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Mixing and stability near the subcritical transition of the 3D Couette flow

4:00 pm Friday, April 17, 2015
Jacob Bedrossian (University of Maryland)

Abstract: We discuss recent developments on the relationship between mixing and the dynamics of small perturbations of the plane, periodic Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number. For sufficiently regular initial data, we determine the stability threshold for small perturbations and characterize the long time dynamics of solutions below the threshold. The primary stability mechanisms at work are the enhanced dissipation and the inviscid damping of the velocity component normal to the shear, both a result of the fluid mixing itself. After detailing these effects, we will discuss some of the important steps in the proof, in particular, the analysis of the weakly nonlinear instabilities connected to the non-normal nature of the linearization. Joint work with Pierre Germain and Nader Masmoudi.

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