  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.
