Abstract
Turbulent Rayleigh-Bénard convection was investigated within a liquid metal layer, Prandtl number , in a square vessel having a moderate aspect ratio, . Laboratory experiments were performed at moderate Rayleigh numbers, . Ultrasonic velocity profiling was used to visualize the spatiotemporal flow structure in two horizontal planes, while temperature fluctuations were monitored simultaneously in the fluid layer. By using multiple ultrasonic sensors, a grid of orthogonal measurement lines was created. This configuration enabled the identification of coherent flow structures showing periodic oscillations. In particular, oscillatory roll-like structures were observed for , while the transition to a new-found, fully three-dimensional cellular structure occurs around . The Fourier analysis of the temperature fluctuations indicates that the convection reaches the developed state of thermal turbulence at this number. This cellular structure of the flow field is recognized as a representation of the large-scale circulation in thermal turbulence for the specific situation of confined convection in the rectangular vessel. The transition from laminar convection to thermal turbulence manifests itself in the occurrence of unstable intermediate regimes accompanied by a stepwise increment in the horizontal scale. We suggest scaling laws for the characteristic velocity and the dominating oscillation frequency and based on that for the horizontal length scale as a function of the Ra number. The comparison to corresponding values of characteristic length scales published for thermal convection in air in larger aspect ratios , T. Hartlep et al., Phys. Rev. Lett. 91, 064501 (2003), A. Pandey et al., Nat. Commun. 9, 2118 (2018), and D. E. Fitzjarrald, J. Fluid Mech. 73, 693 (1976)] reveals a different number dependence of the horizontal wave number.
4 More- Received 3 August 2018
DOI:https://doi.org/10.1103/PhysRevFluids.4.033501
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