‘Thermohaline circulation in a box’: heat and salinity transport in double-diffusive horizontal convection

The Atlantic Meridional Overturning Circulation (AMOC), partially driven by double-diffusive horizontal convection (DDHC), plays a key role in regulating the global climate. Indeed, it governs the transfer of heat, salinity and nutrients between the equator and polar regions. The present study investigates an idealised model system, ‘thermohaline circulation in a box’ or ‘AMOC in a box’, namely DDHC in a well-defined geometry, specifically the flow in a box with horizontal temperature and salinity gradients. By varying the temperature Rayleigh number $\textit{Ra}_T$ and the density ratio $\varLambda$ , or equivalently the salinity Rayleigh number $\textit{Ra}_S$ , four distinct regimes are found. These regimes are distinguished by the global response parameters of the system, namely the temperature Nusselt number $\textit{Nu}_T$ , the salinity Nusselt number $\textit{Nu}_S$ and the friction Reynolds number $\textit{Re}_\tau$ , as well as by the flow structures. The two limiting regimes of horizontal convection, at high and low $\varLambda$ values, follow the Shishkina-Grossmann-Lohse theory for horizontal convection. In the two regimes in between, in which strong competition between temperature and saline buoyancy occurs, a clear thermohaline layering and the presence of oscillating convected salt fingers are found.