Melting dynamics and mixing layer growth near the ice-ocean interface

TL;DR

This work investigates how turbulence regulates ice melting into saline ocean water by solving the 2D Boussinesq equations with a slowly melting upper boundary across a range of density ratios $R_\rho$ and Lewis numbers $Le$. The melt rate transitions from subdiffusive to diffusive as $R_\rho$ increases, while the turbulent mixing layer in the bulk grows super-diffusively as $L(t) \propto t^{1.33}$, a behavior robust to parameter changes. An interfacial boundary layer becomes more pronounced at high $R_\rho$, governing the meltwater flux into the turbulent bulk without suppressing bulk convection, and diffusion effects remain largely confined to the near-interface region. The study also highlights that mixing-length diagnostics are sensitive to threshold choices, which has implications for oceanographic interpretation of mixing and freshwater fluxes near ice margins. Overall, the results advance understanding of melt-driven turbulence and its role in shaping meltwater transport in polar oceans.

Abstract

Ice melting into saline water plays a fundamental role in the dynamics near the ice-ocean interface in polar oceans. The physics of ice melting involves a non-trivial interplay between thermodynamics at the interface, hydrodynamic transport in the bulk and the properties of the ambient ocean. The key control parameters are the density ratio $R_ρ$ proportional to the ambient ocean salinity and the Lewis number $Le = κ_T/κ_S$, which compares the thermal and salt diffusivities. Increasing the salinity is known to slow down melting, with the melt rate transitioning from subdiffusive to diffusive as $R_ρ$ increases. Here, we ssess the role of turbulence in this transition, using highly-resolved numerical simulations of the two-dimensional Boussinesq equations with a slowly melting upper boundary. We analyse the non-stationary growth of the temperature and meltwater mixing layers, varying the Lewis number and the density ratio. While meltwater is continuously entrained by convection inside the bulk, we identify a transition from convection to diffusion close to the interface. This transition is reflected by the formation of an interfacial boundary layer that regulates the flux of meltwater pouring into the turbulent bulk for $R_ρ\gtrsim 10$. Using mixing-layer diagnostics based on meltwater-concentration thresholds, we observe that the turbulent layer grows super-diffusively $\propto t^{1.33}$, while the interfacial boundary layer expands diffusively $\propto t^{0.5}$ but with a non-universal prefactor. These results indicate that double-diffusive effects are here confined to the interface, and highlight potential limitations of diagnostics based on fixed concentration thresholds in oceanographic applications.

Figures (8)

• Figure 1: Initial configuration
• Figure 2: Typical evolution of the temperature (a) and salinity fields (b) for a simulation with $Le = 100$ and $R_\rho = 406$. Panel (c) shows the temporal evolution of the horizontally-averaged salinity profile for $R_\rho = 406$. Panel (d) shows the results for $R_\rho = 1$.
• Figure 3: Time evolution of the Nusselt number $Nu$, varying $R_\rho$ for fixed $Le$ (top) and $Le$ for fixed $R_\rho$ (bottom). The insets display the prefactors $C_s, C_f$ (see text).
• Figure 4: Time evolution of the interfacial temperature $\theta_0$, varying $R_\rho$ at fixed $Le$ (top) and $Le$ at fixed $R_\rho$ (bottom). The insets display the dependence on either $R_\rho$ or $Le$ averaging over times $t \gtrsim 10$.
• Figure 5: Vertical profiles (top) and fluxes (bottom) associated to heat (left panels) and salt (right panels) at successive times for the run at $Le = 100$ and $R_\rho = 406$. In insets, the profiles in terms of the rescaled coordinates $z/L$ along with their mean (thick blue line).