Turbulent Ice–Ocean Boundary Layers in the Well-Mixed Regime: Insights from Direct Numerical Simulations

Abstract

Abstract The meltwater mixing line (MML) model provides a theoretical prediction of near-ice water mass properties that is useful to compare with observations. If oceanographic measurements reported in a temperature–salinity diagram overlap with the MML prediction, then it is usually concluded that the local dynamics are dominated by the turbulent mixing of an ambient water mass with near-ice meltwater. While the MML model is consistent with numerous observations, it is built on an assumption that is difficult to test with field measurements, especially near the ice boundary, namely, that the effective (turbulent and molecular) salt and temperature diffusivities are equal. In this paper, this assumption is tested via direct numerical simulations of a canonical model for externally forced ice–ocean boundary layers in a uniform ambient. We focus on the well-mixed regime by considering an ambient temperature close to freezing and run the simulations until a statistical steady state is reached. The results validate the assumption of equal effective diffusivities across most of the boundary layer. Importantly, the validity of the MML model implies a linear correlation between the mean salinity and temperature profiles normal to the interface that can be leveraged to construct a reduced ice–ocean boundary layer model based on a single scalar variable called thermal driving. We demonstrate that the bulk dynamics predicted by the reduced thermal driving model are in good agreement with the bulk dynamics predicted by the full temperature–salinity model. Then, we show how the results from the thermal driving model can be used to estimate the interfacial heat and salt fluxes and the melt rate. Significance Statement We investigate the turbulent dynamics and thermodynamical properties of water masses below ice shelves using new data from high-resolution simulations. This is important because there are currently too few observations of ice–ocean boundary layer dynamics to construct reliable models of ice-shelf melting as a function of ocean conditions. Our results demonstrate that the turbulent diffusivities of salt and temperature are approximately equal in the well-mixed regime. This implies a linear correlation between the mean temperature and salinity profiles, consistent with the meltwater mixing line prediction that is often used to interpret polar observations. We take advantage of this correlation to propose a reduced model of ice–ocean boundary layers that can predict ice-shelf melt rates at relatively low computational cost.