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We present the results of direct numerical simulations of flow patterns in alow-Prandtl-number ($Pr = 0.1$) fluid above the onset of oscillatory convectionin a Rayleigh-B\'{e}nard system rotating uniformly about a vertical axis.Simulations were carried out in a periodic box with thermally conducting andstress-free top and bottom surfaces. We considered a rectangular box ($L_x\times L_y \times 1$) and a wide range of Taylor numbers ($750 \le Ta \le5000$) for the purpose. The horizontal aspect ratio $\eta = L_y/L_x$ of the boxwas varied from $0.5$ to $10$. The primary instability appeared in the form oftwo-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 acompetition between two sets of mutually perpendicular rolls at the primaryinstability in a square cell ($\eta = 1$) for $Ta < 2700$, but observed a setof parallel rolls in the form of standing waves for $Ta \geq 2700$. Thethree-dimensional convection was quasiperiodic or chaotic for $750 \le Ta <2700$, and then bifurcated into a two-dimensional periodic flow for $Ta \ge2700$. The convective structures consisted of the appearance and disappearanceof straight rolls, rhombic patterns, and wavy rolls inclined at an angle $\phi= \frac{\pi}{2} - \arctan{(\eta^{-1})}$ with the straight rolls.

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