  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 to harmonic forcing. This approach reconciles the
nonmodal nature of these growth mechanisms and the need for a center manifold
to project the leading-order dynamics. Under the hypothesis of strong
nonnormality, 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 nonnormal mechanisms in hydrodynamics: the streamwise
convective nonnormal amplification in the flow past a backward-facing step, and
the Orr and lift-up mechanisms in the plane Poiseuille flow.
