  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.
