Melting dynamics of an ice surface in a turbulent shear flow

We study the dynamics and morphology of a solid as it melts in an idealized setup: we consider an initially flat solid surface between a heated and a cooled plate, with an imposed mean flow. By means of direct numerical simulations, and using the phase-field method, the equations of motion of the fluid phase are coupled with the heat equation within the solid, and a mean flow is sustained by imposing a fixed pressure gradient in the direction parallel to the plates, for Rayleigh numbers in the range 10ˆ5-10ˆ8 and friction Reynolds numbers in the range 10ˆ2-10ˆ3. We study the formation and evolution of patterns and surface roughness, the melt rate, and the heat exchange between the solid and liquid phases while systematically varying the intensity of the imposed mean flow.