Anomalous Convective Flows Carve Pinnacles and Scallops in Melting Ice

We report on the shape dynamics of ice suspended in cold fresh water and subject to the natural convective flows generated during melting. Experiments reveal shape motifs for increasing far-field temperature: Sharp pinnacles directed downward at low temperatures, scalloped waves for intermediate temperatures between $5°\mathrm{C}$ and $7°\mathrm{C}$, and upward pointing pinnacles at higher temperatures. Phase-field simulations reproduce these morphologies, which are closely linked to the anomalous density-temperature profile of liquid water. Boundary layer flows yield pinnacles that sharpen with accelerating growth of tip curvature while scallops emerge from a Kelvin-Helmholtz–like instability caused by counterflowing currents that roll up to form vortex arrays. By linking the molecular-scale effects underlying water’s density anomaly to the macroscale flows that imprint the surface, these results show that the morphology of melted ice is a sensitive indicator of ambient temperature.

Figure 1

Representative morphologies formed by melting ice in laboratory experiments. (a) For sufficiently cold ambient temperatures $T_{\infty }\lesssim 5°\mathrm{C}$, the ice tapers from below to form an inverted pinnacle. (b) For intermediate temperatures $5°\mathrm{C}\lesssim T_{\infty }\lesssim 7°\mathrm{C}$, scalloped patterns form on the surface. (c) Upright pinnacles form for warmer temperatures $T_{\infty }\gtrsim 7°\mathrm{C}$. Photographs capture the late-stage ice removed from water and under diffuse lighting.

Figure 2

Flow velocity (arrows) and temperature (color) fields from phase-field simulations for (a) $T_{\infty }=4°\mathrm{C}$, (b) $5.6°\mathrm{C}$, and (c) $8°\mathrm{C}$ at early (left) and late (right) times. Curves show the flow speed (yellow) and density (pink) profiles at early times. Melting in cold water is associated with upward flow and downwards tapering of the ice as in (a), whereas warmer temperatures involve downwards flow and tapering at the top as in (c). Intermediate temperatures yield shear flows involving rising fluid near the surface and sinking outer flows, driving an instability that later patterns the surface.

Figure 3

Dynamics of pinnacle formation. Panels (a)–(d) show interfaces for $T_{\infty }=4°\mathrm{C}$ and $T_{\infty }=8°\mathrm{C}$ extracted over time (dark to light blue) in experiments and simulations. The corresponding tip curvatures are plotted in (e), which exhibit rapid sharpening to microscales. At early times, all data follow the scaling law ${\kappa }_0(t)={\kappa }_0(0)(1-t/t_s{)}^{-4/5}$, as shown in (f) by the linear behavior $1-t/t_s$ of the transformed quantity $[{\widehat{\kappa }}_0(t/t_s){]}^{-5/4}=[{\kappa }_0(t/t_s)/{\kappa }_0(0){]}^{-5/4}$.

Figure 4

Dynamics of scallop formation. Panels (a) and (b) show extracted interfaces over time for $T_{\infty }=5.6°\mathrm{C}$ in experiment and simulation, respectively. Panel (c) plots the cusp-to-cusp wavelength of the scallops versus their vertical location or height, confirming the scaling $\lambda \sim h^{-3/4}$ predicted by an analysis of the viscous Kelvin-Helmholtz instability. Additional simulations (filled squares) for a taller body and thus higher Ra confirm the trend over wider ranges of the variables.