Transition from convection rolls to large-scale cellular structures in turbulent Rayleigh-Bénard convection in a liquid metal layer

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  • Transition from convection rolls to large-scale cellular structures in turbulent Rayleigh-Benard convection in a liquid metal layer

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Turbulent Rayleigh-Benard convection was investigated within a liquid metal layer, Prandtl number Pr = 0.03, in a square vessel having a moderate aspect ratio, Gamma = 5. Laboratory experiments were performed at moderate Rayleigh numbers, 7.9 x 10(3) < Ra < 3.5 x 10(5). 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 Ra less than or similar to 6 x 10(4), while the transition to a new-found, fully three-dimensional cellular structure occurs around Ra = 7 x 10(4). The Fourier analysis of the temperature fluctuations indicates that the convection reaches the developed state of thermal turbulence at this Ra 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 [Pr = 0.7, 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 Ra number dependence of the horizontal wave number.

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