Vortex rings in an unbounded heavy fluid with piecewise-constant density
The principal models for the theoretical analysis of vortex rings are Hill's spherical vortex and Maxwell's toroidal vortex. It is proposed to investigate a mathematical model for vortex rings which leads to flows more closely resembling those observed experimentally. This model describes the evolution of a bounded homogeneous heavy fluid mass in an unbounded homogeneous heavy fluid medium (a fluid ''spot'' in a fluid medium). The density of the spot may differ from that of the medium. The fluid is assumed to be ideal and incompressible; its components inside and outside the spot are nonmiscible, so that the spot and the surrounding medium are separated by a fluid boundary; diffusion across the boundary and surface tension are neglected. We will consider flows in which the boundary of the spot is a surface of discontinuity of the velocity component tangential to it.
unbounded homogeneous heavy fluid medium
scientific article; zbMATH DE number 3970293