Meltwater transport and mixing layer growth near the ice--ocean interface

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 $R_\rho$ proportional to the ambient ocean salinity and the Lewis number $Le = \kappa_T/\kappa_S$, 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 $R_\rho$ 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 $R_\rho \gtrsim 10$. 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.