A laboratory and theoretical study of the boundary layer adjacent to a vertical melting ice wall in salt water

Abstract

In an experimental and theoretical study we model the convection generated in the polar oceans when a fresh-water ice wall melts in salt water of uniform far-field temperature T∞, and salinity S∞. Our laboratory results show that there are three different flow regimes which depend on T∞ and S∞. First, when T∞ and S∞ lie between the maximum density curve and the freezing curve, the flow is only upward. Secondly, for the oceanic case 30 [les ] S∞ [les ] 35‰ and T∞ < 20°C, the flow consists of a laminar bidirectional flow at the bottom of the ice and a turbulent upward flow along the remainder of the ice wall. The laminar flow consists of an upward flowing layer approximately 2 mm thick inside of a downward flowing outer layer approximately 10 mm thick. Thirdly, for the same range of S∞ but for T∞ > 20°C, the flow reverses: at the top of the ice there is a laminar bidirectional flow above a downward turbulent flow. To model the turbulent upward flow theoretically, we numerically solve the governing equations in similarity form with a spatially varying eddy diffusivity that depends on the density difference between the ice-water interface and the far-field. The laboratory data then allows us to evaluate the dependence of eddy diffusivity on T∞ and S∞. The results show that the magnitude of the eddy diffusivity is of the same order as the molecular viscosity and that both mass injection at the interface and opposed buoyancy forces must be included in a realistic flow model. Finally, we use an integral approach to predict the far-field conditions that yield the high-temperature flow reversal and obtain a result consistent with our observations.