Steady Disturbances to Viscous, Highly Conducting Laminar Boundary Layer Flow over a Nonconducting Wall with Parallel Magnetic Field

摘要

Steady disturbances to laminar boundary layer flow over a flat wall bounding a nonconducting rigid medium in the presence of a parallel magnetic field are examined. Disturbances are assumed due to both small wall irregularities and to weak incident waves when these may exist in the uniform stream outside of the boundary layer. The viscosity and electrical resistivity are assumed to be small, and heat conduction is assumed to be absent. It is shown that, adjacent to the wall, there is a critical layer in which the flow behavior depends on the relative smallness of the viscosity and the resistivity. Outside this layer, the flow is adequately given by a solution of the degenerate equation obtained by taking the viscosity and the resistivity zero. The resulting emitted waves, current sheet, wall pressure, and upstream behavior depend critically on the relative smallness of the viscosity and resistivity. (Author)