Balanced dynamics in the Tropics

For the shallow-water equations on an equatorial beta plane, the properties of low-frequency Rossby waves and (mixed) Rossby-gravity waves are investigated. It is shown that in the low-frequency limit the horizontal divergence of these solutions is zero and their geopotential satisfies = f, where f = y is the Coriolis parameter and is the stream function of the non-divergent velocity field. This type of balance is rather different from the geostrophic balance satisfied by Kelvin waves. It can be used to formulate a balanced potential vorticity equation in the single variable that, while filtering out Kelvin waves and inertia-gravity waves, exactly reproduces Rossby waves and Rossby-gravity waves in the low-frequency limit.