  Direct Numerical Simulations of turbulent convection in a large aspect-ratio
box are carried out in the range of Rayleigh number $7 \times 10^4 \le Ra \le 2
\times 10^6$ at Prandtl number Pr=0.71. A strong correlation between the
vertical velocity and temperature is observed in the turbulent regime at almost
all the length scales. Frequency spectra of all the velocities and temperature
show a $-5/3$ law for a wide band of frequencies. The variances of horizontal
velocities at different points in the flow yield a single power-law.
Probability density functions of velocities and temperature are close to
Gaussian only at higher Rayleigh numbers. The mean and variance of temperature
clearly show boundary layers, surface layers and a near-homogeneous bulk
region. The boundary layer thickness decreases and bulk-homogeneity is enhanced
on increasing the Rayleigh numbers. The wave number spectra of the turbulent
kinetic energy exhibit Kolmogorov like ($E(k)\sim k^{-5/3}$) and
Bolginao-Obukhov like ($E(k)\sim k^{-11/5}$) behaviour respectively in the
central and near-wall regions of the container. An approximate balance between
the production due to buoyancy and the dissipation is found in the turbulent
kinetic energy budget. Taylor's approximate equation of the production due to
turbulent stretching and the dissipation of turbulent enstrophy is modified by
the inclusion of buoyancy production in the enstrophy budget. The present
results support the previously proposed $2/7$ power-law dependence of the
average Nusselt number on the Rayleigh number by yielding an exponent of 0.272,
but do not necessarily support the proposed classification of "soft" and "hard"
turbulence on the basis of this exponent.
