We consider flow patterns for exact solutions of the (3 + 1)-dimensional nonlinear nondissipative quasi-geostrophic potential vorticity equation, also known as the Charney–Obukhov equation, for Rossby vortices in the ocean propagating along the zonal direction with a constant velocity V. The following results are obtained: (a) For a given value of V the vortices are localized in the vicinity of one or several planes \(z = z_{ci} ,_{{}} i = 1,_{{}} 2,_{{}} ..._{{}} L\) , where \(0 \le z_{ci} \le H\) and L is the number of such planes, which are determined by the zonal flow included in the exact solution of the Charney-Obukhov equation; (b) Heton-like model of a baroclinic dipole, whose vortices are localized in two horizontal XY-planes, located one above the other. The heton can propagate both to the west and to the east with a velocity significantly exceeding the Rossby wave speed, this heton model is realized both in cylindrically symmetric solutions and in spherically symmetric solutions; (c) We consider a non-central “collision” of vortex monopoles and dipoles localized in the horizontal XY-plane, depending on their polarization and orientation in space. The “collision” of vortices is described as a sequence of stationary states, each of which is an exact solution to the Charney-Obukhov equation. The result of a non-central “collision”: two unipolar vortices merge, two oppositely polarized vortices form a dipole, two oppositely directed dipoles form a tripole upon “collision”.
