Summary
An initial value investigation into the two dimensional linearized problem of surface wave propagation in a fluid of limited and unlimited depth due to harmonically oscillating sources has been made. An asymptotic analysis of the problem has been carried out in a considerable detail for a clear understanding of both the steady state and the transient solutions. The limiting behaviour of the asymptotic solution as timeT tends to infinity has also been given due attention. Lastly, the corresponding steady state solution is obtained as a limiting case, and a discussion about the wave motions is made in some detail.
Zusammenfassung
Das zweidiensionmale linearisierte Anfangswertproblem der Ausbreitung von Oberflächenwellen in einer Flüssigkeit endlicher bzw. unendlicher Tiefe wird betrachtet. Die Wellen werden durch harmonisch oszillierende Quellen verursacht. Eine asymptotische Betrachtung wird zum klaren Verständnis des stationären wie auch des Übergangsverhaltens ausführlich durchgeführt. Betrachtet wird auch das Verhalten der asymptotischen Lösung für große Zeiten; die stationäre Lösung wird als Grenzfall erhalten. Abschließend wird die Wellenbewegung ausführlich diskutiert.
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Debnath, L. On transient development of surface waves due to two dimensional sources. Acta Mechanica 11, 185–202 (1971). https://doi.org/10.1007/BF01176555
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DOI: https://doi.org/10.1007/BF01176555