Electromagnetic Control of a Transitional Boundary Layer

We investigate numerically the transition to turbulence in a flat-plate boundary layer controlled by electromagnetic forces. The fluid considered is incompressible, Newtonian and low electrically conductive. Similar to boundary layer suction, when applying a steady, wall-parallel, and streamwise oriented Lorentz force, the Blasius velocity profile is transformed to an exponential one. Since the critical Reynolds number increases to by two orders of magnitude, Transition to turbulence is delayed, and finally drag is reduced. Direct numerical simulation (DNS) of both linear (2D) and nonlinear (3D) stages of the transition process were performed, as well as a linear stability analysis (LSA) of the intermediate velocity profiles. The obtained results confirm the expected increased stability of the controlled flow. Transition to turbulence is delayed by either damping primary instability, or, in the nonlinear case, by suppressing the emerge of Omega-vortices which usually preceeds the breakdown to turbulence. Surprisingly, our calculations suggest interesting stability characteristics of the intermediate velocity profiles. The decay rate of small disturbances in DNS is maximum in a region near the onset of control and decreases as the velocity profile evolves towards the exponential shape. In LSA, critical Reynolds numbers of intermediate profiles are found to be larger than for the exponential profile.