Dispersion, Nonlinearity, and Viscosity in Shallow‐Water Waves
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 119, Issue 4
Abstract
The roles of frequency dispersion, nonlinearity, and laminar viscosity in the evolution of long waves over distances of many wavelengths in constant water depth are investigated with numerical solutions of the Boussinesq equations. Pronounced frequency doubling and trebling is predicted, and the initial evolution to a wave shape with a pitched‐forward front face and peaky crests is followed by development of a steep rear face and a nearly symmetric crest/trough profile. While reducing overall energy levels, laminar viscosity acts to prolong cycling of third moments and to inhibit the onset of disordered evolution characteristic of nonlinear, inviscid systems. Preliminary laboratory results show some qualitative similarities to the numerical simulations. However, these laboratory experiments were not suitable for detailed model‐data comparisons because dissipation in the flume could not be accounted for with either laminar or quadratic damping models. More carefully controlled experiments are required to assess the importance of viscosity (and the accuracy of the Boussinesq model) in the evolution of nonlinear waves over distances of many wavelengths.
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Information
Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 119 • Issue 4 • July 1993
Pages: 351 - 366
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Feb 25, 1991
Published online: Jul 1, 1993
Published in print: Jul 1993
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