Aspect ratio effect on side and basal melting in fresh water

The aspect ratio effect on side and basal melting in fresh water is systematically investigated across a range of Rayleigh numbers and ambient temperatures using direct numerical simulations. The side mean melt rate follows a scaling relation in the side-melting dominant regime, where is the Rayleigh number, and is the width-To-height aspect ratio of the ice block. In the basal-melting dominant regime, the basal mean melt rate follows a scaling relation at low Rayleigh numbers, but transitions to a scaling relation at higher Rayleigh numbers. This scaling transition is attributed to the formation of a bottom cavity resulting from flow separation at high Rayleigh numbers. The overall mean melt rate exhibits a non-monotonic dependence on the aspect ratio, driven by the competition between side and basal melting. The proposed theoretical model successfully captures the observed non-monotonic behaviour, and accurately predicts the overall mean melt rate over the considered range of Rayleigh numbers and ambient temperatures, especially in the side-and basal-melting dominant regimes. More specifically, the side, basal and overall mean melt rates follow a linear scaling relation for ambient temperatures, with being the Stefan number (the ratio between sensible heat and latent heat), but deviations from this scaling relation and a non-monotonic dependence on the ambient temperature are observed at lower ambient temperatures, which can be attributed to the density anomaly effect.