Intermittency in the large N-limit of a spherical shell model for turbulence

Details Intermittency in the large N-limit of a spherical shell model for turbulence Intermittency in the large N-limit of a spherical shell model for turbulence

1997-01-17

arxiv.org/abs/chao-dyn/9701015v1

Nonlinear Sciences

Chaotic Dynamics

10 pages, Latex, 3 Postscript figures, to be published on Europhys. Lett

Scientific paper

10.1209/epl/i1997-00151-4

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.

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