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On the linear capillary-gravity wave problem

Zum linearen Kapillar-Schwerewellenproblem

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Summary

The two dimensional problem of the transient development of capillary-gravity waves on the free surface of an incompressible inviscid fluid is investigated. The fluid occupies the semi-infinite space bounded by a fixed vertical barrier and the cases of finite uniform depth and infinite depth are considered. A boundary condition is derived for the liquid-solid intersection and it is shown how this provides for a unique solution. The solution of the problem is obtained by using integral transforms and the asymptotic form of the free surface displacement is obtained.

Zusammenfassung

Das zweidimensionale Problem des Übergangsverhaltens von Kapillar- und Schwerewellen auf der freien Oberfläche einer inkompressiblen Flüssigkeit ohne innere Reibung wird untersucht. Die Flüssigkeit befindet sich in einem unendlichen Halbraum, der durch ein festes vertikales Hindernis begrenzt wird. Die Fälle von gleichförmiger endlicher und unendlicher Tiefe werden behandelt. Eine Randbedingung für die Grenzfläche von Flüssigkeit und fester Wand wird angegeben und es wird gezeigt, daß dadurch eine eindeutige Lösung bestimmt wird. Die Lösung dieses Problems ergibt sich durch eine Integraltransformation und die asymptotische Form der Verschiebung der freien Oberfläche wird erhalten.

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References

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Authors and Affiliations

  1. Department of Mathematics, The University of Southampton, 509 5NH, Southampton, UK

    J. C. Murray

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  1. J. C. Murray
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Murray, J.C. On the linear capillary-gravity wave problem. Acta Mechanica 23, 247–259 (1975). https://doi.org/10.1007/BF01174022

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  • DOI: https://doi.org/10.1007/BF01174022

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