Temporal intermittency in a shell model turbulence in terms of covariant Lyapunov vectors

Abstract

We study temporal intermittency in the GOY shell model of turbulence by using the covariant Lyapunov vectors (CLVs). We find that physical and isolated modes in Lyapunov modes proposed by Yang et al (2009 Phys. Rev. Lett. 102 074102) exist in the shell model turbulence. Furthermore, we analyze differences between burst and laminar periods in the turbulent attractor in terms of the CLVs. In particular, we study the burst and the laminar periods by using two kinds of dynamical quantities defined by the CLVs. One is a set of finite time Lyapunov exponents which correspond respectively to the CLVs. We find that the order of magnitudes of the finite time Lyapunov exponents in the burst period changes more frequently with time than in the laminar period. Moreover, we find that an effective dimension, defined by the number of Lyapunov modes of which the order of magnitude changes, in the burst period is higher than in the laminar period. The other quantity is an angle between the stable and the unstable manifolds along the turbulence attractor. We obtain the result that an orbit in the burst period passes near nonhyperbolic points more frequently than in the laminar period. From this result, we conjecture that the tangency structure of the stable and the unstable manifolds is related to the intermittency.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’.