Three-dimensional vortex flow in a closed volume and some anomalous phenomena in the Earth's atmosphere

The possibilities of the formation and characteristics of a special type of stationary concentrated vortices $\nabla \times \mathbf{u} = k\mathbf{u}$ are studied with respect to the Earth's atmosphere. A generalization of this type of vortices to a spherical coordinate system is presented, belonging to the class of Gromeki–Beltrami, N.E. Zhukovsky, and S.G. Chefranov flows. Two types of new solutions to the problem of a concentrated vortex with two and three velocity vector components are constructed: $(1)$ the centers of the Cartesian and spherical coordinate systems coincide; $(2)$ the spherical vortex is located above a solid surface. The distributions of vector fields of velocities and pressure in a concentrated vortex are found. This solution expands the problem of a concentrated vortex in a cylindrical coordinate system studied previously by the authors. The influence of the thickness of the spherical layer on the change in flow characteristics is analyzed. The use of the obtained characteristics of concentrated vortices to interpret a number of observed anomalous phenomena in the atmosphere, such as UFOs and ball lightning, is discussed, the explanation of frequently involves mechanisms that lie beyond the boundaries of modern physics.