| Abstract: | The article discusses the two-dimensional flow of an incompressible liquid between two infinitely close concentric spheres, due to an initial distribution of the vorticity differing from zero. The concept of point singularities (vortices, sources, and sinks) at a sphere is introduced. Equations of motion are obtained for point vortices, as well as invariants of the motion, known for the plane case [1]. The simplest case of the mutual motion of a pair of vortices is considered. Equations are obtained for the motion of point vortices at a rotating sphere. Integral invariants for the continuous distribution of the vorticity are obtained, having the dynamic sense of the total kinetic energy and the momentum of the liquid at the sphere. The effect of the topology of the sphere on the dynamics of the vorticity is noted, and a comparison is made with the plane case.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 57–65, November–December, 1977. |
