CASCADE STRUCTURES AND SCALING EXPONENTS IN A DYNAMICAL MODEL OF TURBULENCE - MEASUREMENTS AND COMPARISON

A detailed examination of the cascade statistics and scaling exponents is carried out for a dynamical-system model of fully developed turbul ence called the GOY shell model. The convergence in time of the probab ility density functions and moments of the velocity fluctuations and t heir scaling exponents is studied with particular care. With a large s ample size (5 x 10(9)), we demonstrate that there exists a finite cuto ff for the velocity fluctuations at each inertial-range wave-number sh ell and the properties of the cutoff determine the scaling exponents o f all moments. This cutoff represents the most intermittent structures in the cascade dynamics and exhibits a power-law dependence on wave n umber. The accurately determined scaling exponents permit a detailed c omparison with various phenomenological models describing the statisti cs of the energy cascade. The consideration of the first and second de rivatives of the scaling exponents with respect to the order of the mo ments p provides the evidence that the hierarchical-structure model [S he and Leveque, Phys. Rev. Lett. 72, 336 (1994)] predicts the best fun ctional dependence on p of the scaling exponents in the GOY shell mode l.