Turbulence in helium-gas free convection

Results on a Rayleigh-B\'enard experiment in helium gas at 5 K in a cylindrical cell of aspect ratio 1 are presented. The Rayleigh number spans a range from 10⁵ to 10¹². A large-scale coherent flow is observed via the correlation of two adjacent temperature probes. This flow-velocity measurement shows clear transitions between different turbulent states. In hard turbulence, the dimensionless velocity [V/({κ}/L)] scales with the Rayleigh number, with an exponent close to 1/2. The horizontal temperature difference across the cell is another measure of the different turbulent states. The temperature signals in the side-wall region (the large mean vertical velocity region) give clear pictures of various turbulent states. The measured velocity has been compared with the calculated free-fall velocity and also the heat transfer rate with the one calculated from the flow advection. The coherent frequency ωₚ is found to be associated with the large-scale flow. In the side-wall region the power spectrum of the local temperature signal has a power-law dependence for Rayleigh numbers between 10⁸ and 10¹¹. Both the exponent and the range of the power law change with the Rayleigh number. For Rayleigh numbers above 10¹¹, a power law independent of Rayleigh number (exponent 1.4) develops at low frequency.