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Harbour excitations by incident wave groups

Published online by Cambridge University Press:  26 April 2006

Jiang-Kang Wu  and
Philip L.-F. Liu
Jiang-Kang Wu
Affiliation:
Joseph DeFrees Hydraulics Laboratory, School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA Present address: Ocean Engineering Program, Texas A&M University, College Station, TX 77843, USA.
Philip L.-F. Liu
Affiliation:
Joseph DeFrees Hydraulics Laboratory, School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA
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Abstract

By using the multiple-scales perturbation method, analytical solutions are obtained for the second-order low-frequency oscillations inside a rectangular harbour excited by incident wave groups. The water depth is a constant. The width of the harbour entrance is of the same order of magnitude as the wavelength of incident carrier (short) waves, but small in comparison with the wavelength of the wave envelope. Because of the modulations in the wave envelope, a second-order long wave is locked in with the wave envelope and propagates with the speed of the group velocity. Outside the harbour, locked long waves also exist in the reflected wave groups, but not in the radiated wave groups. Inside the harbour, the analytical expressions for the locked long waves are obtained. Owing to the discontinuity of the locked long waves across the harbour mouth, second-order free long waves are generated. The free long waves propagate with a speed of (gh)½ inside and outside the harbour. The free long waves inside the harbour may be resonated in a low-frequency range which is relevant to the harbour resonance.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 217 , August 1990 , pp. 595 - 613
Copyright
© 1990 Cambridge University Press

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