Weak nonlinearity for strong non-normality

We propose a theoretical approach to derive amplitude equations governing the weakly nonlinear evolution of nonnormal dynamical systems when they experience transient growth or respond harmonic forcing. This reconciles nonmodal nature these mechanisms and need for center manifold project leading-order dynamics. Under hypothesis strong nonnormality, we take advantage fact that small operator perturbations suffice make inverse resolvent propagator singular, which encompass in multiple-scale asymptotic expansion. The methodology is outlined generic system, four application cases highlight common hydrodynamics: streamwise convective amplification flow past backward-facing step, Orr lift-up plane Poiseuille flow.