The thermohydrodynamics of dilute superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ mixtures is applied to a circular container with insulating sidewalls and rigid isothermal ends. For small downward heat flow, the boundary conditions yield a uniform temperature gradient and superflow but a nonuniform normal flow. Linearized perturbations about this conducting state become unstable at a critical Rayleigh number that (at ∼1 K) differs only slightly from that for a classical one-component fluid in the same container. Despite the preferred direction of the unperturbed normal flow, infinitesimal-amplitude convection can occur in either of two degenerate modes. The splitting of these modes observed by Warkentin, Haucke, Lucas, and Wheatley probably involves nonlinear corrections.

• Received 26 March 1982

DOI:https://doi.org/10.1103/PhysRevB.26.1174