Energy Amplification of Steady Disturbances in Growing Boundary Layers

Abstract

The importance and necessity of linear growth mechanisms in transition to turbulence at subcritical Reynolds numbers has recently been recognized [1]. In the absence of exponentially growing linear modes, transiently growing disturbances can provide the amplification of disturbance energy that ultimately may result in turbulent fluid motion. This transient growth is due to the non-orthogonal structure of the linear eigenfunction which, in turn, is a consequence of the non-selfadjoint nature of the linearized Navier-Stokes equations. Many flows have been analyzed with regards to their transient amplification potential. Most of the analyses have concentrated on the temporal stability problem, and all of them have assumed a parallel mean flow which substantially simplifies the computations (see [2] for a review).