Local Versus Global Concepts in Hydrodynamic Stability Theory

(Received 25 July 1996, received in final form 3 October 1996, accepted 25 October 1996)

Abstract
Linear and nonlinear issues in the problem of the subcritical transition to turbulence are examined on the basis of a full phase-space analysis of a simplified model that mimics hydrodynamics governed by the Navier-Stokes equations. The simplicity of the model, which involves only two variables and displays both non-normal linear terms and energy conserving nonlinear terms, allows us to perform a complete study. This study strongly suggests to take with care conclusions extrapolated from "local" arguments deriving from linear stability theory, since actual stability boundaries can be decided only from the knowledge of the relevant attraction basins, which is "global" in essence.