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

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 each for friction parameter H $\ensuremath{\gtrsim}$ 300 in MHD-Couette flow, and 1000 Shercliff flow. At low H, linear nonlinear growth led to saturation a traveling wave, where waves conjoin. For larger H\ensuremath{\ge}10, nonlinearity isolates TS one wall. H=10 turbulence is sustained distinct inertial subrange formed. H\ensuremath{\ge}30 state relaminarized, bulk production due flattened base