  On the basis of the lattice Boltzmann method we have done a numerical
experiment of a forced turbulence in real space and time. Our new findings are
summarized into two points. First in the analysis of the mean-field behavior of
the velocity field using the exit-time statistics we have verified Kolmogorov's
scaling and Taylor's hypothesis for the first time in the simulation for the
Navier-Stokes equation. Second in the analysis of the intermittent velocity
fluctuations using a non-equilibrium probability distribution function and the
wavelet denoising we have clarified that the coherent vortices sustain the
power-law velocity correlation in the non-equilibrium state.
