Time scaling in the convection onset of a supercritical fluid

A review is presented on the laboratory experiments and simulations on the convection onset of a supercritical fluid, He, in a Rayleigh-Bénard cell after the start of a steady heat flow q from the bottom wall at the time t=0. The experiments were conducted at several temperatures along the critical isochore and over a wide range of q, and measured the temperature drop ∆T(t) across the fluid layer. It was empirically found that the various characteristic times ti observed in the profile of ∆T(t), and also in the convection growth determined by numerical simulations, could each be expressed by ti /τD as function of the Rayleigh number, where τD is the diffusive relaxation time. This scaled representation is to be expected, as has been shown in a general demonstration by Michael Cross (unpublished) and its implications are discussed. A comparison of the profiles ∆T(t) from experiments and simulations are presented and various unresolved discrepancies will be discussed.