On the role of linear mechanisms in transition to turbulence

Abstract

Recent work has shown that linear mechanisms can lead to substantial transient growth in the energy of small disturbances in incompressible flows even when the Reynolds number is below the critical value predicted by linear stability (eigenvalue) analysis. In this note it is shown that linear growth mechanisms are necessary for transition in flows governed by the incompressible Navier–Stokes equations and that non-normality of the linearized Navier–Stokes operator is a necessary condition for subcritical transition.