Basal melting driven by turbulent thermal convection

TL;DR

This study investigates how turbulent thermal convection influences basal melting processes, revealing that melting dynamics resemble classical Rayleigh-Bénard convection with weak heat flux enhancement and minimal interface roughness, across different dimensions.

Contribution

It introduces a convective-melting model extending Rayleigh-Bénard systems and provides extensive numerical simulations analyzing melting behavior and heat transfer in 2D and 3D.

Findings

Melting behavior closely resembles Rayleigh-Bénard convection.

Heat flux is only weakly increased compared to classical convection.

Interface remains relatively smooth regardless of parameters.

Abstract

Melting and, conversely, solidification processes in the presence of convection are key to many geophysical problems. An essential question related to these phenomena concerns the estimation of the (time-evolving) melting rate, which is tightly connected to the turbulent convective dynamics in the bulk of the melt fluid and the heat transfer at the liquid-solid interface. In this work, we consider a convective-melting model, constructed as a generalization of the Rayleigh-B\'enard system, accounting for the basal melting of a solid. As the change of phase proceeds, a fluid layer grows at the heated bottom of the system and eventually reaches a turbulent convection state. By means of extensive Lattice-Boltzmann numerical simulations employing an enthalpy formulation of the governing equations, we explore the model dynamics in two and three-dimensional configurations. The focus of the analysis is on the scaling of global quantities like the heat flux and the kinetic energy with the Rayleigh number, as well as on the interface morphology and the effects of space dimensionality. Independently of dimensionality, we find that the convective-melting system behavior shares strong resemblances with that of the Rayleigh-B\'enard one, and that the heat flux is only weakly enhanced with respect to that case. Such similarities are understood, at least to some extent, considering the resulting slow motion of the melting front (with respect to the turbulent fluid velocity fluctuations) and its generally little roughness (compared to the height of the fluid layer). Varying the Stefan number, accounting for the thermodynamical properties of the material, also seems to have only a mild effect, which implies the possibility to extrapolate results in numerically delicate low-Stefan setups from more convenient high-Stefan ones.