Recent progress in hydrodynamic stability at high Reynolds numbers

Hao Jia, Univ. of Minnesota, Twin Cities

Abstract: Hydrodynamic stability of incompressible fluid flows is a classical topic, studied already by Rayleigh, Kelvin, Orr, Sommerfeld, Heisenberg, among many others. The focus then was on the possible existence of unstable eigenvalues for the linearized equation (the so-called Orr-Sommerfeld equations) around physically relevant flows such as laminar flows, in an attempt to explain the onset of turbulence. In recent years, tremendous progress has been made in the understanding of the asymptotic dynamics--not just spectrum--in the perturbative regime of shear flows and vortices, especially in the two dimensional case, for both the inviscid and slightly viscous fluid. It turns out that the question of stability in incompressible fluid flows is much more subtle than previously imagined. In this talk, we will introduce some recent results. In particular we will emphasize three fundamental stabilizing mechanisms in incompressible fluid flows: inviscid damping, enhanced dissipation and vorticity depletion, as well as the destabilizing "Orr mechanism", in the context of a recent proof on the sharp transition threshold for Kolmogorov flows on a non-square torus.

Tea and refreshments available from 3:00-3:25 p.m. in the Assmus Conference Room (CU 212).

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