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 T2 near T0 = 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 T1 was recorded. The penetration parameter [Pscr ]≡(T1−T2)/(T1−T0) 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 Rc 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 Rc and is interpreted in terms of the inverted bifurcation associated with the onset of cellular convection of non-Boussinesq systems. The other, for R > Rc, is believed to correspond to the transition from cellular to two-dimensional flow. Near Rc 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 Rc than is the case for Boussinesq systems.