×

Nonlinear numerical investigation on higher harmonics at Lee side of a submerged bar. (English) Zbl 1237.74186

Summary: The decomposition of a monochromatic wave over a submerged object is investigated numerically in a flume, based on a fully nonlinear HOBEM (higher-order boundary element method) model. Bound and free higher-harmonic waves propagating downstream the structure are discriminated by means of a two-point method. The developed numerical model is verified very well by comparison with the available data. Further numerical experiments are carried out to study the relations between free higher harmonics and wave nonlinearity. It is found that the nth-harmonic wave amplitude is growing proportional to the nth power of the incoming wave amplitude for weakly nonlinear wave condition, but higher-harmonic free wave amplitudes tend to a constant value for strong nonlinear wave condition.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] S. Beji and J. A. Battjes, “Experimental investigation of wave propagation over a bar,” Coastal Engineering, vol. 19, no. 1-2, pp. 151-162, 1993. · doi:10.1016/0378-3839(93)90022-Z
[2] H. R. Luth, R. Klopman, and N. Kitou, “Kinematics of waves breaking partially on an offshore bar; LDV measurements of waves with and without a net onshore current,” Tech. Rep. H-1573, Delft Hydraulics, 1994.
[3] D. S. Jeng, C. Schacht, and C. Lemckert, “Experimental study on ocean waves propagating over a submerged breakwater in front of a vertical seawall,” Ocean Engineering, vol. 32, no. 17-18, pp. 2231-2240, 2005. · doi:10.1016/j.oceaneng.2004.12.015
[4] Y. S. Cho, J. I. Lee, and Y. T. Kim, “Experimental study of strong reflection of regular water waves over submerged breakwaters in tandem,” Ocean Engineering, vol. 31, no. 10, pp. 1325-1335, 2004. · doi:10.1016/j.oceaneng.2003.07.009
[5] C. Rambabu and J. S. Mani, “Numerical prediction of performance of submerged breakwaters,” Ocean Engineering, vol. 32, no. 10, pp. 1235-1246, 2005. · doi:10.1016/j.oceaneng.2004.10.023
[6] P. A. Madsen, R. Murray, and O. R. S\varphi rensen, “A new form of Boussinesq equaitons with improved linear dispersion characteristics,” Coastal Engineering, vol. 15, no. 4, pp. 371-388, 1991. · doi:10.1016/0378-3839(91)90017-B
[7] P. A. Madsen and O. R. S\varphi rensen, “Bound waves and triad interactions in shallow water,” Ocean Engineering, vol. 20, no. 4, pp. 359-388, 1993. · doi:10.1016/0029-8018(93)90002-Y
[8] A. P. Engsig-Karup, J. S. Hesthaven, H. B. Bingham, and T. Warburton, “DG-FEM solution for nonlinear wave-structure interaction using Boussinesq-type equations,” Coastal Engineering, vol. 55, no. 3, pp. 197-208, 2008. · doi:10.1016/j.coastaleng.2007.09.005
[9] K. Z. Fang and Z. L. Zou, “Boussinesq-type equations for nonlinear evolution of wave trains,” Wave Motion, vol. 47, no. 1, pp. 12-32, 2010. · Zbl 1231.35164 · doi:10.1016/j.wavemoti.2009.07.002
[10] J. Grue, “Nonlinear water waves at a submerged obstacle or bottom topography,” Journal of Fluid Mechanics, vol. 244, pp. 455-476, 1992. · doi:10.1017/S0022112092003148
[11] J. Brossard and M. Chagdali, “Experimental investigation of the harmonic generation by waves over a submerged plate,” Coastal Engineering, vol. 42, no. 4, pp. 277-290, 2001. · doi:10.1016/S0378-3839(00)00064-8
[12] C. R. Liu, Z. H. Huang, and S. K. Tan, “Nonlinear scattering of non-breaking waves by a submerged horizontal plate: experiments and simulations,” Ocean Engineering, vol. 36, no. 17-18, pp. 1332-1345, 2009. · doi:10.1016/j.oceaneng.2009.09.001
[13] D. Z. Ning, B. Teng, R. Eatock Taylor, and J. Zang, “Nonlinear numerical simulation of regular and focused waves in an infinite water depth,” Ocean Engineering, vol. 35, no. 8-9, pp. 887-899, 2008. · doi:10.1016/j.oceaneng.2008.01.015
[14] M. Brorsen and J. Larsen, “Source generation of nonlinear gravity waves with the boundary integral equation method,” Coastal Engineering, vol. 11, no. 2, pp. 93-113, 1987. · doi:10.1016/0378-3839(87)90001-9
[15] J. N. Newman, “The approximation of free-surface Green functions,” in Wave Asymptotics, P. A. Martin and G. R. Whickham, Eds., pp. 107-142, Cambridge University Press, Cambridge, UK, 1992. · Zbl 0803.76015
[16] B. Teng, Y. Gou, and D. Z. Ning, “A higher order BEM for wave-current action on structures-direct computation of free-term coefficient and CPV integrals,” China Ocean Engineering, vol. 20, no. 3, pp. 395-410, 2006.
[17] D. Z. Ning and B. Teng, “Numerical simulation of fully nonlinear irregular wave tank in three dimension,” International Journal for Numerical Methods in Fluids, vol. 53, no. 12, pp. 1847-1862, 2007. · Zbl 1223.76006 · doi:10.1002/fld.1385
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.