Mathematical modelling of the formation and evolution of surface ice

Abstract

During the fall season in cold regions when the air temperature drops below freezing levels, it removes heat from the water surface and creates a supercooled surface layer. In weak turbulent flows, the supercooled surface layer initiates the formation of ice particles on the water surface, which could evolve into various types of surface ice runs. In this paper a mathematical model of the formation and evolution of surface ice is presented. A heat balance model at the water surface is applied to calculate the heat loss from the water. The turbulent kinetic energy and the energy dissipation rates are modelled to find the eddy viscosity that affects the mixing rate. The mathematical model is then calibrated and verified using experimental data collected at the Hydraulics Research and Testing Laboratory at the University of Manitoba. The model simulates the supercooling process reasonably well for all surface ice conditions.