Summary
Fundamental properties of the dispersion relations for internal gravity wave modes in stratified shear flows are derived as generalizations of the corresponding well known properties found in the absence of shear. Some problems associated with the expansion of internal wave fields in the normal modes are discussed briefly. Such problems may result from a lack of completeness or of orthogonality of the normal modes.
Zusammenfassung
Grundlegende Eigenschaften der Dispersionsrelationen für die Eigenfunktionen (Moden) interner Schwerewellen bei Scherströmungen in geschichteten Medien werden als Verallgemeinerung der entsprechenden, bekannten Eigenschaften scherungsfreier Strömungsfelder abgeleitet. Einige Probleme, die mit der Entwicklung des internen Wellenfeldes nach Eigenfunktionen zusammenhängen, werden kurz diskutiert. Solche Probleme können auftreten, wenn das System der Eigenfunktionen nicht vollständig oder orthogonal ist.
Résumé
Les propriétés fondamentales des relations de dispersion pour les modes des ondes de gravité internes dans des écoulements stratifiés, avec cisaillement, sont obtenues par généralisation des propriétés bien connues, correspondant au cas où il n'y a pas de cisaillement. On discute brièvement quelques problèmes liés à l'expansion des champs d'ondes internes dans les modes normaux. De tels problèmes peuvent résulter d'imperfections ou de l'orthogonalité des modes normaux.
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Bell, T.H. Effects of shear on the properties of internal gravity wave modes. Deutsche Hydrographische Zeitschrift 27, 57–62 (1974). https://doi.org/10.1007/BF02226477
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DOI: https://doi.org/10.1007/BF02226477