Resonant triad interactions of gravity waves in cylindrical basins

Durey, M. and Milewski, P. A. (2023) Resonant triad interactions of gravity waves in cylindrical basins. Journal of Fluid Mechanics, 966, A25. (doi: 10.1017/jfm.2023.441)

Abstract

We present the results of a theoretical investigation into the existence, evolution and excitation of resonant triads of nonlinear free-surface gravity waves confined to a cylinder of finite depth. It is well known that resonant triads are impossible for gravity waves in laterally unbounded domains; we demonstrate, however, that horizontal confinement of the fluid may induce resonant triads for particular fluid depths. For any three correlated wave modes arising in a cylinder of arbitrary cross-section, we prove necessary and sufficient conditions for the existence of a depth at which nonlinear resonance may arise, and show that the resultant critical depth is unique. We enumerate the low-frequency triads for circular cylinders, including a new class of resonances between standing and counter-propagating waves, and also briefly discuss annular and rectangular cylinders. Upon deriving the triad amplitude equations for a finite-depth cylinder of arbitrary cross-section, we deduce that the triad evolution is always periodic, and determine parameters controlling the efficiency of energy exchange. In order to excite a particular triad, we explore the influence of external forcing; in this case, the triad evolution may be periodic, quasi-periodic or chaotic. Finally, our results have potential implications on resonant water waves in man-made and natural basins, such as industrial-scale fluid tanks, harbours and bays.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Durey, Dr Matthew
• Authors: Durey, M., and Milewski, P. A.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Fluid Mechanics
• Publisher: Cambridge University Press
• ISSN: 0022-1120
• ISSN (Online): 1469-7645
• Published Online: 03 July 2023
• Copyright Holders: Copyright © 2023 The Authors
• First Published: First published in Journal of Fluid Mechanics 966: A25
• Publisher Policy: Reproduced in accordance with the publisher copyright policy