E. Leveque et Zs. She, CASCADE STRUCTURES AND SCALING EXPONENTS IN A DYNAMICAL MODEL OF TURBULENCE - MEASUREMENTS AND COMPARISON, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 55(3), 1997, pp. 2789-2799
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.