Passive scalar advection in the vicinity of two point vortices in a deformation flow

The dynamics of passive fluid particles in the vicinity of two point vortices with arbitrary intensities, embedded in a steady external deformation flow, is studied. The motion of passive fluid particles is described by a nonintegrable 1.5 degrees of freedom dynamical system. Though the external flow is stationary, the additional half degree of freedom appears because the vortices’ motion about their stationary positions is periodic. Then, this periodic motion plays the role of a periodic perturbation for the system describing the passive particle dynamics. Therefore, chaotic advection of passive fluid particles in the vicinity of these two vortices can occur. If the vortices, however, are situated at their stationary positions, they become motionless, and the dynamical system describing the passive particles’ dynamics is also stationary. In the case of motionless vortices, a classification of the phase portraits of the passive particle motion is conducted by analyzing the number of critical points. When the vortices do not lie at their stationary position, the system becomes nonstationary. In this case, the existence of impenetrable transport barriers for chaotic advection is shown. These barriers are destroyed when stochastic layers merge; these layers widen as the deviation of the vortex position from the stationary points, increases. The efficiency of chaotization is analyzed by means of Poincaré sections and accumulated Lyapunov exponents.