Effect of rigid boundaries on the onset of convective instability in a triply diffusive fluid layer

The onset of convection in a triply diffusive, incompressible motionless Newtonian fluid layer of infinite horizontal extent bounded by rigid parallel walls is studied by means of a linear stability analysis. The qualitative features of most of the results carry over from the case of stress-free boundaries studied earlier by Pearlstein, Harris, and Terrones [J. Fluid Mech. 202, 443 (1989)]. One striking feature that does not carry over from the stress-free case, however, is the possibility of quasiperiodic bifurcation from the steady motionless state via two pairs of complex conjugate temporal eigenvalues with incommensurable imaginary parts crossing into the right half-plane at the same combination of Rayleigh numbers. The impossibility of this type of quasiperiodic bifurcation from the rest state in the rigid case is discussed in terms of the topology of the disconnected neutral curves. The numerical method employed is suitable for the computation of disconnected oscillatory neutral curves in other stability problems for which a low-order exact dispersion relation does not exist.