kth_logo.gif

Article

Energy growth in viscous channel flows.

Authors: Reddy, S., Henningson, D.S.H.
Document Type: Article
Pubstate: Published
Journal: J. Fluid Mech.
Volume: 252   209-238
Year: 1993

Abstract

The authors study various aspects of this energy growth for two- and three-dimensional Poiseuille and Couette flows using energy methods, linear stability analysis, and a direct numerical procedure for computing the transient growth. They examine conditions for no energy growth, the dependence of the growth on the streamwise and spanwise wavenumbers, the time dependence of the growth, and the effects of degenerate eigenvalues. They show that the maximum transient growth behaves like O(R/sup 2/), where R is the Reynolds number. They derive conditions for no energy growth by applying the Hille-Yosida theorem to the governing linear operator and show that these conditions yield the same results as those derived by energy methods, which can be applied to perturbations of arbitrary amplitude. These results emphasize the fact that subcritical transition can occur for Poiseuille and Couette flows because the governing linear operator is non-normal.