  A detailed study of the Rayleigh-B\'enard convection in two-dimensions with
free-slip boundaries is presented. Pseudo-spectral method has been used to
numerically solve the system for Rayleigh number up to $3.3 \times 10^7$. The
system exhibits various convective states: stationary, oscillatory, chaotic and
soft-turbulent. The `travelling rolls' instability is observed in the chaotic
regime. Scaling of Nusselt number shows an exponent close to 0.33. Studies on
energy spectrum and flux show an inverse cascade of kinetic energy and a
forward cascade of entropy. This is consistent with the shell-to-shell energy
transfer in wave number space. The shell-to-shell energy transfer study also
indicates a local energy transfer from one shell to the other.

Fluid Dynamics