Seminar Event Detail

Differential Equations

Date:  Thursday, December 03, 2015
Location:  4088 East Hall (4:00 PM to 5:00 PM)

Title:  On the subcritical transition of the 3D Couette flow

Abstract:   We discuss 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 this threshold. For rougher data, we obtain an estimate of the stability threshold which agrees closely with numerical observations. The primary linear stability mechanism is an anisotropic enhanced dissipation effect which results from the mixing caused by the large mean shear; the main linear instability mechanism is a non-normal instability known as the lift-up effect. Understanding weakly nonlinear effects and devising the correct norms to estimate them form the core of the analysis we undertake. Joint work with Pierre Germain and Nader Masmoudi.


Speaker:  Jacob Bedrossian
Institution:  Univ. Maryland, College Park

Event Organizer:     


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