Oscillatory instability and fluid patterns in low-Prandtl-number Rayleigh-Bénard convection with uniform rotation

Abstract

We present the results of direct numerical simulations of flow patterns in a low-Prandtl-number ($Pr=0.1$) fluid above the onset of oscillatory convection in a Rayleigh-Bénard 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 ($L_x\times L_y\times 1$) and a wide range of Taylor numbers ($750\le Ta\le 5000$) for the purpose. The horizontal aspect ratio $\eta =L_y/L_x$ of the box was varied from $0.5$ to $10$. The primary instability appeared in the form of two-dimensional standing waves for shorter boxes ($0.5\le \eta <1$ and $1<\eta <2$). The flow patterns observed in boxes with $\eta =1$ and $\eta =2$ were different from those with $\eta <1$ and $1<\eta <2$. We observed a competition between two sets of mutually perpendicular rolls at the primary instability in a square cell ($\eta =1$) for $Ta<2700$, but observed a set of parallel rolls in the form of standing waves for $Ta\ge 2700$. The three-dimensional convection was quasiperiodic or chaotic for $750\le Ta<2700$, and then bifurcated into a two-dimensional periodic flow for $Ta\ge 2700$. The convective structures consisted of the appearance and disappearance of straight rolls, rhombic patterns, and wavy rolls inclined at an angle $\varphi =\frac{\pi }{2}-\arctan ({\eta }^{-1})$ with the straight rolls.

32 pages, 14 figures, 1 table

References in corpus (2)

• Benchmarking and scaling studies of a pseudospectral code Tarang for turbulence simulations
• Pattern dynamics near homoclinic bifurcation in Rayleigh-Bénard convection

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