Onset of convection in dilute superfluid 3He-4He mixtures. II. Closed cylindrical container

The thermohydrodynamics of dilute superfluid 3He-4He 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 roughly-equal1 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