CONVECTION IN HE-3-SUPERFLUID-HE-4 MIXTURES .1. A BOUSSINESQ ANALOG

Dilute mixtures of He-3 in superfluid He-4 have Prandtl numbers easily tunable between those of liquid metals and water: 0.04 < Pr < 2. More over, owing to the tight coupling of the temperature and concentration fields, superfluid mixture convection is closely analogous to classic al Rayleigh-Benard convection, i.e. superfluid mixtures convect as if they were classical, single-component fluids, well described by the Bo ussinesq equations. This work has two goals. The first is to put the t heory of superfluid mixture convection on a firmer basis. We accomplis h this by combining experiment and analysis to measure superfluid effe cts on the onset of convection. In the process, we demonstrate quantit ative control over superfluid effects and, in particular, that deviati ons from classical convective behaviour can be made small or at worst no larger than finite aspect ratio effects. The size of superfluid eff ects at convective onset can be less than a few percent for temperatur es 1 < T < 2 K. Comparison of the measured properties of superfluid mi xture roll instabilities above the onset of convection (e.g. skewed va ricose, 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 Pa rt 2, is to exploit the unique Pr range of superfluid mixtures and the variable aspect ratio (Gamma) capabilities of our experiment to surve y convective instabilities in the broad, and heretofore largely unexpl ored, parameter space 0.12 < Pr < 1.4 and 2 < Gamma < 95. The aim is t o identify and characterize time-dependence and chaos, and to discover new dynamical behaviour in strongly nonlinear convective hows.