2-PARAMETER EXPANSION IN THE RENORMALIZATION-GROUP ANALYSIS OF TURBULENCE

The renormalization of the solution of the Navier-Stokes equation for randomly stirred fluid with long-range correlations of the driving for ce is analysed near two dimensions. It is shown that a local term must be added to the correlation function of the random force for the corr ect renormalization of the model at two dimensions. The interplay of t he short-range and long-range terms in the large-scale behaviour of th e model is analysed near two dimensions by the field-theoretic renorma lization group. A regular expansion in 2 epsilon = d - 2 and delta = 2 - lambda, is constructed, where d is the space dimension and lambda t he exponent of the powerlike correlation function of the driving force . It is shown that in spite of the additional divergences, the asympto tic behaviour of the model near two dimensions is the same as in highe r dimensions, contrary to recent conjectures based on an incorrect ren ormalization procedure.