港湾振荡下港内低频波浪的数值研究
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摘要
该文采用完全非线性Boussinesq模型模拟了由双色波群诱发的狭长型矩形港内的二阶长波共振现象。基于一个港内低频波浪的分离方法,系统研究了港湾处于最低的四个共振模态下入射短波的波长和波幅对港内锁相长波和自由长波的波幅以及它们的相对成分的影响。研究表明:在该文所研究的特定港口和短波频率、波幅范围内,锁相长波和自由长波波幅均随着短波波长的增大而增大,并且第一共振模态下的锁相长波与自由长波的振幅比往往要大于其他三个模态下的值。在各共振模态下,锁相长波与自由长波的波幅均随入射短波波幅成平方关系变化,但它们的振幅比却几乎不受入射短波波幅的影响。
The second-order long wave oscillation phenomena inside an elongated rectangular harbor induced by bichromatic wave groups are simulated with a fully nonlinear Boussinesq model. Based on a low-frequency wave separation procedure, this paper investigates how the amplitudes of bound and free long waves and their relative components change with respect to the wavelengths and amplitudes of the incident short waves under the condition of the lowest four resonant modes systematically. It shows that for the given harbor and the given ranges of the short wave frequency and amplitude, the amplitudes of bound and free long waves increase with the short wavelength; and the ratios of them in the first mode are inclined to be larger than those in the next three modes. For all the four resonant modes, both of the amplitudes of bound and free long waves change quadratically with the amplitudes of the incident short waves. However, the ratios of them are almost not affected by the short wave amplitudes.
The second-order long wave oscillation phenomena inside an elongated rectangular harbor induced by bichromatic wave groups are simulated with a fully nonlinear Boussinesq model. Based on a low-frequency wave separation procedure, this paper investigates how the amplitudes of bound and free long waves and their relative components change with respect to the wavelengths and amplitudes of the incident short waves under the condition of the lowest four resonant modes systematically. It shows that for the given harbor and the given ranges of the short wave frequency and amplitude, the amplitudes of bound and free long waves increase with the short wavelength; and the ratios of them in the first mode are inclined to be larger than those in the next three modes. For all the four resonant modes, both of the amplitudes of bound and free long waves change quadratically with the amplitudes of the incident short waves. However, the ratios of them are almost not affected by the short wave amplitudes.
引文
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[2]López M,Iglesias G.Long wave effects on a vessel at berth[J].Applied Ocean Research,2014,47:63―72.
[3]Bowers E C.Harbour resonance due to set-down beneath wave groups[J].Journal of Fluid Mechanics,1977,79(1):71―92.
[4]Mei C C,Agnon Y.Long-period oscillations in a harbour induced by incident short waves[J].Journal of Fluid Mechanics,1989,208:595―608.
[5]Wu J K,Liu P L-F.Harbour excitations by incident wave groups[J].Journal of Fluid Mechanics,1990,217:595―613.
[6]Thotagamuwage D T,Pattiaratchi C B.Observations of infragravity period oscillations in a small marina[J].Ocean Engineering,2014,88:435―445.
[7]Guerrini M,Bellotti G,Fan Y,et al.Numerical modelling of long waves amplification at Marina di Carrara Harbour[J].Applied Ocean Research,2014,48:322―330.
[8]高俊亮,马小舟,王岗,等.波群诱发的非线性港湾振荡中低频波浪的数值研究[J].工程力学,2013,30(2):50―57.Gao Junliang,Ma Xiaozhou,Wang Gang,et al.Numerical study on low-frequency waves in nonlinear harbor resonance induced by wave groups[J].Engineering Mechanics,2013,30(2):50―57.(in Chinese)
[9]Kirby J T.Boussinesq models and applications to nearshore wave propagation,surfzone processes and wave-induced currents[J].Elsevier Oceanography Series,2003,67:1―41.
[10]Kirby J T,Long W,Shi F.Funwave 2.0 Fully nonlinear boussinesq wave model on curvilinear coordinates[R].Newark:Center for Applied Coastal Research Dept.of Civil&Environmental Engineering,University of Delaware,2003.
[11]Wei G,Kirby J T,Grilli S T,et al.A fully nonlinear Boussinesq model for surface waves.Part 1.Highly nonlinear unsteady waves[J].Journal of Fluid Mechanics,1995,294:71―92.
[12]王岗,马小舟,马玉祥,等.短波对港池长周期振荡的影响[J].工程力学,2010,27(4):240―245.Wang Gang,Ma Xiaozhou,Ma Yuxiang,et al.Long-period harbor resonance induced by short waves[J].Engineering Mechanics,2010,27(4):240―245.(in Chinese)
[13]Losada I J,Gonzalez-Ondina J M,Diaz-Hernandez G,et al.Numerical modeling of nonlinear resonance of semi-enclosed water bodies:Description and experimental validation[J].Coastal Engineering,2008,55(1):21―34.
[14]Mei C C.The applied dynamics of ocean surface waves[M].New York:Wiley,1983:183―206.
[15]Longuet-Higgins M S,Stewart R W.Radiation stresses in water waves;a physical discussion,with applications[J].Deep-Sea Research,1964,11:529―562.
[16]Longuet-Higgins M S,Stewart R W.Radiation stress and mass transport in gravity waves,with application to‘surf beat’[J].Journal of Fluid Mechanics,1962,13(4):481―504.