Oscillating growth in convection dominated systems

In this work, the study of oscillating norm behavior in linear evolutionary systems is addressed. A link between the occurrence of oscillating patterns in the energy evolution of the solutions and the nonorthogonality of linear global modes is illustrated; moreover, a distinction between transient and asymptotic oscillations is made. The analysis carried out shows that special frequency signatures associated to transient oscillations can be explained by means of suitable ``synchronizations'' between global modes, and some frequency selection rules are also proposed. The physical importance of such oscillating behaviors is stressed by reconsidering the model for the linear stability of the falling liquid curtain studied by Schmid and Henningson and by considering different physical models arising in the context of the linearized formulation of some convection dominated systems over finite length domains.