Onset of buoyancy convection in a horizontal layer of a supercritical fluid heated from below

We study the onset of buoyancy convection induced in a horizontal layer of a supercritical fluid heated from below. The physical situation, which we investigate, is as follows: the initial fluid temperature is set above the critical temperature. The following two cases are investigated: (a) the bottom surface temperature is raised at time zero and (b) a constant heat flux is given from the bottom surface at time zero. In both cases, the top surface temperature is kept at the initial fluid temperature. First, we analyse the temperature propagations on short time scales. We then investigate the onset conditions of buoyancy convection by linear stability analysis, by which the critical Rayleigh number and the critical wave number are obtained. We finally analyse the delay in the onset of buoyancy convection and the wave number of the convection induced in the supercritical fluid system. We find that power laws apply to the delay and the wave number with respect to the deviation of the initial fluid temperature from the critical temperature. The powers are, in fact, expressed by the critical exponents of some physical properties. This result suggests that the critical exponents can be estimated by measuring the onset times and wave numbers of convection experimentally.