  Direct numerical simulations are conducted for double diffusive convection
(DDC) bounded by two parallel plates, with fluid properties similar to the
values of seawater. The DDC flow is driven by an unstable salinity difference
and stabilized at the same time by a temperature difference. For these
conditions the flow can be in the finger regime. We develop scaling laws for
three key response parameters of the system: The non-dimensional salinity flux
$Nu_S$ mainly depends on the salinity Rayleigh number $Ra_S$, which measures
the strength of the salinity difference, and exhibits a very weak dependence on
the density ratio $\Lambda$, which is the ratio of the buoyancy forces induced
by two scalar differences. The non-dimensional flow velocity $Re$ and the
non-dimensional heat flux $Nu_T$ are dependent on both $Ra_S$ and $\Lambda$.
However, the rescaled Reynolds number $Re\Lambda^{\alpha^{\rm eff}_u}$ and the
rescaled convective heat flux $(Nu_T-1)\Lambda^{\alpha^{\rm eff}_T}$ depend
only on $Ra_S$. The two exponents are dependent on the fluid properties and are
determined from the numerical results. Moreover, the behaviors of $Nu_S$ and
$Re\Lambda^{\alpha^{\rm eff}_u}$ agree with the predictions of the
Grossmann-Lohse theory which was originally developed for the
Rayleigh-B\'{e}nard flow. The non-dimensional salt-finger width and the
thickness of the velocity boundary layers, after being rescaled by
$\Lambda^{\alpha^{\rm eff}_u/2}$, collapse and obey a similar power-law scaling
relation with $Ra_S$. When $Ra_S$ is large enough, salt fingers do not extend
from one plate to the other and horizontal zonal flows emerge in the bulk
region. We then show that the current scaling strategy can be successfully
applied to the experimental results of a heat-copper-ion system~(Hage and
Tilgner, Phys. Fluids, 22, 076603, 2010).

Fluid Dynamics;Geophysics