Evolution of mixed Rossby gravity waves

A Green's function is derived, which can be used to study and predict the evolution of the velocity and pressure fields associated with the mixed Rossby gravity wave component of the totality of motions due to forcing on an equatorial beta plane. Initial value problems can also be solved with the aid of the Green's function. Since energy associated with the Rossby gravity mode always travels east, the Green's function can be employed to predict what signal should arrive to the east of a given location if the time history of the fields are known at that position. Various simple analytical examples are discussed. A numerical ocean general circulation model is used to demonstrate the usefulness of the Green's function formalism.