Summary
The steady velocity field of the fluid particles is investigated when gravity waves propagate with constant angular velocity about a vertical axis. In a preliminary inviscid analysis, motion in horizontal circles is predicted. A method based on boundary-layer concepts is presented and motion in axial planes is shown to accompany the swirl. The radial and circumferential velocity components at the edge of the bottom boundary layer are calculated in a typical case. In deep fluids, horizontal circular motion is indicated by both inviscid and viscous theories, and a comparison is made of the corresponding circumferential velocities for particles near the free surface.
Zusammenfassung
Das stationäre Geschwindigkeitsfeld von Flüssigkeitsteilchen wird, für den Fall von Gravitationswellen, die mit konstanter Winkelgeschwindigkeit um eine vertikale Achse rotieren, untersucht. In einer einführenden reibungsfreien Untersuchung wird Bewegung in horizontalen Kreisen vorhergesagt. Eine auf Grenzschichtbegriffen basierende Methode wird dargestellt, und es wird gezeigt, daß Bewegung in Axialebenen zum Wirbel hinzukommt. In einem charakteristischen Fall werden Radial- und Tangentialgeschwindigkeit am Rand der Bodengrenzschicht berechnet. Sowohl die Theorie der reibungsfreien wie auch die der reibungsbehafteten Strömung in tiefen Flüssigkeiten führen auf horizontale Kreisbewegung. Ein Vergleich der entsprechenden Tangentialgeschwindigkeiten der Teilchen nahe der freien Oberfläche wird durchgeführt.
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Dore, B.D. On steady particle motion in circular gravity waves. Acta Mechanica 17, 227–245 (1973). https://doi.org/10.1007/BF01183757
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DOI: https://doi.org/10.1007/BF01183757