Metcalfe, G; Behringer, RP, *Convection in *^{3}He-superfluid-^{4}He mixtures. Part 1. A Boussinesq analogue,
Journal of Fluid Mechanics, vol. 307
(1996),
pp. 269-296 .
**Abstract:**

*Dilute mixtures of 3He in superfluid 4He have Prandtl numbers easily tunable between those of liquid metals and water: 0.04 < Pr < 2. Moreover, owing to the tight coupling of the temperature and concentration fields, superfluid mixture convection is closely analogous to classical Rayleigh-Bénard convection, i.e. superfluid mixtures convect as if they were classical, single-component fluids, well described by the Boussinesq equations. This work has two goals. The first is to put the theory of superfluid mixture convection on a firmer basis. We accomplish this by combining experiment and analysis to measure superfluid effects on the onset of convection. In the process, we demonstrate quantitative control over superfluid effects and, in particular, that deviations from classical convective behaviour can be made small or at worst no larger than finite aspect ratio effects. The size of superfluid effects at convective onset can be less than a few percent for temperatures 1 < T < 2 K. Comparison of the measured properties of superfluid mixture roll instabilities above the onset of convection (e.g. skewed varicose, oscillatory, and particularly near the codimension-2 point) to the properties predicted by Boussinesq calculations further verifies that superfluid mixtures convect as classical fluids. With superfluid effects understood and under control, the second goal, presented in Part 2, is to exploit the unique Pr range of superfluid mixtures and the variable aspect ratio (Γ) capabilities of our experiment to survey convective instabilities in the broad, and heretofore largely unexplored, parameter space 0.12 < Pr < 1.4 and 2 < Γ < 95. The aim is to identify and characterize time-dependence and chaos, and to discover new dynamical behaviour in strongly nonlinear convective flows.*