Basal melting driven by turbulent thermal convection

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-Bénard 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-Bénard 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.

arXiv comment22 pages, 10 figures (flow visualizations in low resolution), videos are not included

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• Nonlinear interactions between an unstably stratified shear flow and a phase boundary
• Circular objects do not melt the slowest in water
• Theoretical framework for designing phase change material systems
• Sea ice aging by diffusion-driven desalination
• Surface light modulation by sea ice and phytoplankton survival in a convective flow model
• Modelling sea ice and melt ponds evolution: sensitivity to microscale heat transfer mechanisms
• Freezing and ice aging dynamics in saline water under natural convection
• Heat Transfer in Phase Change Materials with Multiple Fin Insertion