The combined effects of buoyancy, rotation, and shear on phase boundary evolution

TL;DR

This study uses numerical simulations to explore how buoyancy, shear, and rotation influence melt rates and interface shapes in a solid-liquid system, revealing complex non-monotonic behaviors and geometric effects.

Contribution

It provides new insights into the combined effects of buoyancy, shear, and rotation on phase boundary evolution in three-dimensional convection.

Findings

Melt rate varies non-monotonically with shear strength.

Interface geometry influences heat flux and melt morphology.

Rotation alters flow orientation and interface structures.

Abstract

We use well-resolved numerical simulations to study the combined effects of buoyancy, pressure-driven shear and rotation on the melt rate and morphology of a layer of pure solid overlying its liquid phase in three dimensions at a Rayleigh number $Ra = 1.25 \times 10^5$. During thermal convection we find that the rate of melting of the solid phase varies non-monotonically with the strength of the imposed shear flow. In the absence of rotation, depending on whether buoyancy or shear dominates the flow, we observe either domes or ridges aligned in the direction of the shear flow respectively. Furthermore, we show that the geometry of the phase boundary has important effects on the magnitude and evolution of the heat flux in the liquid layer. In the presence of rotation, the strength of which is characterized by the Rossby number, Ro, we observe that for Ro = O(1) the mean flow in the interior is perpendicular to the direction of the constant horizontal applied pressure gradient. As the magnitude of this pressure gradient increases, the geometry of solid-liquid interface evolves from the voids characteristic of melting by rotating convection, to grooves oriented perpendicular or obliquely to the direction of the pressure gradient.