Characterization of intermittency at the onset of turbulence in the forced and damped nonlinear Schrödinger equation

In this paper we characterized intermittent transitions from temporal ă chaos to turbulence in the forced and damped nonlinear Schrodinger ă equation. We demonstrate using finite time Lyapunov exponents that ă during the transition a fraction of unstable periodic orbits embedded in ă a low dimensional chaotic attractor loses transversal stability, in a ă way that nearby trajectories are expelled away from its vicinity (a ă mechanism referred to as intermittency induced by Unstable Dimension ă Variability). During the transition, an appropriate decomposition of the ă Fourier phase space into transversal and longitudinal modes is ă performed. The analysis of modes dynamics sheds new light in the ă understanding of intermittency in spatially extended dynamical systems. ă Subsequently a perturbation is applied to the system in order to control ă the intermittent extreme events and reduce their occurrence. (C) 2016 ă Elsevier B.V. All rights reserved.