Equivalent Modons in Simple Shear

Abstract

We use a perturbation technique to construct modon solutions that are valid in the presence of weak, linear north-south shear to help assess the application of modons to atmospheric blocking. The model equation is equivalent barotropic and describes the quasi-geostrophic motion in the thin upper layer of a two-layer system in which the lower layer is deep and has no motion other than the imposed shear flow. This model is shown to be a geophysically relevant limit of the more complicated model adopted by McWilliams, who uses a truncated modal projection to establish the connection between the quasi-geostrophic equations and the atmosphere. The new solutions are found to be stable and robust in numerical calculations, but we do not explore the full parametric range of interest.