The Cooling Box Problem: Accounting for the Dynamic Surface Temperature*

Rayleigh-Benard convection is often modelled with a constant surface temperature. How-

ever, the surface temperature of many geophysical systems, such as lakes, is coupled to the

atmospheric forcing. In this presentation, we present two-dimensional numerical simulations

that account for this dynamic surface temperature using a single additional parameter β.

With an appropriately defined dynamical Rayleigh number, we recover many of the

results from the standard Rayleigh-Benard model. We hope that this work will simplify the

application of Rayleigh-Benard theory in geophysical contexts, such as lakes.