Current Effects on Nonlinear Wave Scattering by a Submerged Plate
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 140, Issue 5
Abstract
On the basis of a time-domain higher-order boundary element method, a two-dimensional fully nonlinear numerical wave flume is developed to investigate the nonlinear interactions between a regular wave and a submerged horizontal plate in the presence of uniform currents. A two-point method is used to discriminate bound (i.e., nonlinearly forced by and coupled to free waves) and free harmonic waves propagating upstream and downstream from the structure. The proposed model is verified against experimental and other numerical data for wave-current interaction without obstacles and nonlinear wave scattering by a submerged plate in the absence of currents. A first-order analysis shows that the reflection coefficient increases in the following current (i.e., current in the same direction as the incident wave) and decreases in the opposing current (i.e., current in the opposite direction to the incident wave). Moreover, the plate length for the maximum reflection to occur is not sensitive to the current. A second-order analysis indicates that downstream from the plate, the current has a stronger influence on the secondary free mode than on the first free mode. The energy transfer between the fundamental wave and the higher harmonics is intensified by a following current but weakened by an opposing current. The second free harmonic wave amplitude is affected more by the opposing current than it is by the following current.
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Acknowledgments
The authors gratefully acknowledge financial support from the National Natural Science Foundation of China (Grant Nos. 51179028, 51222902, and 51221961), the National Basic Research Program of China (973 Program, Grant No. 2011CB013703), and the Fundamental Research Funds for the Central Universities (DUT13YQ104). Q.-P. Zou thanks Maine Sea Grant, National Science Foundation Grant No. 1337895, and the start-up fund by University of Maine.
References
Baddour, R. E., and Song, S. W. (1990). “Interaction of higher-order water waves with uniform currents.” Ocean Eng., 17(6), 551–568.
Beji, S., and Battjes, J. A. (1993). “Experimental investigation of wave propagation over a bar.” Coast. Eng., 19(1–2), 151–162.
Brebbia, C. A., and Walker, S. (1980). Boundary element technique in engineering, Newnes-Butterworths, London.
Bretherton, F. P., and Garrett, G. J. R. (1968). “Wavetrains in inhomogeneous moving media.” Proc. R. Soc. Lond. A., 302(1471), 529–554.
Brossard, J., and Chagdali, M. (2001). “Experimental investigation of the harmonic generation by waves over a submerged plate.” Coast. Eng., 42(4), 277–290.
Brossard, J., Perret, G., Blonce, L., and Diedhiou, A. (2009). “Higher harmonics induced by a submerged horizontal plate and a submerged rectangular step in a wave flume.” Coast. Eng., 56(1), 11–22.
Carter, R. W. (2005). “Wave energy converters and a submerged horizontal plate.” Ph.D. thesis, Univ. of Hawaii, Manoa, Hawaii.
Carter, R. W., Ertekin, R. C., and Lin, P. (2006). “On the reverse flow beneath a submerged plate due to wave action.” Proc., 25th Int. Conf. on Offshore Mechanics and Arctic Engineering, ASME, New York, 595–602.
Chen, Q., Madsen, P. A., and Basco, D. R. (1999). “Current effects on nonlinear interactions of shallow-water waves.” J. Waterway, Port, Coastal, Ocean Eng., 176–186.
Graw, K. U. (1992). “The submerged plate as a wave filter: Stability of the pulsating flow phenomenon.” Proc., 23rd Int. Coastal Engineering Conf., ASCE, Reston, VA, 1153–1160.
Grue, J. (1992). “Nonlinear water waves at a submerged obstacle or bottom topography.” J. Fluid Mech., 244, 455–476.
Grue, J., Mo, A., and Palm, E. (1988). “Propulsion of a foil moving in water waves.” J. Fluid Mech., 186, 393–417.
Guevel, P., Landel, E., Bouchet, R., and Manzone, J. M. (1986). Le phénomène du mur d'eau oscillant et son application pour protéger un site côtier soumis à l'action de la houle, Permanent International Association of Navigation Congresses, Brussels, Belgium.
Huang, C. J., and Dong, C. M. (1999). “Wave deformation and vortex generation in water waves propagating over a submerged dike.” Coast. Eng., 37(2), 123–148.
Koo, W., and Kim, M. H. (2007). “Current effects on nonlinear wave-body interactions by a 2D fully nonlinear numerical wave tank.” J. Waterway, Port, Coastal, Ocean Eng., 136–146.
Ligget, J. A., and Liu, P. L. F. (1983). The boundary integral equation method for porous media flow, George Allen & Unwin, London.
Liu, C. R., Huang, Z. H., and Keat Tan, S. (2009). “Nonlinear scattering of non-breaking waves by a submerged horizontal plate: Experiments and simulations.” Ocean Eng., 36(17–18), 1332–1345.
Ning, D. Z., and Teng, B. (2007). “Numerical simulation of fully nonlinear irregular wave tank in three dimension.” Int. J. Numer. Methods Fluids, 53(12), 1847–1862.
Ning, D. Z., Teng, B., Zhao, H., and Hao, C. (2010). “A comparison of two methods for calculating solid angle coefficients in a BIEM numerical wave tank.” Eng. Anal. Bound. Elem., 34(1), 92–96.
Orer, G., and Ozdamar, A. (2007). “An experimental study on the efficiency of the submerged plate wave energy converter.” Renewable Energy, 32(8), 1317–1327.
Patarapanich, M. (1984). “Maximum and zero reflection from submerged plate.” J. Waterway, Port, Coastal, Ocean Eng., 171–181.
Patarapanich, M., and Cheong, H. F. (1989). “Reflection and transmission characteristics of regular and random waves from a submerged horizontal plate.” Coast. Eng., 13(2), 161–182.
Peng, W., Lee, K. H., Shin, S. H., and Mizutani, N. (2013). “Numerical simulation of interactions between water waves and inclined-moored submerged floating breakwaters.” Coast. Eng., 82, 76–87.
Rahman, M. A., Mizutani, N., and Kawasaki, K. (2006). “Numerical modeling of dynamic responses and mooring forces of submerged floating breakwaters.” Coast. Eng., 53(10), 799–815.
Rey, V., Capobianco, R., and Dulou, C. (2002). “Wave scattering by a submerged plate in presence of a steady uniform current.” Coast. Eng., 47(1), 27–34.
Rey, V., and Touboul, J. (2011). “Forces and moment on a horizontal plate due to regular and irregular waves in the presence of current.” Appl. Ocean Res., 33(2), 88–99.
Saad, Y., and Schultz, M. H. (1986). “GMRES: A generalized minimal residual algorithm for solving nonsymmetrical linear systems.” J. Sci. Stat. Comput., 7(3), 856–869.
Siew, P. F., and Hurley, D. G. (1977). “Long surface waves incident on a submerged horizontal plate.” J. Fluid Mech., 83(1), 141–151.
Tanizawa, K. (1996). “Long time fully nonlinear simulation of floating body motions with artificial damping zone.” Soc. Naval Architects Jap., 180, 311–319.
Ting, F. C. K., and Kim, Y. K. (1994). “Vortex generation in water waves propagating over a submerged obstacle.” Coast. Eng., 24(1–2), 23–49.
Zaman, M. H., Togashi, H., and Baddour, R. E. (2008). “Deformation of monochromatic water wave trains propagating over a submerged obstacle in the presence of uniform currents.” Ocean Eng., 35(8–9), 823–833.
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Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 140 • Issue 5 • September 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jul 23, 2013
Accepted: Jan 24, 2014
Published online: Mar 4, 2014
Discussion open until: Aug 4, 2014
Published in print: Sep 1, 2014
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