TY - GEN

T1 - Bragg interactions of a cnoidal wave with rigid bottom ripples

AU - Tang, Chii-Jau

AU - Lee, Tzu Chiang

PY - 2010/9/10

Y1 - 2010/9/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77956331338&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77956331338&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:77956331338

SN - 9781880653777

T3 - Proceedings of the International Offshore and Polar Engineering Conference

SP - 787

EP - 794

BT - Proceedings of the 20th (2010) International Offshore and Polar Engineering Conference, ISOPE-2010

T2 - 20th International Offshore and Polar Engineering Conference, ISOPE-2010

Y2 - 20 June 2010 through 25 June 2010

ER -