Multiple similarity solutions of buoyancy induced flows for ice melting in cold pure water

Abstract

A model of laminar buoyancy induced plane flows driven by the thermal transport near a vertical ice wall melting in cold pure water is studied. Computed results show that the convective inversions are found with a temperature ratio parameter R varying in [0, 1 2 ]. Numerical solutions are obtained in two disjoint intervals of R which are separated by a gap on which no solution exists. Multiple solutions are found at some R in these regions. With R near the lower edge of the gap, the solutions are similar. However, pairs of solutions with R varying above the upper limit of the gap are found drastically different. They indicate physically the potential existence of a large amount of energy for any trend arising that drives one flow state to another.