Potential vorticity and the electrostatics analogy: Ertel—Rossby formulation

Abstract

The isomorphism between the theory of electrostatics and the quasi‐geostrophic potential vorticity is extended to the Ertel‐Rossby potential vorticity. Anomalies of mass‐weighted potential vorticity are defined relative to an arbitrary zonal‐mean or horizontal‐average flow and given in terms of the divergence of a vector field. the vector is the sum of linear and non‐linear contributions and can be written as a dielectric tensor acting on the geopotential gradient. the linear components of the tensor differ from those for the quasi‐geostrophic potential vorticity only if there exists a vertical variation of background potential vorticity, such as occurs at the tropopause, or if there is shea..