Wave boundary layer at the ice–water interface: theory and experiment

Marginal ice zones (MIZs) are distinguished by the highly heterogeneous condition of sea ice, e.g., floes of various sizes, pancake, brash and frazil ice, ice ages, brine content, ice thickness and concentration, etc. This makes it challenging to model wave propagation in MIZs, either theoretically or numerically, since there remain similar limitations to mathematically describing such an ice cover on the ocean surface. In this study, we re-consider the problem of linear gravity waves in two layers of fluids with a viscous ice layer overlaying water of deep depth, giving a comprehensive 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 the ice. For the turbulent wave boundary layer, water eddy viscosity is used. Speculation of the Eulerian steady streaming is made based on the Reynolds stress distribution, offering a preliminary insight into the wave-induced mean drifts 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 both field and lab waves, significantly outperforming those results assuming an inviscid water. Also discussed are the PIV (particle imaging velocimetry) measurements from the experiment of wave propagation through broken surface ice in a salt water tank in a temperature-controlled facility at the US Army Corps of Engineers Cold Regions Research and Engineering Laboratory (CRREL). Preliminary analysis of the PIV data has provided strong evidence of such a wave boundary layer at the water–ice interface. The measured vertical profiles of fluid velocities and wave-induced Reynolds stress have trends similar to the theoretical predictions, despite the quantitative discrepancies in terms of numerical values. To our knowledge, this is only the second such experiment to measure the three-dimensional fluid velocity fields due to the wave motion under surface ice. This is to be followed by the phase II experiment (scheduled in 2023) in which the ice thickness and other properties will be configured to improve the similitude with field applications.