One Partially Invariant Solution of Hydrodynamic Equations for the Atmosphere

The hydrodynamic equations for the atmosphere in $f$-plane approximation admit an infinite-dimensional Lie group of transformations obtained by L. V. Ovsyannikov in 1967. A partially invariant solution of these equations which possesses functional arbitrariness is analysed in this paper. Finding a solution is reduced to the Hopf equations integration and finite formulae.