Nerli, A.; Camarri, S.; Salvetti, M. V. A conditional stability criterion based on generalized energies. (English) Zbl 1114.76022 J. Fluid Mech. 581, 277-286 (2007). Summary: An energy criterion for conditional stability is proposed, based on the definition of generalized energies, obtained through a perturbation of the classical \(L^{2}\) (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. We also discuss the effects of different choices in the construction of generalized energy on the prediction of critical amplitude threshold in the subcritical regime. Cited in 2 Documents MSC: 76E05 Parallel shear flows in hydrodynamic stability Keywords:L(2) kinetic energy; critical amplitude threshold PDFBibTeX XMLCite \textit{A. Nerli} et al., J. Fluid Mech. 581, 277--286 (2007; Zbl 1114.76022) Full Text: DOI