The physics of potential vorticity

Abstract

Since the principle of the potential vorticity was published by Hans ERTEL more than sixty years ago (originally in 1942 and later in 1955) a lot of practical applications with numerical or analytical character, as well as interpretative reconstructions and repetitions have been contributed in proof of the law's expediency and plausibility. Apart from such efforts, this study pursues another topic: it is essentially focussed on the material reality of the potential vorticity and the various fundamental physical attributes coupled with it. At first, the question for a basic understanding of the physics of potential vorticity is treated with reference to its related vector fields in consideration of analogous laws of electrostatics, as well as in a consistent development within both an integral and local balance equations technique. Subsequently, the specific essence of the potential vorticity dynamics, as it is laid bare through its (two) constitutive vector field differential equations, is argued in comparison to Maxwell's electromagnetic framework. Important similarities are face to face with clear differences. Finally, variations to the potential vorticity are treated by means of a discourse about a generalized scalar vortex field equation. Among other things, it is shown how the potential vorticity dynamics, as a special case, can be reconstructed from this theorem. The same theorem comprises quite similarly the dynamics of helicity and thus reveals, supposing a special linkage, how it results in a partial equivalence with the dynamics of potential vorticity. In this case, helicity and potential vorticity are identical expressions to describe rotational characteristics.