Author : Jacob Bedrossian
Release : 2020-09-28
Genre : Mathematics
Kind : eBook
Book Rating : 175/5 ( reviews)
Book Synopsis Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case by : Jacob Bedrossian
Download or read book Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case written by Jacob Bedrossian. This book was released on 2020-09-28. Available in PDF, EPUB and Kindle. Book excerpt: The authors study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. They prove that for sufficiently regular initial data of size $epsilon leq c_0mathbf {Re}^-1$ for some universal $c_0 > 0$, the solution is global, remains within $O(c_0)$ of the Couette flow in $L^2$, and returns to the Couette flow as $t rightarrow infty $. For times $t gtrsim mathbf {Re}^1/3$, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of ``2.5 dimensional'' streamwise-independent solutions referred to as streaks.