Viscous Baroclinic-Barotropic Instability in the Tropics: Is It the Source of Both Easterly Waves and Monsoon Depressions?

This study investigates the impact of eddy viscosity on equatorially trapped waves and the instability of the background shear in a simple barotropic–baroclinic model. It is the first study to include eddy viscosity in the study of tropical wave dynamics. This study also unifies the study of baroclinic and barotropic instabilities by using a coupled barotopic and baroclinic model of the tropical atmosphere. Linear wave theory is combined with a systematic Galerkin projection of the baroclinic dynamical fields onto parabolic cylinder functions. This study investigates varying shear strengths, eddy viscosities, and their combined effects. In the absence of shear, baroclinic and barotropic waves decouple. The baroclinic waves themselves separate into triads, forming the equatorially trapped wave modes known as Matsuno waves. However, when a strong eddy viscosity is included, the structure and propagation characteristics of these equatorial waves are significantly altered. Different wave types interact, leading to strong mixing in the meridional direction and coupling between meridional modes. This coupling destroys the Matsuno mode separation and offers pathways for these waves to couple and interact with one another. These results suggest that viscosity does not simply suppress growth; it may also reshape the propagation characteristics of unstable modes. In the presence of a background shear, some wave modes become unstable, and barotropic and baroclinic waves are coupled. Without eddy viscosity, instability begins with small scale and slowly propagating modes, at arbitrary small shear strengths. This instability manifests as an ultra-violet catastrophe. As the shear strength increases, the catastrophic instability at small scales expands to high-frequency waves. Meanwhile, instability peaks emerge at synoptic and planetary scales along several Rossby mode branches. When a small eddy viscosity is reintroduced, the catastrophic small-scale instabilities disappear, while the large-scale Rossby wave instabilities persist. These westward-moving modes exhibit a mixed barotropic–baroclinic structure with signature vortices straddling the equator. Some vortices are centered close to the equator, while others are far away. Some waves resemble synoptic-scale monsoon depressions and tropical easterly waves, while others operate on the planetary scale and present elongated shapes reminiscent of atmospheric-river flow patterns.