Melting of floating ice cylinders in fresh and saline environments

Abstract

We experimentally investigated the melting of floating ice cylinders. Experiments were carried out in a tank, with ice cylinders with radii between 5 cm and 12 cm, floating horizontally with their axis perpendicular to gravity. The water in the tank was at room temperature, with salinities ranging from 0 g/L to 35 g/L. These conditions correspond to Rayleigh numbers in the range $10^5 \lesssim \mathrm{Ra} \lesssim 10^9$. The relative density and thus the floating behaviour was varied by employing ice made of H$_2$O-D$_2$O mixtures. In addition, we explored a two-layer stable stratification. We studied the morphological evolution of the cross-section of the cylinders and interpreted our observations in the context of their interaction with the convective flow. The cylinders only capsize in fresh water but not when the ambient is saline. This behaviour can be explained by the balance between the torques exerted by buoyancy and drag, which change as the cylinder melts and rotates. We modelled the oscillatory motion of the cylinders after a capsize as a damped non-linear oscillator. The downward plume of the ice cylinders follows the expected scalings for a line-source plume. The plume's Reynolds number scales with Rayleigh number in two regimes, namely $\mathrm{Re} \propto \mathrm{Ra}^{1/2}$ for $\mathrm{Ra} < O(10^7)$ and $\mathrm{Re} \propto \mathrm{Ra}^{1/3}$ for $\mathrm{Ra} > O(10^7)$, and the heat transfer (nondimensional as Nusselt number) scales as $\mathrm{Nu} \propto \mathrm{Ra}^{1/3}$. Although the addition of salt substantially alters the solutal, thermal and momentum boundary layers, these scaling relations hold irrespectively of the initial size or the water salinity. While important differences exist between our experiments and real icebergs, our results can qualitatively be connected to natural phenomena occurring in fjords and around isolated icebergs.