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Abstract:
In Rayleigh–Bénard convection, the size of a flow domain and its aspect ratio Γ (a ratio between the spatial length and height of the domain) affect the shape of the large-scale circulation. For some aspect ratios, the flow dynamics includes 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 2.9×104≤Ra≤1.6×106 and square cuboid domains with Γ=2, 2.5, 3 and 5. Our study demonstrates that a repeating pattern of a JRV encountered at aspect ratio Γ≈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-organised within the domain; the number of the realised units is expected to scale as Γ2 with sufficiently large and growing Γ. We find the oscillatory modes for all investigated Γ; however, they are more pronounced for Γ=2.5 and 5. Future studies for large-aspect-ratio domains of different shapes would enhance our understanding of how the JRVs adjust and reorganise at such scaled-up geometries, and answer the question of whether they are indeed the smallest superstructure units.
