The Group Velocity and Green's Function for Rossby waves

Here we show that the group velocity diagram of Rossby waves is an ellipse whose focus lies at the origin. The simple result supplements the Longuet-Higgins (1964) interpretation in which the wave normal curve is an offset circle, in elucidating the propagation properties of Rossby waves. The stationary phase method demonstrates that the radiation patterns generated by a time harmonic spatially compact source consists of two sets of hyperbolae exhibiting westward "Mach-Froude"-like cones, in a manner analogous to the generation of capillary-gravity waves by a moving object on the surface of water. These results are confirmed by the Green's function for the system which consists of a westward propagating wave superimposed on the Hankel function of zero order, appropriate to the 2-D Helmholtz equation