  A general exact weak solution to the nonlinear 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.
