Local Versus Global Concepts in Hydrodynamic Stability Theory

Linear and nonlinear issues in the problem of the subcritical transition to turbu- lence are examined on the basis of a full phase-space analysis of a simplified model that mimics hydrodynanJics 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 the- ory, since actual stability boundaries can be decided only from the knowledge of the relevant attraction basins, which is "global" in essence.