The Cooling Box Problem: Experimental Parameterization of the Dynamic Surface Temperature

Rayleigh-Bénard convection is often modelled with a constant surface temperature. However, the surface temperature of many geophysical systems, such as lakes, is coupled to the atmospheric forcing. In this presentation, we present both two- and three-dimensional numerical simulations that account for this dynamic surface temperature using an additional coupling parameter $eta$. Results from these simulations show good agreement with laboratory experiments. We hope that this work will simplify the application of Rayleigh-Bénard theory in geophysical contexts, such as lakes.