Nonlinear Dynamics: Coherent Structures

Analytical and computational studies of hydrodynamic and reacting flows are extremely challenging, due in part to nonlinearities of the underlying systems, long-range coupling, and stochasticity. Recent developments in high-resolution, high frequency experimental data capture offer an alternative approach to extracting key features of such flows. However, this approach elicits new issues, including how noise and other external effects are to be delineated from dynamics.

We adapt dynamic mode decomposition to extract “robust constituents” of a flow from experimental data. The first step involves identifying “robust dynamic modes” which are those that persist in multiple, nominally identical realizations of the flow. Searching for common eigenvalues and eigenfunctions yields a selection of dynamic modes that form robust flow “constituents.” The delineation of dynamics and noise is recast as a differentiation of the flow into robust constituents and non-robust features. The methodology has been used to identify robust flow constituents in several classes of combustion and fluid flows. We will illustrate the approach through an analysis of experimental data from combustion flow past a v-shaped bluff body configuration.