An optimality condition on the minimum energy threshold in subcritical instabilities

Carlo Cossu (1)

1 LadHyX - Laboratoire d'hydrodynamique

For flows subject to subcritical instabilities the stability of the basic flow can be guaranteed only for perturbations of energy lower than a critical threshold d. The computation of this threshold for the Navier-Stokes equations is still out of reach. More surprisingly, this computation has not been attempted for low dimensional models of subcritical transition. In this Note guidelines are provided for the computation of the minimum energy threshold d and of the corresponding nonlinear optimal perturbations. In particular it is demonstrated that nonlinear optimal perturbations are constrained by the requirement that they must satisfy a local minimum condition. These results are applied to the analysis of four-dimensional models proposed in F. Waleffe, Phys. Fluids 7 (1995) and Phys. Fluids 9 (1997). To cite this article: C. Cossu, C. R. Mecanique 333 (2005). © 2005 Académie des sciences. Published by Elsevier SAS. All rights reserved.

Domains: Fluid mechanics [physics.class-ph]; Fluids mechanics [physics.class-ph]

Carlo Cossu. An optimality condition on the minimum energy threshold in subcritical instabilities. Comptes Rendus Mécanique, 2005, 333 (4), pp.331-336. ⟨10.1016/j.crme.2005.02.002⟩. ⟨hal-01023376⟩