Oscillatory large-scale circulation in liquid-metal thermal convection and its structural unit

Abstract

In Rayleigh-Bénard convection (RBC), the size of a flow domain and its aspect ratio $\Gamma$ (a ratio between the spatial length and height of the domain) affect the shape of the large-scale circulation (LSC). For some aspect ratios, the flow dynamics include a three-dimensional oscillatory mode known as a jump-rope vortex (JRV), however, the effects of varying aspect ratios on this mode are not well investigated. In this paper, we study these aspect-ratio effects in liquid metals, for a low Prandtl number $Pr=0.03$. Direct numerical simulations and experiments are carried out for a Rayleigh number range $2.9\times 10^4\le Ra\le 1.6\times 10^6$ and square cuboid domains with $\Gamma =2$, $2.5$, $3$ and $5$. Our study demonstrates that a repeating pattern of a JRV encountered at an aspect ratio $\Gamma \approx 2.5$ is the basic structural unit that builds up to a lattice of interlaced JRVs at the largest aspect ratio. The size of the domain determines how many structural units are self-organized within the domain; the number of the realized units is expected to scale as ${\Gamma }^2$ with sufficiently large and growing $\Gamma$. We find the oscillatory modes for all investigated $\Gamma$, however, they are more pronounced for $\Gamma =2.5$ and $\Gamma =5$. Future studies for large-aspect ratio domains of different shapes would enhance our understanding of how the JRVs adjust and reorganize at such scaled-up geometries, and answer the question of whether they are indeed the smallest superstructure units.

arXiv comment26 pages, 16 figures

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