Summary
By combining the results due to Jeffrey and Mvungi [1], with the work of Jeffrey and Saw Tin [2, 3], the transmission and reflection properties of an acceleration wave propagating on the surface of water at rest in a vertical walled channel of arbitrary continuously varying width and piecewise continuously varying depth are determined. An explicit expression derived for the amplitude of the transmitted wave as a function of position by Jeffrey and Mvungi is used to find the effect of a discontinuous change of depth on the wave amplitude and to derive a criterion for the breaking of the wave.
Zusammenfassung
Durch Kombination der Resultate von Jeffrey und Mvungi [1] mit denen von Jeffrey and Saw Tin [2, 3] wird die Transmission und die Reflexion einer Beschleunigungswelle an der Oberfläche von ruhendem Wasser berechnet, in einem Kanal mit vertikalen Wänden, dessen Weite beliebig kontinuierlich und dessen Tiefe abschnittsweise kontinuierlich variiert. Ein expliziter Ausdruck für die Amplitude der durchgelassenen Welle in Funktion der Lage nach Jeffrey und Mvungi wird dazu benützt, um den Effekt einer Diskontinuität in der Tiefe zu finden und ein Kriterium für das Brechen der Welle herzuleiten.
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Jeffrey, A., Mvungi, J. A note on the effect of submerged obstacles on water waves in a channel. Z. angew. Math. Phys. 32, 756–763 (1981). https://doi.org/10.1007/BF00946986
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DOI: https://doi.org/10.1007/BF00946986