An extended equatorial plane: linear spectrum and resonant triads

Abstract

The usual equatorial ߭plane supports a range of wave types, including trapped baroclinic Rossby waves, a Yanai wave and a Kelvin wave, which are known to be important in equatorial wave dynamics, both linear and nonlinear. Here, we extend this model to the whole sphere, using a Mercator projection, in which the Coriolis parameter is retained in full, but the metric coefficients are approximated by their values at the equator. We find that while the trapped baroclinic waves are preserved in this model, the barotropic waves are also trapped, with consequences for nonlinear resonant triad interactions.