Abstract
In Rayleigh–Bénard convection, the size of a flow domain and its aspect ratio
$\varGamma$
(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
$2.9 \times 10^4 \leq {{Ra}} \leq 1.6 \times 10^6$
and square cuboid domains with
$\varGamma =2$
,
$2.5$
,
$3$
and
$5$
. Our study demonstrates that a repeating pattern of a JRV encountered at aspect ratio
$\varGamma \approx 2.5$
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-organised within the domain; the number of the realised units is expected to scale as
$\varGamma ^2$
with sufficiently large and growing
$\varGamma$
. We find the oscillatory modes for all investigated
$\varGamma$
; however, they are more pronounced for
$\varGamma =2.5$
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.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics,Applied Mathematics