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 meltwater transport involves a non-trivial interplay between the thermodynamics at the interface, hydrodynamic transport in the bulk and the properties of the ambient ocean. The key control parameters are the density ratio

, which is proportional to the ambient salinity and measures the balance between the temperature and salinity effects on density, together with the Lewis number

italic Le equals kappa Subscript upper T Baseline divided by kappa Subscript upper S Baseline Le = κ T / κ S $\textit{Le} = \kappa _T/\kappa _S$

, which compares thermal and solutal diffusivities. In quiescent horizontal configurations, increasing the salinity is known to slow down melting, with the melt rate transitioning from subdiffusive to diffusive as

upper R Subscript rho R ρ $R_\rho$

increases. Here, we assess 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 thermal and solutal mixing layers, varying the Lewis number and the density ratio. While meltwater transport is continuously driven by convection within 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. The boundary layer has little effect on thermal transport, but strongly suppresses solutal transport for

upper R Subscript rho Baseline greater than or equivalent to 10 R ρ ≳ 10 $R_\rho \gtrsim 10$

, only allowing a fraction

proportional to upper R Subscript rho Superscript negative 1 ∝ R ρ − 1 $\propto R_{\rho }^{-1}$

of the input flux to reach the bulk. Using mixing-layer diagnostics based on solutal-concentration thresholds, we observe that the turbulent layer grows super-diffusively

proportional to t Superscript 1.33 ∝ t 1.33 $\propto t^{1.33}$

, while the interfacial boundary layer expands diffusively

proportional to t Superscript 0.5 ∝ t 0.5 $\propto t^{0.5}$

but with a non-universal prefactor depending on the Lewis number and density ratio. The superdiffusive growth of the mixing layer challenges the commonly assumed picture of a fully diffusive regime at high salinity. Overall, our 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.