Boundary Shear Stress in Rectangular Ice-Covered Channels

Abstract

This paper develops an analytical approach to evaluate the mean boundary shear stress in rectangular ice-covered channels. The flow cross section was divided into an upper ice layer and a lower bed layer at the plane of zero shear stress, determined analytically from an order of the Boussinesq approximation involving the eddy viscosity concept, together with Prandtl’s mixing length theory. The conformal mapping procedure was used to obtain the functional relationships for the division curves within each flow layer. Based on the force balance in each flow subregion, an analytical model for the average bed, ice, and side-wall shear stresses was developed. The two-power law for describing vertical velocity profiles in asymmetric channels was adopted to determine the location of zero shear stress and its parameters, determined using coupled equations for the flat-bed friction factor and an empirical relationship for the bed-form friction factor. A comparison between the results of the present model and the collected data from literature shows that the proposed method does well in predicting the mean boundary shear stress in rectangular ice-covered channels.