Convection in a very compressible fluid: Comparison of simulations with experiments

The time profile DeltaT(t) of the temperature difference, measured across a very compressible fluid layer of supercritical He-3 after the start of a heat flow, shows a damped oscillatory behavior before steady-state convection is reached. The results for DeltaT(t) obtained from numerical simulations and from laboratory experiments are compared over a temperature range where the compressibility varies by a factor of approximate to40. First the steady-state convective heat current j(conv) as a function of the Rayleigh number Ra is presented, and the agreement is found to be good. Second, the shape of the time profile and two characteristic times in the transient part of DeltaT(t) from simulations and experiments are compared, namely (1) t(osc), the oscillatory period, and (2) t(p), the time of the first peak after starting the heat flow. These times, scaled by the diffusive time tau(D) versus Ra, are presented. The agreement is good for t(osc)/tau(D), where the results collapse on a single curve showing a power-law behavior. The simulation hence confirms the universal scaling behavior found experimentally. However for t(p)/tau(D), where the experimental data also collapse on a single curve, the simulation results show systematic departures from such a behavior. A possible reason for some of the disagreements, both in the time profile and in t(p), is discussed.