Jupiter's Equatorial Zone (EZ) is characterized by atmospheric dynamics influenced by strong zonal jets. Initially, we perform a linear stability analysis of two-layer geostrophic flows to explore the growth and evolution of instabilities associated with equatorial jets. Stability diagrams reveal that the most unstable baroclinic modes shift to lower wavenumbers with increasing zonal velocities, indicating sensitivity to the strength of the zonal wind. We show notable differences in phase velocities between barotropic and baroclinic jets. Phase portraits of the dynamic structures of various wave types, including barotropic and baroclinic Kelvin waves, Yanai waves, Rossby waves, and inertia-gravity waves, are illustrated in this analysis. Subsequently, we employ a two-layer moist convective Rotating Shallow Water (2mcRSW) model to investigate the nonlinear interactions between ammonia-driven convective processes in the shallow upper atmosphere and large-scale atmospheric features in Jupiter's EZ. We analyze the evolution of nonlinear instabilities in moist-convective flows by perturbing a background zonal velocity field with the most unstable mode. Findings include the amplification of cyclonic and anticyclonic vortices driven by moist convection at the boundaries of the zonal jets and the suppression of convective vortices in equatorial bright zones. This study underscores the role of moist convection in generating upper atmosphere cloud clusters and lightning patterns, as well as the chevron-shaped pattern observed on the poleward side of the zonal jets. Finally, we propose a novel mechanism for the formation of Y-shaped structures on Jupiter, driven by equatorial modons coupled with convectively baroclinic Kelvin waves (CCBCKWs). This mechanism suggests that Y-shaped structures result from large-scale localized heating in a diabatic environment, which, upon reaching a critical threshold of negative pressure or positive buoyancy anomaly, generates a hybrid structure. This hybrid structure consists of a quasi equatorial modon, a coherent dipolar structure, coupled with a CCBCKW that propagates eastward in a self-sustaining and self-propelled manner. Initially, the hybrid moves steadily eastward; however, the larger phase speed of the CCBCKW eventually leads to its detachment from the quasi equatorial modon. The lifetime of this coupled structure varies from interseasonal to seasonal timescales. Moist convection is a necessary condition for triggering the eastward-propagating structure.

(1) Stability Analysis Insights: The study reveals the most unstable modes, dispersion relation, and their phase portraits in Jupiter's Equatorial Zone, with distinct patterns observed in barotropic and baroclinic stability analyses.

(2) Moist Convection Effects: Nonlinear simulations show that moist convection amplifies cyclonic and anticyclonic vortices, significantly impacting large-scale circulations in the vicinity of zonal jets and the poleward drift of emerged vortices.

(3) Y-shaped Cloud Formation: Y-shaped cloud structures on Jupiter are explained by the equatorial adjustment of a large-scale localized warm pool in a diabatic environment, which leads to a hybrid structure of baroclinic modons and Kelvin waves, with an interseasonal to seasonal lifetime.