Linear stability is a fundamental tool used in fluid dynamics to assess whether small disturbances grow or decay. However, it doesn’t always tell the full story. In non-normal systems, perturbations can undergo substantial transient growth even when the system is linearly stable. Understanding whether this amplification can trigger a transition, however, requires analysing the interplay between non-normality and nonlinearity, which remains a significant challenge.
In this talk, I will introduce the role of non-normality in fluid flows and present a new asymptotic framework for analysing the weakly nonlinear dynamics arising from large non-normal amplification. I will illustrate the approach for a model ODE problem and two-dimensional shear flow, showing that the obtained reduced equations capture subcritical transitions driven by forcing and varied initial conditions.