Elimination of turbulence modes using a conditional average with asymptotic freedom

The part of the nonlinear term in the Navier-Stokes equation which represen ts coupling to the small-scale modes may be averaged out by introducing a w eak conditional average with asymptotic freedom in wavenumber. A residual d eterministic part, while important for individual realizations, makes a neg ligible contribution to the renormalization of the dissipation rate. This i s because the full ensemble average, needed to establish the energy balance , relaxes the constraint on the conditional average.