Linear inviscid damping and enhanced dissipation for the Kolmogorov flow

Abstract

In this paper, we prove the linear inviscid damping and voticity depletion phenomena for the linearized Euler equations around the Kolmogorov flow. These results confirm Bouchet and Morita's predictions based on numerical analysis. By using the wave operator method introduced by Li, Wei and Zhang, we solve Beck and Wayne's conjecture on the optimal enhanced dissipation rate for the 2-D linearized Navier-Stokes equations around the bar state called Kolmogorov flow. The same dissipation rate is proved for the Navier-Stokes equations if the initial velocity is included in a basin of attraction of the Kolmogorov flow with the size of ${\nu }^{\frac{2}{3}+}$, here $\nu$ is the viscosity coefficient.

arXiv comment92 pages

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Cited by in corpus (9)

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• Inviscid damping and enhanced dissipation of the boundary layer for 2D Navier-Stokes linearized around Couette flow in a channel
• Separation of time-scales in drift-diffusion equations on ${\mathbb{R}}^2$
• Stable mixing estimates in the infinite Péclet number limit
• On variable viscosity and enhanced dissipation