Compression of magnetic field in a viscous boundary layer

Galloway, Proctor, and Weiss have shown by numerical experiment that the magnetic field extending across a convective cell in a highly conducting viscous fluid may be concentrated into sheets with energy density B ²/8 larger than the kinetic energy density 1/2v ² of the convection by a factor (v/)^1/2 or more. This paper employs conventional boundary layer theory for high Reynolds number to provide a simple analytical example illustrating this remarkable effect of field concentration.This work was supported by the National Aeronautics and Space Administration under grant NGL 14-001-001.