Local Versus Global Concepts in Hydrodynamic Stability TheoryReport as inadecuate

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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.

Author: Olivier Dauchot Paul Manneville

Source: https://hal.archives-ouvertes.fr/


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