Numerical Assessment of Celerity Scaling Laws for Ice Ripples in Turbulent Shear Flows
Please login to view abstract download link
An interface-resolved numerical framework is employed to investigate the morphodynamics of melting ice in turbulent shear flows, with a focus on the formation and evolution of streamwise-traveling ripples at the ice–water boundary. Such ripples arise at high shear rates, enhance local melt rates, and modify hydrodynamic drag [1], yet their dynamics remain challenging to predict due to the strong coupling between turbulence, heat transfer, and interfacial evolution. In particular, the ripple migration velocity (celerity) provides a compact measure of ice roughness evolution and reflects underlying heat-flux perturbations and flow conditions at the ice–ocean interface [2]. We perform direct numerical simulations (DNS) of a turbulent open-channel flow interacting with an evolving ice–water interface. The governing equations consist of the incompressible Navier–Stokes equations coupled to an energy equation and a phase-field formulation for melting and freezing. All equations are solved using a pseudo-spectral, parallel, GPU-accelerated solver [3], enabling fully resolved simulations of turbulence and interfacial dynamics at high shear rates. A parametric study is conducted to quantify the dependence of key morphodynamical features on thermal and hydrodynamic control parameters. Specifically, simulations are performed at three Stefan numbers spanning two orders of magnitude to assess the role of latent heat, and at three shear Reynolds numbers up to Reτ = 1600 to characterize shear effects. The resulting ice morphologies are analyzed in terms of ripple celerity, roughness amplitude, and characteristic wavelength. The simulations reveal systematic trends in ripple geometry and migration speed with varying shear and latent heat. Building on these results, we propose a scaling law for ripple celerity as a function of Reynolds and Stefan numbers. The proposed scaling is consistent with linear stability theory predictions [2] and extends their validity beyond the small-amplitude limit and into regimes characterized by small Stefan numbers, providing quantitative insight into ice morphodynamics under strongly turbulent melting conditions.
