The sub-microscale dynamics of double-diffusive convection

Abstract

This study investigates the dynamics of fingering convection on scales much smaller than the typical size of individual salt fingers. On such scales, salinity patterns exhibit the spontaneous emergence of sharp fronts induced by finger-scale strain. In contrast, velocity and temperature fields are largely devoid of sub-microscale variability, which is attributed to the rapid molecular dissipation of heat and momentum. The presence of fine salinity structures fundamentally limits the efficiency of direct numerical simulations (DNS) of double-diffusive processes. In the oceanographic context, the computational cost of resolving sub-microscale salinity features exceeds that of temperature-only DNS by up to four orders of magnitude, severely restricting the types of double-diffusive systems that can be studied numerically. To address this complication, we introduce the sub-microscale filtering (SMF) algorithm, which resolves temperature and velocity while parameterizing the sub-microscale dynamics of salinity. The proposed closure draws inspiration from the Smagorinsky scheme, which represents unresolved processes by the downgradient strain-dependent momentum flux. The SMF model is successfully validated through fully resolved simulations.