On the Lyapunov spectrum of an ensemble of vortices

Abstract

In space- and time-dependent dynamical systems, Lyapunov vectors correspond to spatio-temporal patterns of instability. These patterns can be used to parse and predict the interaction and break-down of coherent structures. The computation of Lyapunov vectors, however, is computationally demanding and has hitherto been restricted to systems with a comparatively low attractor dimension. We aim to study the dynamics of vortices in developed turbulence with an attractor dimension of order O(100). To this end, we compute the linear stability spectrum of an unstable periodic orbit embedded in the turbulent attractor and consider it a proxy for the Lyapunov spectrum. Along the periodic orbit at least 25 Lyapunov vectors can give the largest growth rate locally in time and space. We highlight one instance of a mutually induced instability of a vortex pair localized in the high-strain interstitial region.