Nonlinear Nonmodal Stability Theory

Abstract

This review discusses a recently developed optimization technique for analyzing the nonlinear stability of a flow state. It is based on a nonlinear extension of nonmodal analysis and, in its simplest form, consists of finding the disturbance to the flow state of a given amplitude that experiences the largest energy growth at a certain time later. When coupled with a search over the disturbance amplitude, this can reveal the disturbance of least amplitude—called the minimal seed—for transition to another state such as turbulence. The approach bridges the theoretical gap between (linear) nonmodal theory and the (nonlinear) dynamical systems approach to fluid flows by allowing one to explore phase space at a finite distance from the reference flow state. Various ongoing and potential applications of the technique are discussed.