Anya Wolterman, Till J. W. Wagner, Lucas Zoet, Nimish Pujara
Wave erosion of ice cliffs is one of the main mechanisms for waterline ablation of icebergs, glacier fronts and ice-shelf fronts. Despite its importance, this process is neither well understood nor extensively tested in controlled experiments and only coarsely parameterised in geophysical and climate models. We examine the surface-wave-driven melting of a vertical ice wall using both theory and laboratory experiments, with an emphasis on the flow-induced heat transport in the theory and on measurements of the melt rate profile under different wave conditions in the experiments. In both the theory and the experiments, we find that the wave-induced melt rate decays exponentially with depth. By analysing the oscillatory boundary layer flow, we find that an approximate wave-averaged balance of heat transport is given by horizontal diffusion and vertical advection due to an Eulerian boundary layer streaming current. By solving for this balance and obtaining the wave-averaged temperature field, we find an explicit expression for the wave-induced melt rate. Experimental data show a good match to this expression, especially for larger wave amplitudes and colder water temperatures.