Non-Boussinesq and penetrative convection in a cylindrical cell

Abstract

Measurements of Rayleigh numbers R and Nusselt numbers N have been made for a cylindrical cell having a radius to height ratio of 4·72 and containing liquid helium I. The upper surface of the cell was maintained at a constant temperature T 2 near T 0 = 2·178 K where the fluid density has a maximum. The heat input to the cell bottom was varied quasi-statically while the lower surface temperature T 1 was recorded. The penetration parameter [Pscr ]≡( T 1 − T 2 )/( T 1 − T 0 ) ranged between 0·1 and 3 for our experiments. For [Pscr ] < 1, the initial slope of N ( R ) for R near the critical Rayleigh number R c was independent of [Pscr ]. For ${\cal P}\;{\mathop {\raise-2pt\hbox{$>$}}\limits^{\raise-8pt\hbox{$\sim$}}}\;1$ , two hysteresis loops of N ( R ) were observed. One of them occurred very near R c and is interpreted in terms of the inverted bifurcation associated with the onset of cellular convection of non-Boussinesq systems. The other, for R > R c , is believed to correspond to the transition from cellular to two-dimensional flow. Near R c and with [Pscr ] > 2 we also observed multistability, with the states believed to correspond to different numbers of convective cells. For large [Pscr ] the onset of time-dependent flow occurred much closer to R c than is the case for Boussinesq systems.