Midlatitude Waves

Free-wave solutions for a mode of the LCS model are obtained that are valid at midlatitudes (away from the equator). The dispersion relation for Rossby waves is derived when the Coriolis parameter f is constant, and under a realistic restriction it is shown to be valid even when f varies. The concepts of critical frequency $$\sigma _{cr}$$ and critical latitude $$\theta _{cr}$$ are introduced. Kelvin waves are found along both zonal and meridional coasts. Along a meridional coast and when f varies, Kelvin waves exist only poleward of $$\theta _{cr}$$ ( $$\beta $$ -plane Kelvin waves); as for f-plane Kelvin waves, $$\beta $$ -plane Kelvin waves decay offshore, but they also have a weak westward propagation. Equatorward of $$\theta _{cr}$$ , Rossby waves radiate offshore along ray paths that are directed meridionally, as well as westward. Similar properties exist even if the coast if the coast is slanted (i.e., not directed precisely north-south), the major difference being that the value of $$\theta _{cr}$$ is decreased.