  We conduct direct numerical simulations for turbulent Rayleigh-B\'{e}nard
(RB) convection, driven simultaneously by two scalar components (say,
temperature and salt concentration) with different molecular diffusivities, and
measure the respective fluxes and the Reynolds number. To account for the
results, we generalize the Grossmann-Lohse theory for traditional RB
convections~(Grossmann and Lohse, J. Fluid Mech., 407, 27-56; Phys. Rev. Lett.,
86, 3316-3319; Stevens et al., J. Fluid Mech., 730, 295-308) to this two-scalar
turbulent convection. Our numerical results suggest that the generalized theory
can successfully predict the overall trends for the fluxes of two scalars and
the Reynolds number. In fact, for most of the parameters explored here, the
theory can even predict the absolute values of the fluxes and the Reynolds
number with good accuracy. The current study extends the generality of the
Grossmann-Lohse theory in the area of the buoyancy-driven convection flows.
