinear problem. [ABSTRACT FROM AUTHOR]