Measuring spatial coupling in inhomogeneous dynamical systems

We propose coherence as a tool to quantify spatiotemporal dynamics, in particular, in spatially inhomogeneous dynamical systems. We demonstrate coherence to be an appropriate measure of predictability and, hence, spatial coupling in nonlinear systems, using analysis and via experimental results from a circular jet flow. Coherence measurements reveal sizable regions of strong spatial coupling in this spatially developing open flow, in contrast to much smaller coupling regions indicated by conventional correlation. Decaying coherence, indicating spatiotemporal dynamics, is also found in the jet, and possible physical mechanisms are discussed. In addition, the causes for coherence decay are explained analytically.