Stability of straining flow with surface cooling and temperature-dependent viscosity

The stability of uniform straining flow in a semi-infinite body of viscous fluid subjected to surface cooling is examined. The viscosity of the fluid is assumed to be a prescribed function of temperature. If the viscosity variations caused by the cooling are sufficiently large the straining flow is linearly unstable to a mode in which the rate of extension of the viscous thermal boundary layer becomes localized. The parameters of the problem are the viscosity contrast in the fluid and a dimensionless measure of the rate of strain relative to the rate of cooling. The conditions under which instability occurs are determined and the physical mechanisms responsible are examined. The results are applied to discuss the formation of some surface features in lava flows.