Vertically sheared horizontal flow with mass sources: A canonical balanced model

Canonical balanced dynamic equations involving vertically sheared horizontal flow with heat or mass sources have emerged recently in systematic multi-scale modeling of the equatorial wave guide on a wide range of spatio-temporal scales. Here, a new self-contained derivation of these equations is developed briefly in a context for potential applications to the hurricane embryo. These canonical balanced equations are studied through a combination of exact solutions and simple numerics. The results below include elementary exact solutions given by velocity fields that are linear in the spatial coordinates combined with an exact nonlinear stability analysis for vertical vorticity amplification in such a preconditioned environment. Other elementary solutions studied here include the evolution of radial eddies, which represent "hot towers" in the hurricane embryo in a suitable radial preconditioned background environment.