Gourjii A. Chaotic advection of fluid by vortex flows

The phenomenon of chaotic advection of ideal and viscous fluids in the velocity field of localized and distributed vortex structures in an unbounded space, the internal and external flows is comprehensively studied in work. The problem of description of the regular and chaotic advection of selected fluid by the vortex flows is decided. The analytical solution of new classes of plane and axisymmetrical problems of vortex dynamics are found: the problem of an interaction of the system of point vortices with a wedge-shaped surface using the conformal transformation method, the problem of an interaction of vortex rings inside an infinite cylinder filled with an ideal uncompressible fluid, the problem of motion of viscid uncompressible fluid in the Stocks approaching inside a rectangular cavity with the moving boundary segments with the advanced reduction method.