Instability of streaks in channel flow with streamwise magnetic field

S. Dong^1,2 - D. Krasnov² - B. W. Li¹ - T. Boeck²

¹ Key Laboratory of Electromagnetic Processing of Materials, Ministry of Education, Northeastern University, P. O. Box 314, 110004 Shenyang, China
² Institute of Thermodynamics and Fluid Mechanics, Ilmenau University of Technology, P. O. Box 100565, 98684 Ilmenau,Germany

Abstract
The instability of streaky flow in a channel under the presence of a homogeneous streamwise magnetic field is investigated in the framework of the linear problem. The secondary optimal perturbations, evolving on the top of steady streaks, are computed through an iterative procedure by solving the direct and adjoint governing equations. Two different amplitudes of the streaks are investigated in a wide range of Hartmann numbers at a fixed subcritical Reynolds number. Exponential instability as well as transient amplification of perturbations occurring at different streamwise wavenumbers are suppressed by the imposed a magnetic field. A simple scaling between the most exponentially unstable wavenumber and the magnetic interaction parameter can be explained by the balance of inertial and Lorentz force terms. Figs 7, Refs 18.