TECHNICAL NOTES
May 1, 1997

Solitary Wave Solution to Boussinesq Equations

Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 123, Issue 3

Abstract

The exact solitary wave solution to the Boussinesq equations, which was given in an implicit integral form, is further studied in the present note. Through numerical curve fitting, an explicit closed-form empirical solution whose profile is nearly identical to the exact solution is obtained. Discussion and comparison between solitary wave solutions based on the Boussinesq model and higher-order theories of the Euler equation are presented.

Get full access to this article

View all available purchase options and get full access to this article.

References

1.
Daily, J. W., and Stephan, S. C. (1952). “The solitary wave.”Proc., 3rd Conf. on Coast. Engrg., 13–30.
2.
Fenton, J. D.(1972). “A ninth-order solution for the solitary wave.”J. Fluid Mech., Cambridge, England, 53, 257–271.
3.
Grimshaw, R.(1971). “The solitary wave in water of variable depth. Part 2.”J. Fluid Mech., Cambridge, England, 46, 611–622.
4.
Laitone, E. V.(1960). “The second approximation to cnoidal and solitary waves.”J. Fluid Mech., Cambridge, England, 9, 430–444.
5.
Lee, S. J., Yates, G. T., and Wu, T. Y.(1989). “Experiments and analysis of upstream-advancing solitary waves generated by moving disturbances.”J. Fluid Mech., Cambridge, England, 199, 569–593.
6.
Longuet-Higgins, M. S., and Fenton, J. D.(1974). “On the mass, momentum, energy and circulation of a solitary wave II.”Proc., Royal Soc., London, England, Ser. A, 340, 471–493.
7.
Pennell, S. A., and Su, C. H.(1984). “A seventeenth-order series expansion for the solitary wave.”J. Fluid Mech., Cambridge, England, 149, 431–443.
8.
Tanaka, M.(1986). “The stability of solitary waves.”Phys. of Fluids, 29(3), 650–655.
9.
Teng, M. H. (1990). “Forced emissions of nonlinear water waves in channels of arbitrary shape,” PhD thesis, California Inst. of Technol., Pasadena, Calif.
10.
Teng, M. H., and Wu, T. Y.(1992). “Nonlinear water waves in channels of arbitrary shape.”J. Fluid Mech., Cambridge, England, 242, 211–233.
11.
Teng, M. H., and Wu, T. Y.(1994). “Evolution of long water waves in variable channels.”J. Fluid Mech., Cambridge, England, 266, 303–317.
12.
Wang, K. H., Wu, T. Y., and Yates, G. T.(1992). “Three-dimensional scattering of solitary waves by vertical cylinder.”J. Wtrwy., Port, Coast., and Oc. Engrg., ASCE, 118, 551–566.
13.
Weidman, P. D., and Maxworthy, T.(1978). “Experiments on strong interactions between solitary waves.”J. Fluid Mech., Cambridge, England, 85, 417–431.
14.
Wu, T. Y.(1981). “Long waves in ocean and coastal waters.”J. Engrg. Mech., ASCE, 107, 501–522.
15.
Yates, G. T. (1995). “Various Boussinesq solitary wave solutions.”Proc., 5th Int. Offshore and Polar Engrg. Conf., Int. Soc. of Offshore and Polar Engrs., (ISOPE), Colo., Vol. 3, 70–76.
16.
Yates, G. T., and Wang, K. H. (1994). “Solitary wave scattering by a vertical cylinder: experimental study.”Proc., 4th Int. Offshore and Polar Engrg. Conf., Int. Soc. of Offshore and Polar Engrs. (ISOPE), Colo., Vol. 3, 118–124.

Information & Authors

Information

Published In

Go to Journal of Waterway, Port, Coastal, and Ocean Engineering
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 123Issue 3May 1997
Pages: 138 - 141

History

Published online: May 1, 1997
Published in print: May 1997

Permissions

Request permissions for this article.

Authors

Affiliations

Michelle H. Teng, Associate Member, ASCE
Asst. Prof., Dept. of Civ. Engrg., Univ. of Hawaii at Manoa, Honolulu, HI 96822.

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share