Transition to turbulence in quasi-two-dimensional MHD flow driven by lateral walls

Abstract

We investigate MHD-Couette--Shercliff flows driven by lateral wall motion with turbulent transitions observed only at supercritical Re. Linearly, the Tollmien--Schlichting (TS) wave instability was isolated at each wall for friction parameter H $\ensuremath{\gtrsim}$ 300 in MHD-Couette flow, and H $\ensuremath{\gtrsim}$ 1000 for Shercliff flow. At low H, linear and nonlinear growth led only to saturation to a traveling wave, where the waves at each wall conjoin. For larger H\ensuremath{\ge}10, nonlinearity isolates the TS wave to one wall. At H=10 turbulence is sustained and a distinct inertial subrange formed. For H\ensuremath{\ge}30 the turbulent state relaminarized, with low bulk production due to the flattened base flow.