Linear stability analysis for high-velocity boundary layers in liquid- metal magnetohydrodynamic flows
The paper is concerned with the linear stability analysis of the fully developed liquid-metal flow in a rectangular duct of uniform cross section with thin metal walls subjected to a strong, uniform, transverse magnetic field. For large Hartmann numbers the steady flow consists of a uniform core region and boundary layers adjacent to the sides of the duct. There exist large velocities in boundary layers which are parallel to the applied magnetic field. A small harmonic disturbance is superimposed on the basic flow and the resulting linearized equations are studied to reveal its stability characteristics. This is reduced to the solution of two independent eigenvalue problems. The first problem involves a disturbance vorticity perpendicular to the magnetic field and leads to always decaying solutions. In the second problem the disturbance velocity is parallel to the magnetic field and it is found that there is a critical Reynolds number equal to 313. This value is much lower than the experimental observations and it implies that a nonlinear stability analysis is, in fact, necessary.
scientific article; zbMATH DE number 91132