Collective Interaction of Vortices in Two-Dimensional Shear Layers

A phenomenological diagram is presented to explain the interaction between a fundamental wave and its sub-harmonic wave in 2D shear layers based on linear stability theory. These diagrams indicate that there are only four classes of subharmonic interactions, which are symmetric collective interaction, the first class of asymmetric collective interaction, the second class of collective interaction and tearing. Each of them can be determined uniquely by a couple of parameters m and p, where m is the ratio of wavenumber and p is a parameter of phase difference between the fundamental wave and its subharmonic wave. For each class of subharmonic interactions, a couple of parameters m and p have been deduced from the phenomenological diagram. We think that they are significant for accurate flow control of shear layers.