The time- and thickness scales in the MHD-Rayleigh problem. A formal analysis

The MHD Rayleigh problem was qualitatively analyzed in a systematic manner. Starting from the complete system of equations, simple subsystems were derived using the magnetic Prandtl number as a parameter. These subsystems are characteristic for the various boundary layer regions to be recognized. Initially a purely viscous and a much thicker e.m. layer exist. These layers develop an interactive character in a characteristic time T, the value of which is given. The viscous layer develops into a Hartmann layer of constant thickness and the e.m. layer develops into an Alfven wave with an electrically diffusing front.