Lyapunov spectrum of a model of two-dimensional turbulence

Abstract

A scalar model of two-dimensional Navier-Stokes turbulence first proposed by Gledzer is shown to realize the power law E(k)\ensuremath{\sim}${k}^{\mathrm{\ensuremath{-}}3}$ in its chaotic state, which is found to obey the same scaling law as that of the enstrophy-cascade theory. All the Lyapunov exponents are calculated for several values of viscosity, and they are found to have a scaling property in the interior of attractor. The calculated distribution function of the Lyapunov exponents appears to have a singularity at null Lyapunov exponent.