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Oscillatory instability and fluid patterns in low-Prandtl-number Rayleigh-B\'{e}nard convection with uniform rotation
We present the results of direct numerical simulations of flow patterns in a
low-Prandtl-number () fluid above the onset of oscillatory convection
in a Rayleigh-B\'{e}nard system rotating uniformly about a vertical axis.
Simulations were carried out in a periodic box with thermally conducting and
stress-free top and bottom surfaces. We considered a rectangular box () and a wide range of Taylor numbers () for the purpose. The horizontal aspect ratio of the box
was varied from to . The primary instability appeared in the form of
two-dimensional standing waves for shorter boxes ( and ). The flow patterns observed in boxes with and
were different from those with and . We observed a
competition between two sets of mutually perpendicular rolls at the primary
instability in a square cell () for , but observed a set
of parallel rolls in the form of standing waves for . The
three-dimensional convection was quasiperiodic or chaotic for , and then bifurcated into a two-dimensional periodic flow for . The convective structures consisted of the appearance and disappearance
of straight rolls, rhombic patterns, and wavy rolls inclined at an angle with the straight rolls.Comment: 32 pages, 14 figures, 1 tabl
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