Oscillatory instability and fluid patterns in low-Prandtl-number Rayleigh-B\'{e}nard convection with uniform rotation

• Published in: arXiv.org 2014-02
• Main Authors: Pharasi, Hirdesh K, Kumar, Krishna
• Format: Article
• Language: English
• Subjects: Aspect ratio; Bifurcations; Boxes; Computer simulation; Convection; Rolls; Stability; Standing waves; Two dimensional flow
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1402.4226

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.