Self-Propulsion of floating ice blocks caused by melting in water

TL;DR

This work demonstrates that asymmetric floating ice blocks can self‑propel in warm water due to buoyancy‑driven convection generated by melting, with a quantitative 2D propulsion model that links melting velocity $v_m$ to the horizontal propulsion force balanced by drag. The authors calibrate a melting velocity via the Stefan condition and capture the resulting translation by a gravity‑driven current exiting beneath the block, yielding terminal speeds on the order of a few millimeters per second in freshwater, scaling with bath temperature and block geometry as $U_b \propto (T_b-T_c)^{8/9}$ and $U_b\propto L^{1/3}$. Extending to saltwater, they show that cooling‑induced sinking flows can dominate the melt‑water buoyancy effect, producing similar propulsion directions but generally reducing the speed due to competing momentum transport in the melt layer; nonetheless, the mechanism remains potentially relevant for large icebergs in sufficiently warm oceans. The study provides a framework to assess melting‑driven propulsion in natural contexts, suggesting that such convection‑driven forces could contribute non‑negligibly to iceberg drift alongside winds, currents, and Coriolis effects, especially in warmer subpolar regions. Overall, the findings illuminate a robust, geometry‑dependent propulsion mechanism arising from phase change heat transfer and buoyancy, with implications for ice dynamics in both laboratory and oceanic environments.

Abstract

We show that floating ice blocks with asymmetric shapes can self-propel with significant speeds due to buoyancy driven currents caused by melting. In water baths with temperatures between $10\,^\circ$C and $30\,^\circ$C, model right-angle ice wedges are found to move in the direction opposite to the gravity current which descends along the longest inclined side. We describe the measured speed as a function of the length and angle of the inclined side, and the temperature of the bath in terms of a propulsion model which incorporates the cooling of the surrounding fluid by the melting of ice. The heat pulled from the surrounding liquid by the melting ice block generates a thermal convection flow, leading to momentum exchange and to a net propulsion force. The translation velocity is explained by balancing the propulsion force by drag. We further show that the ice block moves robustly in a saltwater bath with ocean-like salinity and maintains the same direction of motion as in freshwater. A simplified model is further developed to describe the propulsion of asymmetric ice blocks in saltwater, incorporating the effects of rising meltwater and the sinking of the surrounding bath water due to cooling. For sufficiently large temperature, we find that the cooling-induced sinking flow generates a stronger force than the upward flow from the meltwater. Consequently, the net propulsion force is in the same direction and nearly the same magnitude as that observed in freshwater. These findings suggest that melting-driven propulsion may be relevant to the motion of icebergs in sufficiently warm oceanic environments.

Figures (18)

• Figure 1: Principle of melting-driven propulsion experiments. (a) A schematic of a melting ice block floating in a water bath. The block is a right-angled triangle prism. The hypotenuse has a length $L$ and is inclined at an angle $\theta$ relatively to the horizontal. The ice block propels along the horizontal coordinate $x$ with a velocity $\bm{U_b}$ in steady state. (b) A side view image of a right-angle ice block ($L_h = 163$ mm, $W = 124$ mm, $H = 65$ mm, $\theta = 19.5^\circ$, $T_b=22\,^\circ$C). (c) A profile view image of the floating ice block with a parabolic mirror placed behind the tank containing freshwater. The dense cold water leads to convection flow which is visible below the ice block. The mirror is then used for shadowgraph imaging. (d) A shadowgraph picture shows the ice block moving to the right with the convection directed toward the rear of the block (also see Movie S1 sup-doc).
• Figure 2: Observation of a melting pattern on the underside of ice blocks. (a) A view of an ice block floating at the water surface while moving in the direction of the observer after being immersed in the bath for about 8 minutes. A groove pattern generated by melting appears on the bottom inclined face. (b) A schematic cross section of the block illustrating the length-wise grooves. This melting pattern is carved by the backward descending flow. (c) An ice block with bottom surface facing viewer after it is removed from the water bath following approximately 11 minutes of immersion. Typical groove width and depth are about $20$ mm and $5$ mm, respectively. This example corresponds to Data Set L. ($L=176$ mm, $\theta=19.5^\circ$, $T_b=22.1\,^\circ$C).
• Figure 3: Demonstration of the self-propulsion for asymmetric melting ice blocks. (a) Right-angle triangle horizontal ice block position $X_B$ as a function of time $t$ plotted along with a linear fit (dashed line) corresponding to a slope $U_b=3.02$ mm s$^{-1}$. Data Set G. (b) The velocity of the block $U(t)$ obtained from $X_B$. This experiment corresponds to the block depicted in Movie S2 sup-doc, where the block is kicked manually in the direction opposite to the motion induced by propulsion at $t=8$ s. After a transient, the block recovers the same velocity (dashed line).
• Figure 4: Erratic motion for symmetric melting ice blocks. (a) For a symmetric rectangular ice block position $X_B$ shows the slow drift of the block over time (also see Movie S3 sup-doc). The block dimensions: $100\times 40 \times 40$ mm$^3$, $\theta=0^\circ$, $T_b=20.1\,^\circ$C. (b) The corresponding velocity (averaged over $10$ s) shows sudden changes in velocity due to capsizing events at $t=210$ s and $t=506$ s.
• Figure 5: Schematic of the melting driven propulsion mechanism. A time-averaged current due to the thermal convection flow with velocity $\bm{v}$ develops below the ice block in a fluid layer with thickness $\delta_v$ which increases with distance from the front tip. $x'$ is the coordinate along the inclined wall from the rear to the tip of the ice block. The current leaves the control volume indicated by the dashed line below the ice block, over a length $\delta_x$ with a velocity $\bm{v_p}$, generating a horizontal thrust in the opposite direction which is balanced by fluid drag in the stationary regime. Consequently, the ice block moves in the $x$ direction with a steady velocity $\bm{U_b}$.