Interact: Interesting Assorted Problems Involving Geophysical Flows

Sunlight plays a critical role in the thermodynamics of ice-covered water bodies, as shown by recent field observations and numerical studies linking depth-dependent light absorption to the formation of convectively mixed layers beneath the ice. This phenomenon, known as radiatively-driven convection (RDC), emerges in nature under transient conditions and has been associated with Rayleigh–Taylor instabilities, both in its emerging mechanics and the high mixing rates observed in the field. Here, we study RDC using spectrally-resolved equations under the Oberbeck-Boussinesq approximation and a non-monotonic equation of state. We model an initially stably stratified system subjected to time-periodic, depth-dependent internal heating that mimics diurnal solar absorption under ice. Once convection sets in, the characteristic flow magnitude follows the Deardorff scaling, governed by the rate of available potential energy input from sunlight. We further quantify system energetics to estimate the mixing efficiency—the fraction of input energy used for irreversible thermal mixing—reaching values above η_mix = 0.7, consistent with Rayleigh–Taylor mixing and field-based estimations of RDC in lakes. These results underscore the significance of RDC in catalyzing under-ice mixing, with implications for biogeochemical fluxes, ecosystem dynamics, and the seasonal evolution of cryospheric aquatic systems.

Funding acknowledgement

Start-up funding University of Pennsylvania