Determining how nonlinearities in the equation of state affect diffusive interfaces in the ocean

In the ocean, favourable vertical gradients and the differing molecular diffusivities of salinity and temperature cause double diffusive instabilities. At high latitudes, double diffusive instabilities are in the ‘diffusive’ convection regime due to the colder, fresher waters that form atop warmer, saltier waters. Cold conditions at high latitudes also enhance effects of the nonlinear equation of state. Modelling studies of diffusive convection typically use a linear equation of state, thereby not including processes such as cabbeling, the gain in density upon mixing, which arises from nonlinearities in the equation of state. Here, we use a fully nonlinear equation of state in direct numerical simulations (DNS) to investigate the impact of cabbeling on diffusive convection and the resulting ‘diffusive’ interfaces. A one-dimensional molecular diffusion model shows that cabbeling affects the diffusive convection instability by forming unequal density anomalies within the layers either side of a diffusive interface. This asymmetry is not present when the equation of state is linear. The primary driver of the asymmetry between the density anomalies in the nonlinear case is the temperature difference across an interface. In a two-layer system, a larger density anomaly forms below the interface, and our DNS experiments show that this drives an upward migration of the interface agreeing with earlier laboratory results. Our results indicate that cabbeling’s impact on diffusive interfaces in the Arctic Ocean is subtle, while in the Southern Ocean, cabbeling can drive sustained upward migration of interfaces that may influence thermohaline staircase formation and maintenance.