Transition in channel flow with streamwise magnetic field

Abstract

Abstract Transition to turbulence in a magnetohydrodynamic channel flow is studied numerically under a uniform and constant streamwise magnetic field. The laminar–turbulence transition can be triggered with transient growth and subsequent breakdown of linear optimal perturbations in different forms: streamwise mode, a single oblique mode and a pair of symmetric oblique modes. The nonlinear evolution of optimal modes is analyzed via a series of direct numerical simulations at a single subcritical Reynolds number R e = 5000 and different Hartmann numbers H a ranged from 10 to 70. It is found that, the superposition of symmetric oblique modes can trigger the transition most efficiently even with a lower perturbation energy level. The streamwise mode is less efficient and transition can be observed only after adding three dimensional random noise at the moment of strongest energy amplification. The magnetic damping effect is significant at high Hartmann number and no transition is found under a sufficiently strong magnetic field with H a larger than approximately 70. This critical value can be predicted straightforwardly from the linear relationship of friction coefficient of channel flow and magnetic interaction parameter.