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The physics of potential vorticity

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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.

Seit der ursprünglichen Publikation der Theorems über die potentielle Vorticity von Hans ERTEL 1942 (und nochmals in 1955) gab es dazu zahlreiche modellhafte Anwendungen numerischer wie analytischer Art, sowie Rekonstruktionen und Wiederholungen zum Beweis der Zweckmäßigkeit und Plausibilität des Prinzips. Abseits davon verfolgt diese Studie eine ganz andere, die physikalische PV-Wirklichkeit betreffende Thematik. Es wird zum einen die Frage nach dem grundlegenden Verständnis der PV-Physik anhand der konjugierten genuinen Vektorfelder in Bezug zu verwandten elektrostatischen Gesetzen sowie der konsequenten Erfassung in einer integralen-lokalen Feldbilanzdarstellung behandelt. Desweiteren wird die PV-Dynamik in der Terminologie ihrer (beiden) konstitutiven Vektorfeld-Differentialgleichungen im Vergleich zur elektromagnetischen Maxwell'schen Theorie diskutiert: wichtigen Gemeinsamkeiten zwischen der PV- und der elektromagnetischen Physik stehen auch deutliche Unterschiede gegenüber. Schließlich erfolgt ein analytischer Diskurs über eine Feldgleichung einer verallgemeinerten skalaren Wirbelvariable, und wie man aus diesem Theorem den Spezialfall der PV-Dynamik ableitet. Da in entsprechender Weise auch gleichermaßen die Helicity-Dynamik enthalten ist, zeigt sich, als interessante Verknüpfung, dass mit der PV- und Helicity-Dynamik eng verwandte, praktisch identische Rotationscharakteristika beschrieben werden.

Document Type: Research Article


Publication date: 2007-06-01

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  • Meteorologische Zeitschrift (originally founded in 1866) is the joint periodical of the meteorological societies of Austria, Germany and Switzerland. It accepts high-quality peer-reviewed manuscripts on all aspects of observational, theoretical and computational research out of the entire field of meteorology, including climatology. Meteorologische Zeitschrift represents a natural forum for the meteorological community of Central Europe and worldwide.
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