Convectively coupled waves in a sheared environment

We are interested in the effect of background vertical and meridional shear on convectively coupled waves. We perform linear stability analysis for a simple multicloud model for convectively coupled waves. It is found here that high-level vertical shear plays an important role in stabilizing and destabilizing the convectively coupled waves. Typically, vertical shears with high-level easterly wind excite westward moving waves and stabilize all eastward waves including the Kelvin wave while westerly winds destabilize eastward moving and stabilize all westward moving waves, suggesting a mechanism through which Kelvin waves and 2-day waves are initiated respectively in the front and rear of the MJO envelope. A barotropic/meridional shear initiates synoptic scale convectively coupled westward mixed Rossby-gravity and Rossby waves when the shear strength is large enough. Tests performed for the case without moisture and convective coupling demonstrate that the emergence of the MRG and Rossby waves is due essentially to shear instability. Moreover, the meridional shear has an important impact on the horizontal structure of the waves. Due to the meridional shear, the Kelvin wave displays a non-zero meridional velocity that induces a significant contribution towards the horizontal convergence. The 2-day waves adopt a crescent-like shape while the MRG and somewhat the Rossby waves become less trapped in the vicinity of the equator.