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

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 Γ 2 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.