  A spherical shell model for turbulence, obtained by coupling $N$ replicas of
the Gledzer, Okhitani and Yamada shell model, is considered. Conservation of
energy and of an helicity-like invariant is imposed in the inviscid limit. In
the $N \to \infty$ limit this model is analytically soluble and is remarkably
similar to the random coupling model version of shell dynamics. We have studied
numerically the convergence of the scaling exponents toward the value predicted
by Kolmogorov theory (K41). We have found that the rate of convergence to the
K41 solution is linear in 1/N. The restoring of Kolmogorov law has been related
to the behaviour of the probability distribution functions of the instantaneous
scaling exponent.
