Thermal oscillations in a fluid heated from below and cooled to freezing from above

A theoretical discussion is given of the thermal transients and self-sustained oscillations in a fluid, heated at a constant rate below the surface, and cooled from the top strongly enough to allow freezing. Assuming that the fluid is well mixed and that the thickness of the ice is small compared to the fluid depth, it is shown that the system can have zero, one, or two steady states. The ice-covered steady state is stable for small perturbations; however, the ice-free steady state may be unstable with the impulsive addition of a thin ice sheet. Transient developments may include both ice-covered and ice-free states. In the case where no steady state exists the system exhibits periodic self-sustained oscillations. Application of the theory to a laboratory experiment is considered.