We present an approach combining temporal dynamical systems methods with newly proposed spatial coupling measures – namely, coherence and cross-bicoherence – to identify and quantitatively describe low-dimensional dynamics in transitional open flows. The approach is used to describe a forced mixing layer as a low-dimensional temporal dynamical system and interpret its transitional vortex dynamics.
Experiments were performed in an initially laminar plane mixing layer inside an anechoic chamber using forcing of the fundamental instability only; the forcing frequency and amplitude are used as control parameters. Dynamical invariants calculated show that vortex roll-up and the feedback-driven first two pairing dynamics are well-described by one periodic and at least two low-dimensional chaotic attractors; a phase diagram delineating such dynamical states in the control parameter space is presented. The large spatial extents of these feedback-sustained states (verified using coherence and cross-bicoherence), spanning many instability wavelengths downstream, indicate spatial coupling; feedback has also been experimentally verified. At a fixed forcing frequency, as the forcing amplitude is decreased, the spatially coupled, periodic second pairing dynamics becomes chaotic and spatiotemporal (inferred from decay of coherence and cross-bicoherence); the dynamics in the domain that includes the first pairing, however, remains temporal. This loss of spatial coupling is accompanied by a sudden increase in the attractor dimension, and suggests spatiotemporal chaos. The combination of dynamical systems theory and spatial measures seems to be a promising approach to probe spatiotemporal dynamics in other open flows as well.