The Cooling Box Problem: A Freezing Lake in the Lab

Recent field measurements have demonstrated that inland waters are warming rapidly and that seasonally ice-covered lakes are warming faster than those that do not. With limited field studies of lakes in harsh winter conditions, the impact of this changing environment is not clear, particularly from an ecological perspective. Similarly, the physical processes responsible for the warming within these cold-water bodies have not yet been identified. Our research focuses on the surface cooling processes occurring prior-to and immediately after ice formation, with a particular interest in the transport of heat. We model a cooling box problem, similar to the Rayleigh-Bernard problem. However, the nonlinear equation of state of freshwater complicates the traditional Rayleigh-Bernard analysis. We demonstrate that the nonlinear equation of state fundamentally alters the classical results of the Rayleigh-Bernard problem. Using a combination of linear stability analysis, numerical simulation and laboratory experiments, we quantify the mixing within the water column and the resultant surface heat transfer. Modified scaling laws for heat transport and energetics agree well with our data.