Numerical assessment of celerity scaling laws for ice ripples in turbulent shear flows

We investigate the morphodynamics of melting ice in turbulent shear flows using an interface-resolved numerical framework, with a focus on the formation and downstream propagation of quasi-2D scallops (ripples) on the ice–water interface. At high shear rates, these ripples enhance local melting and modify hydrodynamic drag [1], yet their dynamics remain unclear due to the complex coupling between turbulence, heat transfer, and melting-freezing. The ripple migration speed (celerity) provides a compact measure of the ice morphology evolution and reflects variations in heat flux, as well as in flow conditions [2]. Direct numerical simulations (DNS) are performed for a turbulent open-channel flow capped by an evolving ice–water interface. The incompressible Navier–Stokes equations are coupled with an energy equation and a phase-field formulation capable of describing melting and freezing. Simulations are carried out using a pseudo-spectral, parallel, GPU-accelerated solver [3], allowing for fully resolved turbulence and interface dynamics at high shear rates. A parametric study is conducted to assess the influence of thermal and hydrodynamic control parameters. Three Stefan numbers spanning two orders of magnitude are considered to examine the role of latent heat, while three shear Reynolds numbers (up to 1600) are simulated to quantify shear effects. The resulting ice morphologies are analyzed in terms of ripple celerity, roughness amplitude, and characteristic wavelength. The simulations reveal clear dependencies in ripple geometry and migration speed on both shear intensity and latent heat. Based 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 analysis [2], while extending its applicability beyond the small-amplitude limit and into low–Stefan-number regimes, providing new insights into ice morphodynamics in turbulent flows.

[1] Bushuk M., Orton P.M., Holland D.M., Stanton T.P., Stern A.A., Gray C., Laboratory observations of ice–water interface morphodynamics in turbulent shear flow, J. Fluid Mech., 841, 614–646, 2018.
[2] Hsu K.S., Locher F.A., Kennedy J.F., Forced-convection heat transfer from irregular melting wavy boundaries, J. Heat Transfer, 101(4), 598–602, 1979.
[3] Perissutti D., Marchioli C., Soldati A., Time and length scales of ice morphodynamics driven by subsurface shear turbulence, J. Fluid Mech., 1019, A34, 2025.