Abstract
We develop a large-N method for the problem of homogeneous turbulence. The spherical (N) limit yields Kraichnans direct interaction approximation equations. Implications for real turbulence (N=1) are discussed. In particular, we argue that the renormalization-group results obtained by setting the expansion parameter y=4 are incorrect, and that the Kolmogorov exponent has a nontrivial dependence on N, with (N)=3/2. This value is remarkably close to the experimental result 5/3, which must therefore result from higher-order corrections in powers of 1/N. © 1993 The American Physical Society.