Applications of resolvent analysis in fluid mechanics

Abstract

These notes are intended to provide a description of some aspects of applications of resolvent analysis in fluid mechanics. They are targeted at students beginning research in this or related area, with the goal of providing a bridge between the generic linear algebra of textbooks and the archival journal articles implementing these techniques. With regards to mathematical techniques, a working understanding of fundamental concepts of linear algebra, and in particular the singular value decomposition, as well a familiarity with the goals underlying modal analysis are assumed. Requiring more background in fluid mechanics, the reader will already be familiar with the formulation of resolvent analysis from the Navier-Stokes equations. These notes outline approaches to gaining insight into the characteristics of fluid system by viewing the governing equations in terms of linear dynamics driven by endogenous (nonlinear) or exogenous forcing. Such systems may exhibit laminar or turbulent behavior, may be forced or unforced, and may perhaps be under the influence of control actuation. Physical interpretation of resolvent modes, the importance of mode weights and techniques for data reconstruction, and the incorporation of control into the analysis are covered.

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