Wave Boundary Layer at the Ice–Water Interface

Abstract

On re-examining the problem of linear gravity waves in two layers of fluids with a viscous ice layer overlaying water of deep depth, we give a detailed analysis of the fluid velocities, velocity shear, and Reynolds stress associated with wave fluctuations in both the ice layer and the wave boundary layer just beneath it. For the turbulent wave boundary layer, water eddy viscosity is used. Comprehensive discussions on various aspects of the velocity fields are made in terms of a Reynolds number based on the ice-layer thickness and viscosity, and the ice-to-water viscosity ratio. Speculation of the wave-induced steady streaming is made based on the Reynolds stress distribution, offering a preliminary insight into the mean flows in both the ice layer and wave boundary layer in the water. For wave attenuation, the results using a typical ice viscosity and a reasonable water eddy viscosity show good agreement with data over the range of frequencies for field and lab waves, significantly outperforming those assuming an inviscid water.