Onset of convection in a very compressible fluid: the transient toward steady state.

Abstract

We analyze the time profile deltaT(t) of the temperature difference, measured across a very compressible supercritical 3He fluid layer in its convective state. The experiments were done along the critical isochore in a Rayleigh-Bénard cell after starting the vertical constant heat flow q. For q sufficiently well above that needed for the convection onset, the transient deltaT(t) for a given epsilon identical with (T-T(c))/T(c), with T(c)=3.318 K, shows a damped oscillatory profile with period t(osc) modulating a smooth base profile. The smooth profile forms the exponential tail of the transient which tends to the steady-state deltaT( infinity ) with a time constant tau(tail). The scaled times t(osc)/t(D) and tau(tail)/t(D) from all the data could be collapsed onto two curves as a function of the Rayleigh number over approximately 3.5 decades. Here t(D) is the characteristic thermal diffusion time. Furthermore, comparisons are made between measurements of a third characteristic time t(m) between the first peak and the first minimum in the deltaT(t) profile and its estimation by Onuki et al. Also, comparisons are made between the observed oscillations and the two-dimensional simulations by Onuki et al. and by Amiroudine and Zappoli. For epsilon<9 x 10(-3), the experiments show a crossover to a different transient regime. This regime, which we briefly describe, is not understood at present.