Spherical model for turbulence

We develop a large-N method for the problem of homogeneous turbulence. The spherical (N{→}{∞}) limit yields Kraichnan's 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 {ζ} has a nontrivial dependence on N, with {ζ}(N{→}{∞})=3/2. This value is remarkably close to the experimental result {ζ}{}5/3, which must therefore result from higher-order corrections in powers of 1/N.