INTERMITTENCY IN DYNAMIC-MODELS OF TURBULENCE

The purpose of this paper is to gain insight into the dynamical origins of intermittent fluctuations in turbulent flow. To this end stochastic models of turbulence are developed, which borrow their interaction structure from fractal geometry. The dynamics conserve energy and ensure equipartition of energy in equilibrium. The resulting stochastic process models the chaotic motion of Navier-Stokes-generated cascades [J. Eggers and S. Grossmann, Phys. Lett. 156, 444 (1991)]. In all cases we find small-scale intermittency, but the strength of the fluctuations depends crucially on the geometry of the cascade. We calculate the variance of the energy fluctuations in a low-noise expansion and evaluate its anomalous scaling exponent to lowest order in the noise strength. The result agrees well with numerical simulations.