On Magnetic Boundary Layers

The boundary layer on a symmetrical insulated body is examined with the assumptions that the fluid is inviscid and highly conducting, and that outside it the magnetic and velocity fields are everywhere parallel and in a constant ratio. It is shown that when the Alfvén speed is less than the fluid velocity then either reversed flow occurs in the boundary layer on roughly the last half of the body or, more probably, the boundary layer equations break down. If reversed flow occurs, then for a fluid which is slightly viscous but for which σν « 1 (σ = conductivity, ν = kinematic viscosity) the velocity boundary layer breaks down before the onset of reversed flow. In either case the assumption that outside the boundary layer the velocity and magnetic fields are parallel leads to a contradiction and, by analogy with the classical theory of viscous flow, it is inferred that instead, a substantial wake must develop downstream from the body. When the Alfvén speed is greater than the fluid speed then the magnetic boundary layer, if it occurs, must contain reversed flow at the forward stagnation point.