Lyapunov Spectrum of a Chaotic Model of Three-Dimensional Turbulence

Abstract

A model equation of fully developed three-dimensional turbulence is proposed which exhibits the Kolmogorov’s similarity law in its chaotic state. The structure of the chaotic attractor is investigated by examining the Lyapunov spectrum for several values of viscosity. The Lyapunov spectrum has a scaling property in the interior of the attractor. It appears that the distribution function of the Lyapunov exponents has a singularity at a null Lyapunov exponent in the inviscid limit.