  Double-diffusive convection driven by both thermal and compositional buoyancy
in a rotating cylindrical annulus with conical caps is considered with the aim
to establish whether a small fraction of compositional buoyancy added to the
thermal buoyancy (or vice versa) can significantly reduce the critical Rayleigh
number and amplify convection in planetary cores. It is shown that the neutral
surface describing the onset of convection in the double-buoyancy case is
essentially different from that of the well-studied purely thermal case, and
does indeed allow the possibility of low-Rayleigh number convection. In
particular, isolated islands of instability are formed by an additional
"double-diffusive" eigenmode in certain regions of the parameter space.
However, the amplitude of such low-Rayleigh number convection is relatively
weak. At similar flow amplitudes purely compositional and double-diffusive
cases are characterized by a stronger time dependence compared to purely
thermal cases, and by a prograde mean zonal flow near the inner cylindrical
surface. Implications of the results for planetary core convection are briefly
discussed.
