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To overcome the internal limitation of standing wave forces on vertical breakwaters and describe multichromatic multidirectional water waves in front of the breakwaters, a third-order theory, including the classical solutions of two-dimensional long-crested waves and monochromatic unidirectional short-crested waves, for bichromatic bidirectional water waves partially reflected from the breakwaters is developed. A universal law applicable to a higher-order multichromatic multidirectional wave system is proposed, that is, the even-order frequencies are zero, the numbers of the odd-order frequencies constitute a geometric progression.
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Keywords:
- bichromatic bidirectional waves /
- a third-order theory /
- a universal law /
- partially reflected waves
[1] Hsu J R C, Tsuchiya Y, Silvester R 1979 J. Fluid Mech. 90 179
[2] Fenton J D 1985 J. Waterway, Port, Coastal and Ocean Eng. 111 216
[3] Roberts A J 1983 J. Fluid Mech. 135 301
[4] Kimmoun O, Branger H, Kharif C 1999 Eur. J. Mech. B/Fluid 18 889
[5] Ioualalen M , Okamura M , Cornier S , Kharif C, Roberts A J 2006 J. Waterway, Port, Coastal and Ocean Eng. 132 157
[6] Madsen P A, Fuhrman D R 2006 J. Fluid Mech. 557 369
[7] Huang H 2009 Acta Phys. Sin. 58 3655 (in Chinese) [黄 虎 2009 58 3655]
[8] Huang H 2009 Dynamics of Surface Waves in Coastal Waters (Beijing-Berlin: Higher Education Press-Springer)
[9] Mei C C, Stiassnie M, Yue D K P 2005 Theory and Applications of Ocean Surface Waves (Singapore: World Scientific)
[10] Liu Y 2009 Acta Phys. Sin. 58 7452 (in Chinese) [刘 煜 2009 58 7452]
[11] Tadjbakhsh I, Keller J B 1960 J. Fluid Mech. 8 442
[12] Yang L 2009 (MS Thesis) (Shanghai: Shanghai University) (in Chinese) [杨 丽 2009 (硕士学位论文) (上海: 上海大学)]
[13] Huang H, Yang L, Xia Y B 2010 Acta Phys. Sin. 59 2182(in Chinese) [黄 虎、 杨 丽、夏应波 2010 592182]
[14] Yang C N 1998 Chen Ning Yangs Collection (Shanghai: East China Normal University) (in Chinese) [杨振宁1998杨振宁文集(上海:华东师范大学出版社)]
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[1] Hsu J R C, Tsuchiya Y, Silvester R 1979 J. Fluid Mech. 90 179
[2] Fenton J D 1985 J. Waterway, Port, Coastal and Ocean Eng. 111 216
[3] Roberts A J 1983 J. Fluid Mech. 135 301
[4] Kimmoun O, Branger H, Kharif C 1999 Eur. J. Mech. B/Fluid 18 889
[5] Ioualalen M , Okamura M , Cornier S , Kharif C, Roberts A J 2006 J. Waterway, Port, Coastal and Ocean Eng. 132 157
[6] Madsen P A, Fuhrman D R 2006 J. Fluid Mech. 557 369
[7] Huang H 2009 Acta Phys. Sin. 58 3655 (in Chinese) [黄 虎 2009 58 3655]
[8] Huang H 2009 Dynamics of Surface Waves in Coastal Waters (Beijing-Berlin: Higher Education Press-Springer)
[9] Mei C C, Stiassnie M, Yue D K P 2005 Theory and Applications of Ocean Surface Waves (Singapore: World Scientific)
[10] Liu Y 2009 Acta Phys. Sin. 58 7452 (in Chinese) [刘 煜 2009 58 7452]
[11] Tadjbakhsh I, Keller J B 1960 J. Fluid Mech. 8 442
[12] Yang L 2009 (MS Thesis) (Shanghai: Shanghai University) (in Chinese) [杨 丽 2009 (硕士学位论文) (上海: 上海大学)]
[13] Huang H, Yang L, Xia Y B 2010 Acta Phys. Sin. 59 2182(in Chinese) [黄 虎、 杨 丽、夏应波 2010 592182]
[14] Yang C N 1998 Chen Ning Yangs Collection (Shanghai: East China Normal University) (in Chinese) [杨振宁1998杨振宁文集(上海:华东师范大学出版社)]
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