Nonlinear nonmodal stability theory. (English) Zbl 1384.76022

Kerswell, R. R.

Davis, Stephen H. (ed.) et al., Annual review of fluid mechanics. Vol. 50. Palo Alto, CA: Annual Reviews (ISBN 978-0-8243-0750-9/hbk). Annual Review of Fluid Mechanics 50, 319-345 (2018).

Summary: 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.
For the entire collection see [Zbl 1381.76015].

MSC:

76E30	Nonlinear effects in hydrodynamic stability
76F06	Transition to turbulence
76-02	Research exposition (monographs, survey articles) pertaining to fluid mechanics

Keywords:

transition; optimization; energy growth; nonlinear stability