Stability of a layer of viscous magnetic fluid flow down an inclined plane

This paper concerns the linear stability of a layer of viscous magnetic fluid flow down an inclined plane under the influence of gravity and a tangential magnetic field. The stability of a magnetic fluid in a three-dimensional space is first reduced to the stability of the flow in a two-dimensional space by using Squire's transformation. The stability of long waves and short waves is analyzed asymptotically. The stability of waves with intermediate length is obtained numerically. It is found that the magnetic field has a stabilizing effect on both the surface and shear modes and can be used to postpone the instability of such flows.