Impact of Thermally Driven Turbulence on the Bottom Melting of Ice

Direct numerical simulation and laboratory experiments are used to investigate turbulent convection beneath a horizontal ice-water interface. Scaling laws are derived that quantify the dependence of the melt rate of the ice on the far-field temperature of the water under purely thermally driven conditions. The scaling laws, the simulations, and the laboratory experiments consistently yield that the melt rate increases by two orders of magnitude, from ?10(1) to ?10(3) mm day(-1), as the far-field temperature increases from 4 degrees to 8 degrees C. The strong temperature dependence of the melt rate is explained by analyzing the vertical structure of the flow: For far-field temperatures below 8 degrees C, the flow features a stably stratified, diffusive layer next to the ice that shields it from the warmer, turbulent outer layer. The stratification in the diffusive layer diminishes as the far-field temperature increases and vanishes for far-field temperatures far above 8 degrees C. Possible implications of these results for ice-ocean interfaces are discussed. The drastic melt-rate increase implies that turbulence needs to be considered in the analysis of ice-water interfaces even in shear-free conditions.