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A note on gravity waves in a viscous liquid with surface tension

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Summary

The linear theory by Reid [1] on gravity waves in a viscous liquid with surface tension is extended. Asymptotic formulae for the dispersion relation are derived. A critical Morton number equal to 0.044789 is found. Only in liquids with smaller Morton numbers, travelling ripples may exist with group velocity exceeding phase velocity.

Zusammenfassung

Reid's lineare Theorie über Gravitationswellen in einer viskosen Flüssigkeit mit Oberflächenspannung wird erweitert. Abgeleitet werden asymptotische Formeln für das Verteilungsverhältnis und eine kritische Morton-Zahl gleich 0.044789 wird gefunden. Nur in Flüssigkeiten mit geringeren Morton-Zahlen existieren wandernde kleine Wellen mit einer Gruppengeschwindigkeit, die die Phasengeschwindigkeit überschreitet.

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References

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Authors and Affiliations

  1. Dept. of Mechanics, University of Oslo, Norway

    Peder A. Tyvand

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  1. Peder A. Tyvand
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Tyvand, P.A. A note on gravity waves in a viscous liquid with surface tension. Z. angew. Math. Phys. 35, 592–597 (1984). https://doi.org/10.1007/BF00945077

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  • DOI: https://doi.org/10.1007/BF00945077

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