Oscillatory instability and fluid patterns in low Prandtl number Rayleigh B\'{e}nard convection with uniform r
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Author: Hirdesh K. Pharasi, Krishna Kumar
Added by: arkiver
Added Date: 2018-06-30
Subjects: Fluid Dynamics, Physics
Publishers: arXiv.org
PDF Count: 1
Total Size: 3.32 MB
PDF Size: 3.29 MB
Extensions: pdf, torrent
Contributor: Internet Archive
License: Unknown License
Downloads: 11
Views: 61
Total Files: 6
Media Type: texts
Total Files: 2
Description
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-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 ($L_x \times L_y \times 1$) 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 $Ta \geq 2700$. 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 $\phi = \frac{\pi}{2} - \arctan{(\eta^{-1})}$ with the straight rolls.
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