  It is shown for the first time that only an antipodal vortex pair (APV) is
the elementary singular vortex object on the sphere compatible with the
hydrodynamic equations. The exact weak solution of the absolute vorticity
equation on the rotating sphere is obtained in the form of Hamiltonian dynamic
system for interacting APVs. This is the first model describing interaction of
Barrett vortices corresponding to atmospheric centers of action (ACA). In
particular, new steady-state conditions for N=2 are obtained. These analytical
conditions are used for the analysis of coupled cyclone-anticyclone ACAs over
oceans in the Northern Hemisphere.
