The objective of this article is to review some developments in the use of adjoint equations in
hydrodynamic stability theory. Adjoint-based sensitivity analysis finds both analytical and …

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 …

The formation and amplification of streamwise velocity perturbations induced by cross-
stream disturbances is ubiquitous in shear flows. This disturbance growth mechanism, so …

We extend linear input/output (resolvent) analysis to take into account nonlinear triadic
interactions by considering a finite number of harmonics in the frequency domain using the …

This article presents techniques for the analysis of fluid systems. It adopts an optimization-
based point of view, formulating common concepts such as stability and receptivity in terms …

This article introduces and reviews recent work using a simple optimization technique for
analysing the nonlinear stability of a state in a dynamical system. The technique can be …

Multistability is a common phenomenon which naturally occurs in complex networks. Often
one of the coexisting stable states can be identified as being the desired one for a particular …

We propose a general strategy for determining the minimal finite amplitude disturbance that
triggers transition to turbulence in shear flows. This involves constructing a variational …

We consider the nonlinear optimisation of the mixing of a passive scalar, initially arranged in
two layers, in a two-dimensional plane Poiseuille flow at finite Reynolds and Péclet …

Subcritical transition to turbulence requires finite-amplitude perturbations. Using a nonlinear
optimisation technique in a periodic computational domain, we identify the perturbations of …