The occurrence of Yanai waves in constrained geometries

The destabilization of Yanai, or mixed Rossby-gravity, waves has been presented as a possible mechanism for the formation of both the deep equatorial jet and the horizontal alternating zonal jet structures. However, the analytical Yanai wave solutions are in the context of an infinite equatorial geometry, unlike the ocean basins which are clearly constrained. To explore this issue, we begin by presenting the parametric formation of mixed Rossby-gravity waves as the domain transits from a thin equatorial channel into an unbounded system. The formation is shown to exhibit a two-stage behaviour: in large enough channels the classical Yanai wave solutions are recovered but when the domain is sufficiently constrained they can no longer exist. We discuss the length scales for which the Yanai waves occur and how their wave characteristics are altered by the geometry of the domain. Furthermore, the stability of Yanai waves at various stages of parametric formation is analyzed numerically and possible implications on jet formations in small equatorial bodies are discussed.