Horizontal convection driven by temperature and salinity gradients over the top surface

Horizontal convection is studied numerically as a model problem to investigate the convection flow driven by surface density distribution, which is relevant to the ocean environment. Unlike most existing works of thermally driven horizontal convection, we consider the gradients of both temperature and salinity over the top surface. Much more complex flow morphology is obtained in our simulations. Within certain region below the top surface, both mean temperature and salinity show strong dependences on the depth. At one end of the domain they both increase as the depth becomes larger, and multiple layers of horizontal mean flows emerge. At the opposite end the mean temperature and salinity drop simultaneously versus the depth, which favors the fingering double diffusive convection. And indeed we observe salt-finger structures. The vertical fluxes at the surface and the horizontal fluxes within the domain are also discussed for both temperature and salinity fields.