The time profile $\Delta T\left(t\right)\mathrm{}$ of the temperature difference, measured across a very compressible fluid layer of supercritical ${}^3\mathrm{He}$ after the start of a heat flow, shows a damped oscillatory behavior before steady-state convection is reached. The results for $\Delta T\left(t\right)\mathrm{}$ obtained from numerical simulations and from laboratory experiments are compared over a temperature range where the compressibility varies by a factor of ≈40. First the steady-state convective heat current $j^{\mathrm{conv}}$ as a function of the Rayleigh number $\mathrm{Ra}$ 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 $\Delta T\left(t\right)\mathrm{}$ from simulations and experiments are compared, namely (1) $t_{\mathrm{osc}},$ 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 $t_{\mathrm{osc}}/{\tau }_D,$ 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.

• Received 21 May 2003

DOI:https://doi.org/10.1103/PhysRevE.68.056309