| Summary: | International audience Melting and solidification processes in the presence of convection are key to many geophysical problems. An essentialquestion related to these phenomena concerns the estimation of the time-evolving melting rate, which is tightly connectedto the turbulent convective dynamics in the bulk of the melt fluid and the heat transfer at the liquid-solid interface. In thistalk, we consider a convective-melting model, constructed as a generalization of the Rayleigh-Bénard system, accountingfor the basal melting of a solid. As the change of phase proceeds, an unstably-stratified fluid layer grows at the heatedbottom of the system and eventually reaches a turbulent convection state. By means of extensive numerical simulations,we explore the model dynamics in two and three-dimensional configurations (fig. 84). The focus of our analysis is onthe scaling of global quantities as well as on the interface morphology and the effects of space dimensionality. We findthat independently of dimensionality the convective-melting system behavior shares strong resemblances with that ofthe Rayleigh-Bénard one, and that the heat flux is only weakly enhanced with respect to that case. Such similarities areunderstood, at least to some extent, considering the resulting slow motion of the melting front (with respect to the turbulentfluid velocity fluctuations) and its generally little roughness (compared to the height of the fluid layer). Varying the Stefannumber, accounting for the thermodynamical properties of the material, also seems to have only a mild effect, whichimplies the possibility to extrapolate results in numerically delicate low-Stefan setups from more convenient high-Stefanones [1]. Finally, we discuss possible extensions of the study to geophysically relevant problems such as the modeling ofthe evolution of melt-ponds at the surface of Arctic sea-ice.
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