Spherical model for turbulence

We develop a large-N method for the problem of homogeneous turbulence. The spherical (N tends to infinity) 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 zeta has a nontrivial dependence on N. This value is remarkably close to the experimental result zeta = 5/3, which must therefore result from higher-order corrections in powers of 1/N. (Author)