On the wall-bounded model of fingering double diffusive convection

Fingering double diffusive convection with real seawater properties is studied by two-dimensional direct numerical simulations for the wall-bounded domain and compared with the results for fully periodic domain. For fixed unstable salinity difference between two horizontal plates, dominant flow structures change from convection rolls to salt fingers as the stable temperature difference increases. Meanwhile the bulk density ratio calculated by the mean scalar gradients exceeds unity. When the bulk thermal Rayleigh number, which is defined by the mean temperature gradient in the bulk and the domain height, is larger than $10^7$, the characteristic height of salt fingers is much smaller than the domain height and the flow enters the free salt-finger regime. In this regime the transport properties agree quantitatively with those obtained in the fully periodic domain (e.g. Traxler et al. J. Fluid Mech., 677, 530-553, 2011). The salt-finger bulk does not spontaneously break into multi-layer staircases probably due to the fact that solid boundary prevents the development of large-scale secondary instabilities. For the limited range of density ratio at the highest salinity Rayleigh number considered here, the multi-layer state is directly established from the initial condition with uniform salinity distribution and vertically linear temperature distribution.