The combined effects of shear and buoyancy on phase boundary stability

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.

arXiv comment10 pages, 13 figures

References in corpus (3)

• Dissolution instability and roughening transition
• Penetrative Convection at High Rayleigh Numbers
• Turbulent heat exchange between water and ice at an evolving ice-water interface

Cited by in corpus (8)

• Bistability in Rayleigh-Bénard convection with a melting boundary
• Topography generation by melting and freezing in a turbulent shear flow
• Equilibrium states of the ice-water front in a differentially heated rectangular cell
• Melting driven by rotating Rayleigh-Bénard convection
• The combined effects of buoyancy, rotation, and shear on phase boundary evolution
• Nonlinear interactions between an unstably stratified shear flow and a phase boundary
• Theoretical framework for designing phase change material systems
• Freezing and ice aging dynamics in saline water under natural convection