Phenomenological model and numerical analysis of collective interaction of primary vortex

A phenomenological model of collective interaction of primary vortex of mixing layers is built on the linear stability theory in this paper. The model can be used to determine the influence of the phase shift of the subharmonic disturbance wave on the nonlinear evolving process of the primary vortex. The results indicate that the evolving process of the primary vortex can be classified as tearing phenomenon, symmetric collective interaction and asymmetrical collective interaction. The tearing phenomenon and symmetric collective interaction are special phenomena and occur only at particular phase shift points, while the asymmetrical collective interaction is common and proceed through pairing one by one.