The effects of phase change on thermal and thermocapillary instabilities

Fluid flows over phase-changing boundaries find relevance in the study of many problems in astrophysical, geophysical, and engineering settings. A detailed understanding of the nonlinear coupling between fluid flow and the moving boundary is often critical to the evolution of the system. Growth of sea ice in the Earth's polar regions, the dynamics of ice sheets and the Earth's interior, and production of crystals for fabrication of semiconductors are a few examples that highlight their ubiquity across scales.

Here, we consider the stability of a layer of liquid that is bounded by its solid phase at the bottom and a free surface at the top. The liquid has a temperature of maximum density, T_m, and convective motions in the liquid layer ensue when the temperature of the free surface is greater than T_m. We use a combination of linear and asymptotic analyses to explore the effects of the phase-changing boundary, density anomaly, and the free surface on the thermal and thermocapillary instabilities in this system.