Approximations of the Dispersion Relationship of Water Waves
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VIEW CORRECTIONPublication: Journal of Engineering Mechanics
Volume 140, Issue 1
ABSTRACT
A simple explicit formula is presented here to approximate the dispersion relationship of linear water waves, which allows direct and accurate calculation of wavenumber for a given frequency . This formula is valid for all water depths, having an accuracy of the maximum error being 0.33% compared with the true solution (which is typically obtained by iterations or other root-finding numerical algorithms). It can easily be realized on a simple hand calculator (e.g., approved calculators for the Fundamentals of Engineering and the Principles and Practice of Engineering exams), and does not need any iteration, appealing in particular for practical engineering and pedagogical purposes. Another explicit formula, with still higher accuracy but slightly less simple form, is also discussed.
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Acknowledgments
The author thanks two anonymous reviewers whose comments have helped to improve the paper. Support of J.Y., by the U.S. National Science Foundation (Grant No. CBET-0845957) during the period of this work, is gratefully acknowledged.
References
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 140 • Issue 1 • January 2014
Pages: 233 - 235
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Oct 29, 2012
Accepted: Feb 27, 2013
Published online: Mar 1, 2013
Published in print: Jan 1, 2014
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