A planar incompressible and electrically conducting fluid can be described by the 2D Navier-Stokes-MHD system. One simple yet physically relevant laminar state is the Couette flow with a constant homogeneous magnetic field, given by uE=(y,0), BE=(b,0) in the domain T×R. The goal is to estimate how large can be a perturbation of this state while still resulting in a solution close to the laminar regime, thereby preventing the onset of turbulence. We prove that Sobolev regular initial perturbations of size O(Re-2/3), with Re being the Reynolds number, remain close to uE, BE and exhibit dissipation enhancement. The latter quantifies the convergence towards an x-independent state on a time-scale O(Re-1/3), much faster than the standard diffusive one O(Re-1).
This video was produced by the SITE Research Center at New York University, as part of their talk series.
