  Using direct numerical simulations, we study the statistical properties of
reversals in two-dimensional Rayleigh-B\'enard convection for infinite Prandtl
number. We find that the large-scale circulation reverses irregularly, with the
waiting time between two consecutive genuine reversals exhibiting a Poisson
distribution on long time scales, while the interval between successive
crossings on short time scales shows a power law distribution. We observe that
the vertical velocities near the sidewall and at the center show different
statistical properties. The velocity near the sidewall shows a longer
autocorrelation and $1/f^2$ power spectrum for a wide range of frequencies,
compared to shorter autocorrelation and a narrower scaling range for the
velocity at the center. The probability distribution of the velocity near the
sidewall is bimodal, indicating a reversing velocity field. We also find that
the dominant Fourier modes capture the dynamics at the sidewall and at the
center very well. Moreover, we show a signature of weak intermittency in the
fluctuations of velocity near the sidewall by computing temporal structure
functions.
