The dynamics of fluid particles in the vicinity of a self-propagating vortex pair, embedded in a nonstationary shear flow, is studied. When the shear flow is steady, the vicinity of the pair, which is called as a vortex atmosphere, consists of closed stream-lines, which coincide with fluid particlesʼ trajectories. When the shear flow is nonstationary, the trajectoriesʼ behaviour changes drastically, then chaotic advection occurs. It is shown in the Letter that the vortex pair propagation velocity varies with the parameters (amplitude, and frequency) of the nonstationary shear flow. It is demonstrated, that changing of the mean velocity leads to changing of the size of the atmosphere. ► A three-layered model of an inviscid incompressible geophysical flow is formulated. ► A vortex pair is studied in the middle layer when a periodic shear flow is superimposed. ► Dynamics of fluid particles inside the vortex atmosphere of the pair on it is studied. ► When the external flow is nonstationary, then chaotic advection of fluid particles emerges. ► Vortex pairʼs mean velocity of self-propelling changes depending on amplitude and frequency.

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