We investigate the basal melting of ice in fresh water under the influence of external shear flow, and focus on the effects of density inversion and shear strength. Density inversion is modeled by a nonlinear equation of state and characterized by the inversion stability ratio $R$, while shear strength is quantified by the effective Richardson number $R{i}_e$. Different flow regimes are identified. When the density inversion is strong, a stably stratified layer suppresses convection, leading to pure conductive heat transfer and a flat ice-water interface. When density inversion is weak, convection motions are dominated by cells under weak shear and long rolls under strong shear, which result in different morphologies of ice interface. The average height of the surface and convection layer is strongly influenced by $R$ but only weakly by $R{i}_e$, while the interface roughness exhibits nonmonotonic dependence on both parameters due to different flow structures and nonuniform growth of the stably stratified layer. A single scaling relation is determined for the effective Rayleigh number and Nusselt number. Theoretical models are also developed for the heights of interface and convection layer, and the parameters for regime transitions, and agree well with numerical results.

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• Stratified turbulence
• Thermal convection