Further generalized energies for the application of an energy criterion of conditional stability

A previously proposed energy criterion for predicting the conditional stability of incompressible flows, which is based on properly defined generalized energies, is considered. An extension of the procedure for the construction of generalized energies is proposed here, leading to the definition of a broader class of generalized energies which may depend on several free parameters. The optimal free parameters are computed by searching the value for which the energetic stability criterion predicts the maximum critical L 2 energy. The capabilities of the resulting stability criterion are appraised through the application to low-dimensional non-linear quadratic models, mimicking the subcritical instability behavior of particular incompressible flows.