Ducimetière, Yves-MarieBoujo, EdouardGallaire, François2022-08-312022-08-312022-08-31202210.1017/jfm.2022.664https://infoscience.epfl.ch/handle/20.500.14299/190457We propose a theoretical approach to derive amplitude equations governing the weakly nonlinear evolution of non-normal dynamical systems, when they experience transient growth or respond to harmonic forcing. This approach reconciles the non-modal nature of these growth mechanisms and the need for a centre manifold to project the leading-order dynamics. Under the hypothesis of strong non-normality, we take advantage of the fact that small operator perturbations suffice to make the inverse resolvent and the inverse propagator singular, which we encompass in a multiple-scale asymptotic expansion. The methodology is outlined for a generic nonlinear dynamical system, and four application cases highlight common non-normal mechanisms in hydrodynamics: the streamwise convective non-normal amplification in the flow past a backward-facing step, and the Orr and lift-up mechanisms in the plane Poiseuille flow.Nonlinear Dynamical SystemsInstabilitytext::journal::journal article::research article