Stabilizing the Interface in a Saffman-Taylor Problem by Heating

The interface in a Saffman Taylor problem can be stabilized to perturbations of \textit{any wave length} by simply heating from above. The same is true for the Rayleigh Taylor instability. We present simple formulas for estimating the temperature difference required to do this and find that more reasonable temperature differences obtain in the Saffman-Taylor problem because the temperature dependence of the viscosity is ordinarily much stronger than the temperature dependence of the density.