The combined effects of shear and buoyancy on phase boundary stability

TL;DR

This paper investigates how shear and buoyancy influence the stability of solid-liquid interfaces, revealing buoyancy as a primary destabilizer and shear as a stabilizing factor, with potential for re-entrant instability at high shear levels.

Contribution

It provides a linear stability analysis showing buoyancy's destabilizing role and shear's stabilizing effect, clarifying previous experimental observations and theoretical predictions.

Findings

Buoyancy is the main destabilizing factor.

Shear flow inhibits vertical motions, stabilizing the interface.

High shear may lead to re-entrant instability.

Abstract

We study the effects of externally imposed shear and buoyancy driven flows on the stability of a solid-liquid interface. By reanalyzing the data of Gilpin \emph{et al.} [\emph{J. Fluid Mech.}, {\bf 99}(3), 619 (1980)] we show that the instability of the ice-water interface observed in their experiments was affected by buoyancy effects, and that their velocity measurements are more accurately described by Monin-Obukhov theory. A linear stability analysis of shear and buoyancy driven flow of melt over its solid phase shows that buoyancy is the only destabilizing factor and that the regime of shear flow here, by inhibiting vertical motions and hence the upward heat flux, stabilizes the system. It is also shown that all perturbations to the solid-liquid interface decay at a very modest strength of the shear flow. However, at much larger shear, where flow instabilities coupled with buoyancy might enhance vertical motions, a re-entrant instability may arise.