Transport near a vertical ice surface melting in saline water: some numerical calculations

Computed numerical results are presented for the laminar buoyancy-induced flows driven by combined thermal and saline transport near a vertical melting ice surface in saline water. Results are presented which indicate that conventional boundary-layer flow occurs for some combinations of ambient salinity and temperature in the ranges 0 to 31‰ and −1 to 20°C, respectively. These conditions are very common in terrestrial waters. The analysis used herein is the first to model fully the many complicated aspects of these flows. The present analysis includes simultaneous transport of salt and thermal energy as well as the effect of interface motion. The formulation uses the most recently available transport properties and a very accurate equation of state for the density of pure and saline water. The interface temperature and salinity, which are not known a priori , are here determined jointly from the transport equations, and from species-conservation and phase-equilibrium relations at the ice surface. At low ambient temperatures, the flow is found to be dominated by the upward saline buoyancy, resulting in upward flow. However, at high temperatures and low salinities, the downward thermal buoyancy overcomes the upward saline buoyancy near the surface to cause downward flow. For choices of ambient conditions between these extremes, the opposing saline and thermal buoyancy are about equal in strength. The resulting tendency for bi-directional flow at these intermediate circumstances caused numerical stability problems which made it impossible to obtain convergent solutions for some cases. However, calculated solutions were obtained at ambient salinities below 5‰, for ambient temperatures between 8 and 20°C, and at temperatures below 4°C, for ambient salinities between 0 and 31‰. These solutions indicate the limits of the range of conditions for which laminar boundary layer flow occurs. They further suggest that outside these ranges, the flow may be laminar and bi-directional. The very strong buoyancy which characterizes some of these conditions suggests that they may become turbulent at short downstream distances. The computed results are seen to be in excellent agreement with the limited experimental data and observations of previous studies.