Cyclic Steps Created by Flowing Water on Ice Surface

Abstract

The interface between ice and fluid can become unstable and devolve into cyclic steps bounded by hydraulic jumps. These steps are created by flowing water or wind over the ice surface. This study presents an analytical model to reproduce cyclic steps created by water over the ice surface. We apply four governing equations: the momentum equation, the continuity equation, the heat transfer equation in water, and the energy balance equation (the Stefan equation). After calculation, we can generate the variations in the depth-averaged water temperature, the depth-averaged velocity, and the ice elevation over one step wavelength. We can also understand the cyclic step formation process and how the heat transfer capacity of air and water, and the Froude number in the normal flow condition influence the wavelength. The results of the obtained steps in the analysis are compared with experimental observations to validate our model.