Hostname: page-component-7b7567c8c-7pwfn Total loading time: 0 Render date: 2026-11-15T17:05:46.070Z Has data issue: false hasContentIssue false
  • English
  • Français

A conditional stability criterion based on generalized energies

Published online by Cambridge University Press:  22 May 2007

A. NERLI,
S. CAMARRI and
M. V. SALVETTI
A. NERLI
Affiliation:
Scuola Normale Superiore di Pisa, 56127 Pisa, Italy
S. CAMARRI
Affiliation:
Dipartimento di Ingegneria Aerospaziale, Università di Pisa, 56122 Pisa, Italy
M. V. SALVETTI
Affiliation:
Dipartimento di Ingegneria Aerospaziale, Università di Pisa, 56122 Pisa, Italy
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

An energy criterion for conditional stability is proposed, based on the definition of generalized energies, obtained through a perturbation of the classical L2 (kinetic) energy. This perturbation is such that the contribution of the linear term in the perturbation equation to the generalized energy time derivative is negative definite. A critical amplitude threshold is then obtained by imposing the monotonic decay of the generalized energy. The capabilities of the procedure are appraised through the application to three different low-dimensional models. The effects of different choices in the construction of the generalized energy on the prediction of the critical amplitude threshold in the subcritical regime are also discussed.

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 581 , 25 June 2007, pp. 277 - 286
Copyright
Copyright © Cambridge University Press 2007

References

REFERENCES

Baggett, J. S. & Trefethen, L. N. 1997 Low-dimensional models of subcritical transition to turbulence. Phys. Fluids. 9, 1043–1053.CrossRefGoogle Scholar
Cossu, C. 2004 On the minimum threshold energy and the nonlinearly-optimal perturbations in subcritical instabilities. IUTAM Symp. on Non-Uniqueness of Solutions to the Navier-Stokes Equations and their Connection with Laminar-Turbulent Transition, Bristol, UK. Kluwer.Google Scholar
Cossu, C. 2005 An optimality condition on the minimum energy threshold in subcritical instabilities. C. R. Méc. 333, 331–336.CrossRefGoogle Scholar
Dauchot, O. & Manneville, P. 1997 Local versus global concepts in hydrodynamic stability theory. J. Phys. II Paris. 7, 371–389.Google Scholar
Joseph, D. D. 1976 Stability of Fluid Motions. Springer.Google Scholar
Kaiser, R. & Mulone, G. 2005 A note on nonlinear stability of plane parallel shear flows. J. Math. Anal. Appl. 302, 543–556.CrossRefGoogle Scholar
Straughan, B. 2004 The Energy Method, Stability, and Non linear Convection, 2nd edn. Springer.CrossRefGoogle Scholar
Waleffe, F. 1995 Transition in shear flows. Nonlinear normality versus non-normal linearity. Phys. Fluids. 7, 3060–3066.CrossRefGoogle Scholar
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids. 9, 883–900.CrossRefGoogle Scholar