ON THE ROLE OF LINEAR MECHANISMS IN TRANSITION TO TURBULENCE

Recent work has shown that linear mechanisms can lead to substantial t ransient growth in the energy of small disturbances in incompressible hows even when the Reynolds number is below the critical value predict ed by linear stability (eigenvalue) analysis. In this note it is shown that linear growth mechanisms are necessary for transition in hows go verned by the incompressible Navier-Stokes equations and that non-norm ality of the linearized Navier-Stokes operator is a necessary conditio n for subcritical transition.