Discovering Coherent Structures Using Local Causal States*

Coherent structures were introduced in the study of fluid dynamics and were initially defined as regions characterized by high levels of coherent vorticity, i.e. regions where instantaneously space and phase correlated vorticity are high. In a more general spatiotemporal setting, coherent structures can be seen as localized broken symmetries which persist in time. Building off the computational mechanics framework, which integrates tools from computation and information theory to capture pattern and structure in nonlinear dynamical systems, we introduce a theory of coherent structures, in the more general sense. Central to computational mechanics is the causal equivalence relation, and a local spatiotemporal generalization of it is used to construct the local causal states, which are utilized to uncover a system's spatiotemporal symmetries. Coherent structures are then identified as persistent, localized deviations from these symmetries. We illustrate how novel patterns and structures can be discovered in cellular automata and outline the path from them to laminar, transitional and turbulent flows.