Intermittency in a cascade model for three-dimensional turbulence

Abstract

We discuss a possible mechanism for intermittency of the energy dissipation in a model for three-dimensional fully developed turbulence. We compute the structure functions for the velocity field and show that their behavior can be described in the context of a multifractal approach. We also compute the instantaneous maximum Lyapunov exponent and the corresponding (stability) eigenvector. Violent bursts of energy dissipation are related to a sudden increase of the instantaneous Lyapunov exponent, and simultaneous localization of its eigenvector on the high wave numbers at the end of the inertial range. In particular, we relate the correction to the ${\mathit{k}}^{\mathrm{\ensuremath{-}}5/3}$ Kolmogorov law for the energy spectrum to the fractal dimension extracted by temporal sequences both of the instantaneous Lyapunov exponent and of the eigenvector.