Over the course of its mission, the Juno spacecraft has provided unprecedented views of Jupiter and, in that process, has delivered answers to some of the key questions regarding gas giant atmospheres. In particular, it has stimulated novel lines of inquiry regarding gas giant polar cyclogenesis inspired by the images taken by the Jovian Infrared Auroral Mapper on-board Juno. We present a high resolution model of Jupiter’s polar cyclones using a 1.5 layer shallow water model with a quiescent “deep” layer. We employ forced turbulence of the geopotential field to model moist convective features. Perturbations of this form may contribute to polar cyclogenesis, and have been employed in previous works. We explore the effects of a latitudinally varying zonal jet on the development and overall evolution of polar vortex configurations. We argue that weak, residual zonal flows at high latitudes may inhibit mixing and interactions of vortices across these latitudes, resulting in stably clustered, discretized behavior of the polar cyclones. To benchmark our model, we provide characteristic curves of shallow water gravity waves. We find that the curves exhibit the expected gravity wave propagation speeds, v = (gh)1/2, where gh is the geopotential. We employ the Pencil Code for our numerical simulations. Pencil is a finite-difference code using 6th order spatial, and 3rd order temporal accuracy to model complex magnetohydrodynamical systems. We further compare our results to other investigations that employ the use of the EPIC global circulation model and discuss morphological contrast of the simulations.