The description of fluid behavior by coherent structures

Abstract

The goal of many scientific investigations of fluid systems is the accurate description of the dominant fluid behavior. This has commonly been accomplished by computing the stability of the flow, expressed in coherent structures known as modes. The local support of the modes and their temporal or spatial evolution provide critical information about the prevalent dynamical features of the flow. The computation of modes for simple geometries with multiple homogeneous coordinate directions involves the discretization of the linearized equations and the direct solution of the resulting eigenvalue problem. For even moderately complex geometries this procedure becomes prohibitively expensive. Instead, iterative techniques to extract the dispersion relation from numerical simulations are used to compute global modes for complex flow configurations [2, 10]. For flows that are dominated by multiphysics processes (such as the presence of shear and acoustic phenomena) additional transformations may be necessary to access various parts of the spectrum by iterative techniques [4].