Advection of a vortex pair atmosphere in a velocity field of point vortices*

Abstract

Two-dimensional inviscid flows governed by a vortex pair in the presence of another point vortex or vortex pair on an unbounded plane are considered analytically and via numerical simulations. For some integrable cases of vortex motion, the stirring process of a fixed closed volume of surrounding fluid (‘‘atmosphere’’) initially trapped by vortex pair is investigated. Using the full classification of vortex movement types, it is shown that for all cases of vortex pair direct and exchange scattering the stirring process is regular. Some internal atmosphere regions conserve their existence and form after vortex interaction, resulting a ‘‘solitonlike’’ behavior. For general cases of vortex pair mutual trapping, the stirring process is chaotic. For limiting cases of vortex motions, the fluid particles reveal a regular behavior. A simple model for the qualitative description of recent experiments on vortex dipoles interaction is discussed. Although clearly an extreme idealization, the model appears to shed some light on what to expect in laboratory experiments.