Emergence of nonuniform V-states by synchronization

It is shown that a family of nonuniform, m-fold symmetric rotating vortex structures in two dimensions (nonuniform V-states) can emerge in both free and bounded space by subjecting an axisymmetric vortex with a sharp vorticity edge to external rotation and weak strain of appropriate symmetry. The phenomenon is due to nonlinear synchronization (autoresonance) in the system, as the vorticity distribution of the vortex structure self-adjusts to phase lock with slowly varying external rotation. The synchronization is induced by passage through resonance with the isolated eigenmode of the linearized problem, provided the external strain rate is above a threshold. Synchronized, m = 2 nonuniform V -states remain stable after the external strain is switched off. Free m = 3 and 4 states, in contrast, are destroyed via three-wave decay at later times. The negative feedback approach is proposed to stabilize this instability.