The temperature-salinity relationship of the mixed layer

The surface mixed layer of the ocean is often characterized by density compensation between the horizontal temperature and salinity gradients. In this contribution we present a combination of theoretical arguments and numerical simulations to investigate how compensation might emerge as a result of processes at work within the mixed layer. The dynamics of the mixed layer are investigated through a simple model. The model consists of a pair of coupled advection-diffusion equations for heat and salt. The coupling arises through a nonlinear diffusion operator proportional to the buoyancy gradient, which parameterizes the combined effect of slumping and mixing of small-scale horizontal buoyancy gradients. Numerical solutions of the mixed layer model show that the nonlinear diffusion creates compensation between the temperature and salinity gradients, while the stirring field maintains alignment between the two gradients. The results of this work suggest a new parameterization of the horizontal fluxes of heat and salt for numerical models of the mixed layer.