The description of coherent features of fluid flow is essential to our understanding of fluid-dynamical and transport processes. A method is introduced that is able to extract dynamic information from flow fields that are either generated by a (direct) numerical simulation or visualized/measured in a physical experiment. The extracted dynamic modes, which can be interpreted as a generalization of global stability modes, can be used to describe the underlying physical mechanisms captured in the data sequence or to project large-scale problems onto a dynamical system of significantly fewer degrees of freedom. The concentration on subdomains of the flow field where relevant dynamics is expected allows the dissection of a complex flow into regions of localized instability phenomena and further illustrates the flexibility of the method, as does the description of the dynamics within a spatial framework. Demonstrations of the method are presented consisting of a plane channel flow, flow over a two-dimensional cavity, wake flow behind a flexible membrane and a jet passing between two cylinders. The accurate description of the disturbance behaviour in complex geometries poses a great challenge to numerical simulations and physical experiments, as well as to the computational algorithms that extract and quantify this behaviour. At the same time, many industrial applications, such as flow in a combustion chamber, could greatly benefit from a more thorough understanding of the underlying transition and instability mechanisms. Global stability analyses for flows in complex geometries are becoming more commonplace, but the resulting large stability matrix sizes have put considerable strain on computational resources. Direct methods, the method of choice for simple problems, become prohibitively expensive, and iterative schemes have thus to be employed to extract the global stability modes. The Arnoldi scheme (see Edwards et al. 1994) has been particularly successful in this respect. It is based on an approximation of the high-dimensional system matrix by projecting it onto a lower-dimensional Krylov subspace. In this way, the dominant eigenvalues (and corresponding eigenvectors) of the full system can be computed rather efficiently. Convergence can be improved in various ways by shifting, mapping, restarting, locking and purging techniques (Lehoucq & Scott 1997) , but in most cases this is accomplished at the expense of computational efficiency due to the necessity of additional matrix inversions.
An approximation of the Koopman operator can be computed via the Dynamic Mode Decomposition (DMD) algorithm REF .
Dynamic mode decomposition of numerical and experimental data
Journal of Fluid Mechanics
Physics