Equatorially trapped waves in a barotropic-baroclinic background shear flow

The equatorial atmosphere harbors a large spectrum of waves that are trapped near and travel along the equator. These equatorially trapped waves interact nonlinearly with each other and with the extratropical waves. However, the tropical-extratropical interactions are poorly understood. One of the factor which can highly affect the equatorial waves is the background state. One approach to study these complex dynamics is developing simplified or idealized models which capture their main features.

Here, we use a simplified mode consisting of the equatorial beta-plane shallow water equations in a background wind shear. The prescribed shear has both a barotropic and a first-baroclinic components with the zonal structures mimicing the climatological winds at 200 mb in the Winter Hemisphere over the Eastern Pacific Ocean and Western Pacific Oceans. In this model, the relative strength of the barotropic versus the baroclinic components of the background shear are varied systematically so that the effect of two wind types can be observed separately.

We approximate the advected shallow water equations by a Galerkin projection method, in the meridional direction using the first few parabolic cylinder functions as the orthonormal basis. We are interested in the effect of the prescribed wind shear on the propagation and morphological features of the equatorially trapped waves, using both a linear theory and a direct numerical integration. The numerical integration enable us to capture the dynamics of these interactions and energy exchange between various waves through the imposed wind shear.

We emphasize the case of Kelvin waves and Rossby waves which are believed to play a central role in organized tropical convective systems and energy exchange between tropics and extratropics, respectively. We demonstrate that unlike the free Kelvin waves that have no meridional velocity, the shear-forced Kelvin waves exhibit a weak meridional velocity, which, nevertheless, induces a large contribution to the flow convergence as observed in nature. Low-level convergence of moisture is believed to play a central role in sustaining moist convection in tropical convective systems. Furthermore, we show that the trapping of the Rossby waves is highly dependent on both barotropic and baroclinic shear. While the barotropic shear makes the Rossby waves more trapped around the equator, the baroclinic shear makes them less trapped.