Resistive instability of a shearing boundary layer with imbedded shearing magnetic fields

The stability of a special three-dimensional shearing boundary layer with imbedded shearing magnetic fields is studied. Boundary layer solutions are obtained for a finitely, electrically conducting fluid, and then the sixth-order differential equations describing the instability are solved numerically. It is found that the flow is always unstable and that the neutral stability curves pass through the origin of the α-R diagram, where α is the wave number and R is the Reynolds number. An increase of the magnetic field tends to stabilize the flow when the conductivity is small or extremely large. An increase of resistivity has a stabilizing effect at moderate magnetic Prandtl number and a destabilizing effect at high magnetic Prandtl number.