Abstract
A general exact weak solution to the non-linear equation of the conservation of the absolute vorticity in a thin layer of an incompressible medium on a rotating sphere is proposed. It takes into account the helicity of the point vortices and the non-uniformity of the depth of the layer. This is used to develop a model of the observed interactions of spiral atmospheric vortices. The fusion of two-point helical vortices (HVs) on the rotating sphere is considered. We also analyze the prognostic applicability of the dynamics of the HVs for modeling the abrupt changes observed in the trajectories of tropical cyclones and their landfall in comparison with the traditional approach. The analytical condition for chiral symmetry violation related to the direction of the movement of the center of a helical cyclone is obtained.
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