Hydrodynamic Instability Induces Spontaneous Motion of Floating Ice Discs

TL;DR

Hydrodynamic instability driven by water’s density maximum can spontaneously mobilize floating ice discs. Using direct numerical simulations with an immersed boundary in a thermally driven flow, the authors show that a downward buoyant plume forms near $T_{\mathrm{TMD}}$, and nonlinear interactions of RT-instability‑induced perturbations break flow symmetry, producing autonomous disc motion. They identify a universal threshold, the plume Rayleigh number $\mathrm{Ra}_{\mathrm{p}}^* \approx 1.3\times 10^6$, above which motion occurs, and show $\mathrm{Ra}_{\mathrm{p}}^{\max}$ controls onset via $\mathrm{Ra}_{\mathrm{p}}^{\max}=\dfrac{g \alpha_{gt} (T_h-T_{TMD})^{1.895} \mathcal{H}^3}{\nu \kappa}$. The findings unify prior experiments and provide a predictive criterion for motion, with implications for thermally driven transport in geophysical contexts like continental drift and iceberg capsizing.

Abstract

Spinning ice discs in nature have been reported for more than a century, yet laboratory experiments have yielded diverse observations and contradictory explanations, leaving the mechanism behind the disc motion elusive. Here we combine numerical simulations and scaling analysis to investigate a freely moving ice disc in a lab-scale water tank. We observe the disc remaining stationary or experiencing spontaneous motion, depending on the disc-water temperature difference and water depth. The motion is initiated by a buoyancy-driven, downward plume arising from water's density anomaly -- its density peaks near $4^\circ$C. Crucially, the plume breaks rotational and mirror symmetries after descending beyond a critical distance due to a thermoconvective instability, thereby inducing the disc to move autonomously. Our findings quantitatively unify disc behaviors observed across independent experiments and establish a predictive criterion for the onset of disc motion. More broadly, we point to a route for thermally-driven transport: coupling of bulk thermoconvection and moving bodies, relevant to geophysical processes such as continental drift and iceberg capsizing.

Figures (8)

• Figure 1: Simulations reproduce spontaneous motion of an ice disc.\ref{['Fig field disc1']} and \ref{['Fig field disc2']}, Field observations of rotating ice discs on the Presumpscot River (2019; diameter $\approx 91$ m) bangor2019ice and Vigala river (2019; diameter over 20 m) jeeser2019ice, respectively. \ref{['Fig experimental disc']}, Schematic of early laboratory experiments with centimeter-scale ice or plastic discs floating on quiescent water dorbolo2016rotationschellenberg2023rotationkistovich2024selfchaplina2024vortex. The arrowed circle indicates a vertical vortex hypothesized by dorbolo2016rotation. We simulate a chilled, non-melting disc immersed in warm water within a closed tank, as detailed in the main text. Initially ($\tt=5.8$), the temperature field is axisymmetric, and the disc is stationary and centered (\ref{['Fig neumerial disc early']}); by $\tt=86.6$, the field is asymmetric and the disc has shifted off-center spontaneously (\ref{['Fig neumerial disc later']}). \ref{['Fig neumerial disc 2']}, Temporal evolution of the disc velocity and flow asymmetry.
• Figure 2: Thermoconvective flow breaks symmetry spontaneously.\ref{['temperature slice']}, Temperature distribution on a cylindrical slice extended from the disc's lateral side. The slice is divided into four equal azimuthal ($\phi$) sectors. \ref{['unwraped slice 1']}--\ref{['unwraped slice 3']}, Unwrapped temperature distribution over times, highlighting the progressive undulations of the plume front. \ref{['Ti 1']}--\ref{['Ti 3']}, Azimuthal sector-mean temperatures at successive times, corresponding to \ref{['unwraped slice 1']}--\ref{['unwraped slice 3']}, respectively. \ref{['wrapped Ti 3']}, Wrapped representation of \ref{['Ti 3']}, showing broken rotational and mirror symmetries. \ref{['LSA growth']}, Temporal evolution of the amplitude of the plume front.
• Figure 3: Criterion for the onset of disc motion and symmetry breaking.\ref{['Rac at various Th']} and \ref{['Rac at various H']}, Critical plume Rayleigh number $\mathrm{Ra}_{\mathrm{p}}^*$ versus the initial water temperature $T_{\mathrm{h}}$ at fixed tank height $H = 6$ cm, and $\mathrm{Ra}_{\mathrm{p}}^*$ versus $H$ at $T_{\mathrm{h}} = 25 \,^{\circ}\mathrm{C}$, respectively. \ref{['Numerical results below Rac cold water']}, Temporal evolution of disc velocity and flow asymmetry for $T_{\mathrm{h}}=5\,^{\circ}\mathrm{C}$ instead of the baseline $T_{\mathrm{h}}=10\,^{\circ}\mathrm{C}$. \ref{['Numerical results below Rac short tank']}, As in \ref{['Numerical results below Rac cold water']}, but with the baseline $H=6$ cm reduced to $H = 2$ cm.
• Figure 4: Residual flow does not significantly alter instability-driven disc motion .\ref{['Fig Th=Tc plume']}--\ref{['Fig Th=Tc disc']}, Residual flows in an isothermal setting ($T_{\mathrm{h}} = T_{\mathrm{c}} =20 \,^{\circ}\mathrm{C}$; $H =6$ cm) induces transient, short-lived flow asymmetry and disc movement. \ref{['Fig Th>Tc plume']}--\ref{['Fig Th>Tc disc']}, In contrast, with $T_{\mathrm{h}}=20>T_{\mathrm{c}}=-10 \,^{\circ}\mathrm{C}$, a temperature difference triggers RT instability, which---after the residual-flow transient---persistently drives flow asymmetry and disc motion.
• Figure S1: Sedimentation of an isothermally heated particle in a quiescent fluid.\ref{['Fig computation domain']}, A 2D rectangular tank filled with quiescent fluid initially at 290 K. A particle, placed on the centerline of the tank and maintained at 300 K, is hotter and heavier than the surrounding fluid. \ref{['Fig vertical position']}, Temporal evolution of the particle's vertical position from our simulation, benchmarked against xia2024particle.