Using covariant Lyapunov vectors to explore chaotic dynamics with long-range spatial coupling

Exciting progress has been made using powerful ideas from dynamical systems theory to describe chaotic fluid dynamics as a trajectory through an infinite dimensional state space. The covariant Lyapunov vectors (CLVs) describe the magnitude and direction of the growth or decay of small perturbations about the nonlinear trajectory which can provide new physical insights. An important aspect of fluid systems that is often not present in the models used to explore CLVs is the local and long range spatial coupling. For example, the nonlinear convective term in fluid systems can lead to large-scale mean flows in addition to localized coupling. Computing the CLVs for a fluid system is computationally intensive which makes it difficult to study fundamental questions such as this. Instead, we use 1D and 2D lattices of coupled maps with local and long-range spatial couplings which are chosen with fluid systems in mind. We explore these dynamics using the CLVs to gain new insights relevant to chaotic fluid dynamics.