Onset of Convection in a Very Compressible Fluid : The Transient Toward Steady State

Abstract

We analyze the time profile \(\Delta T(t)\) of the temperature difference, measured across a very compressible supercritical \(^3\)He fluid layer in its convective state. The experiments were done along the critical isochore in a Rayleigh-B\'{e}nard cell after starting the vertical constant heat flow \(q\). For \(q\) sufficiently well above that needed for the convection onset, the transient \(\Delta T(t)\) for a given \(\epsilon\equiv(T-T_c)/T_c\), with \(T_c\) = 3.318K, 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 \(\Delta T(\infty)\) 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 \(\sim\) 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 \(\Delta T(t)\) profile and its estimation by Onuki et al. Also comparisons are made between the observed oscillations and the 2D simulations by Onuki et al. and by Amiroudine and Zappoli. For \(\epsilon < 9\times 10^{-3}\) the experiments show a crossover to a different transient regime. This new regime, which we briefly describe, is not understood at present.