Effects of the nonlinear equation of state on the basal melting and freezing of ice layer under the influence of shear flow

Basal ice melting under shear flow is a key process in polar and lacustrine environments, where it is influenced by both external forcing and water's nonlinear equation of state. While previous studies have examined buoyancy-driven convection and shear separately, their interplay with density inversion remains poorly understood. By using direct numerical simulations, we reveal distinct flow regimes and interface morphologies controlled by the inversion stability ratio and effective Richardson number, providing scaling laws for heat transport and a theoretical framework for regime transitions.