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

Abstract

Turbulent Rayleigh-Bénard convection was investigated within a liquid metal layer, Prandtl number Pr = 0.03, in a square vessel having a moderate aspect ratio, = 5. Laboratory experiments were performed at moderate Rayleigh numbers, 7.9 × 10 3 < Ra < 3.5 × 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 6 × 10 4 , while the transition to a new-found, fully three-dimensional cellular structure occurs around Ra = 7 × 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 [

Connections between nonrotating, slowly rotating, and rapidly rotating turbulent convection transport scalings

“…For both nonrotating and slowly rotating convections, we take the characteristic convection length scale to be the global scale of the system in all directions, ∼ H, based on the superstructures that form at high Ra with vertical scales of order H and lateral scales that are typically less than 10H [68][69][70][71][72], which appear to be maintained even in extreme astrophysical and geophysical systems [73]. In the turbulent limit, the free-fall inertial balance is achieved:…”

Free-fall velocities and heat transport enhancement in liquid metal magneto-convection

“…At low magnetic field strength, the convection at sufficiently high Ra forms a large-scale circulation with a three-dimensional cellular structure that fills the entire cell (figure 2a,b,g), whereby upwelling takes place in the centre and all four corners of the vessel. A detailed description of this structure can be found in Akashi et al (2019). The large amplitude oscillation that can be seen in figure 2(a,b) is a typical feature of inertia-dominated liquid metal flows due to their low viscosity and high density (Vogt et al 2018b).…”

“…A detailed description of this structure can be found in Akashi et al. (2019). The large amplitude oscillation that can be seen in figure 2( a , b ) is a typical feature of inertia-dominated liquid metal flows due to their low viscosity and high density (Vogt et al.…”

Jump rope vortex flow in liquid metal Rayleigh–Bénard convection in a cuboid container of aspect ratio

“…The dominant influence of inertia in low-Pr fluids qualifies them as a suitable object of investigation with respect to the formation and the dynamical behaviour of coherent flow structures in turbulent RBC. Several flow regimes were detected by Akashi et al (2019) in the Ra range 7.9 × 10 3 Ra 3.5 × 10 5 . An increase of Ra causes an increasing horizontal wavelength of the flow structure and a conversion from a four-roll pattern via transient four-and three-roll regimes to a cellular flow regime.…”

“…In this paper, we report a combined experimental and numerical work which considers the turbulent RBC in a cuboid container with square horizontal cross-section of aspect ratio 5 and continues a previous experimental study made by Akashi et al (2019). We use the eutectic metal alloy GaInSn (Pr = 0.03) as working fluid.…”