PERTURBATION GROWTH IN SHEAR-FLOW EXHIBITS UNIVERSALITY

Disturbance structures that achieve maximum growth over a specified interval of time have recently been obtained for unbounded constant shear flow making use of closed-form solutions. Optimal perturbations have also been obtained for the canonical bounded shear flows, the Couette, and plane Poiseuille flows, using numerical solution of the linearized Navier-Stokes equations. In this note it is shown that these optimal perturbations have similar spectra and structure indicating an underlying universality of shear flow dynamics that is not revealed by traditional methods based on modal analysis.