Using covariant Lyapunov vectors to investigate the role of spatial interactions in chaotic fluid systems

The chaotic dynamics of many fluid systems involve the complex interplay of short and long-range spatial interactions. We conduct a broad study using covariant Lyapunov vectors (CLVs) to quantify the influence of diffusive and convective spatial couplings on the spatiotemporal chaos of several model systems of relevance to fluid dynamics. Using coupled map lattices we quantify the degree of hyperbolicity, tangent space decomposition, and the localization of the CLVs for a wide range of conditions. For diffusively coupled maps we find that the leading Lyapunov exponent, fractal dimension, and localization of the leading CLV are non-monotonic with increasing diffusion strength. We find that adding convection to a lattice of diffusively coupled maps increases the leading Lyapunov exponent and fractal dimension. We explore how a convective coupling affects the tangent space decomposition and the localization of the CLVs. We quantitatively connect the CLVs with the influence of the spatial couplings where possible. We use the physical insights gained by our study of large lattices of coupled maps to provide guidance for an exploration of chaotic fluid motion using partial differential equations.