Bragg interactions of a cnoidal wave with rigid bottom ripples

Chii-Jau Tang, Tzu Chiang Lee

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The article presents the numerical study on the Bragg resonances of the cnoidal wave with rigid ripples on a mean flat bottom. With the application of a general laminar flow model for nonlinear wave problems (Lee and Tang, 2009), we are able to study the possible strong reflection of the cnoidal wave from rigid ripples with certain tuned spacing around the condition of Bragg resonances. In this study, we consider the weakly-nonlinear, weakly-dispersive, cnoidal waves under the viscous action of the periodic finite-amplitude ripples. The competing orders of magnitude among effects of wave nonlinearity and dispersion on the slowly evolving free surface, viscosity on the induced vortical flow near the uneven bottom, and the tuned ripple spacing on reflected wave-seabed resonances all together makes complicated interaction between the free surface and the ripple bottom. We also employ the phase plot in nonlinear dynamic theory to describe the qualitative nature of wave interaction. The detailed interferential pattern obtained from the intersected crest-lines of the incident and reflected waves is illustrated clearly during Bragg resonances.

Original languageEnglish
Title of host publicationProceedings of the 20th (2010) International Offshore and Polar Engineering Conference, ISOPE-2010
Pages787-794
Number of pages8
Publication statusPublished - 2010 Sep 10
Event20th International Offshore and Polar Engineering Conference, ISOPE-2010 - Beijing, China
Duration: 2010 Jun 202010 Jun 25

Publication series

NameProceedings of the International Offshore and Polar Engineering Conference
Volume3
ISSN (Print)1098-6189
ISSN (Electronic)1555-1792

Other

Other20th International Offshore and Polar Engineering Conference, ISOPE-2010
CountryChina
CityBeijing
Period10-06-2010-06-25

Fingerprint

Laminar flow
Viscosity

All Science Journal Classification (ASJC) codes

  • Energy Engineering and Power Technology
  • Ocean Engineering
  • Mechanical Engineering

Cite this

Tang, C-J., & Lee, T. C. (2010). Bragg interactions of a cnoidal wave with rigid bottom ripples. In Proceedings of the 20th (2010) International Offshore and Polar Engineering Conference, ISOPE-2010 (pp. 787-794). (Proceedings of the International Offshore and Polar Engineering Conference; Vol. 3).
Tang, Chii-Jau ; Lee, Tzu Chiang. / Bragg interactions of a cnoidal wave with rigid bottom ripples. Proceedings of the 20th (2010) International Offshore and Polar Engineering Conference, ISOPE-2010. 2010. pp. 787-794 (Proceedings of the International Offshore and Polar Engineering Conference).
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Tang, C-J & Lee, TC 2010, Bragg interactions of a cnoidal wave with rigid bottom ripples. in Proceedings of the 20th (2010) International Offshore and Polar Engineering Conference, ISOPE-2010. Proceedings of the International Offshore and Polar Engineering Conference, vol. 3, pp. 787-794, 20th International Offshore and Polar Engineering Conference, ISOPE-2010, Beijing, China, 10-06-20.

Bragg interactions of a cnoidal wave with rigid bottom ripples. / Tang, Chii-Jau; Lee, Tzu Chiang.

Proceedings of the 20th (2010) International Offshore and Polar Engineering Conference, ISOPE-2010. 2010. p. 787-794 (Proceedings of the International Offshore and Polar Engineering Conference; Vol. 3).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Tang C-J, Lee TC. Bragg interactions of a cnoidal wave with rigid bottom ripples. In Proceedings of the 20th (2010) International Offshore and Polar Engineering Conference, ISOPE-2010. 2010. p. 787-794. (Proceedings of the International Offshore and Polar Engineering Conference).