Kulik K. Localized vortical objects in two-dimensional hydrodynamics

This thesis is devoted to searching of new exact localized solutions of the two-dimensional equations of ideal hydrodynamics. The solutions found significantly expand the set of quasiparticles, and respectively, the classes of hydrodynamic flows induced by such expanded set of localized vortices. It is proved, that the problem of interaction of founded localized vortex objects - point dipole type vortices, with each other and with known point vortices, allows exact description for a closed finite system. So new vortical objects can be used as hydrodynamic quasiparticles. Simplest cases of interaction of a small number of localized vortices are investi-gated, exactly integrable cases are marked. A complete analysis of possible modes of evolution is carried, criteria for their implementation is found. The case of influence of potential wave on the movement of a point vortex, located at the impenetratable solid boundary is considered. We construct the evolution equation for such system for the cases of the vortex motion near the wall in the field of incident and reflected waves and in the case of wave propagation parallel to the wall. The solutions of equations of motion are obtained, qualitative analysis is done, and as a result we construct typical phase portraits and analyze all possible modes of movement of a point vortex.