  We study the three dimensional Navier-Stokes equation with a random Gaussian
force acting on large wavelengths. Our work has been inspired by Polyakov's
analysis of steady states of two dimensional turbulence. We investigate the
time evolution of the probability law of the velocity potential. Assuming that
this probability law is initially defined by a statistical field theory in the
basin of attraction of a renormalisation fixed point, we show that its time
evolution is obtained by averaging over small scale features of the velocity
potential. The probability law of the velocity potential converges to the fixed
point in the long time regime. At the fixed point, the scaling dimension of the
velocity potential is determined to be ${-{4\over 3}}$. We give conditions for
the existence of such a fixed point of the renormalisation group describing the
long time behaviour of the velocity potential. At this fixed point, the energy
spectrum of three dimensional turbulence coincides with a Kolmogorov spectrum.
