  The paper is devoted to the group analysis of equations of motion of
two-dimensional uniformly stratified rotating fluids used as a basic model in
geophysical fluid dynamics. It is shown that the nonlinear equations in
question have a remarkable property to be self-adjoint.
  This property is crucial for constructing conservation laws provided in the
present paper. Invariant solutions are constructed using certain symmetries.
The invariant solutions are used for defining internal wave beams.
