弱非线性斯托克斯波在非平整海底上传播的新型抛物型方程

黄虎; 周锡礽; 吕秀红

弱非线性斯托克斯波在非平整海底上传播的新型抛物型方程

天津大学建筑工程学院港口工程系, 天津300072

基金项目: 国家教委博士点基金9405623;国家高性能计算基金96103

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- 文章访问数: 744
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出版历程
- 收稿日期: 1998-08-07
- 修回日期: 2000-01-03

A new parabolic equation for propagation of weakly nonlinear Stokes waves over uneven bottom

Department of Harbor Engineering, School of Civil Engineering, Tianjin University, Tianjin 300072

摘要

摘要: 由于缓坡方程计算量大和其本身的缓坡假定而在实际应用中受到了限制,故对斯托克斯波在非平整海底(适用于缓坡和陡坡地形)上传播的Liu和Dingemans的三阶演化方程进行抛物逼近,得到一个新的非线性抛物型方程,它能够包含同类方程未曾考虑的二阶长波效应.通过数值计算结果与Berkhoff等人的经典实验数据的比较,证明所提出的抛物型模型理论具有较高的精度.
- 弱非线性斯托克斯波 /
- 非平整海底 /
- 二阶长波 /
- 非线性抛物型方程 /
- 浅滩实验
Abstract: Considering the limitation of mild-slope equation, requiring a computational effort and the mild-slope assumption, in practical engineering, a new nonlinear parabolic equation including the second-order long-waves ignored in the previous like equation is obtained by way of the parabolic approximation on Liu and Dingemans's third order evolution equation for Stokes waves propagating over uneven bottom applicable to mild and abrupt topography.The model theory can provide more accurate predictions by comparison of the numerical model results with the classic experimental data of Berkhoff et al.
- Weakly nonlinear Stokes waves /
- uneven bottom /
- second-order long-waves /
- nonlinear parabolic equation /
- the shoal experiment

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参考文献(15)

Liu P L-F, Mei C C. Water motion on a beach in the presence of a breakwater 1. Waves. J Geophys Res, 1976, 81:3 079～3 084

Berkhoff J C W. Computation of combined refraction-diffraction. Proc 13th Int Conf Coastal Eng. Vancouver:ASCE, 1972. 471～490

Radder A C. On the parabolic equation method for water-wave propagation. J Fluid Mech, 1979, 95:159～176

Kirby J T, Dalrymple R A. A parabolic equation for the combined refraction-diffraction of Stokes waves by mildly varying to pography. J Fluid Mech, 1983, 136:453～466

Liu P L-F, Tsay T-K. Refraction-diffraction model for weakly nonlinear water waves. J Fluid Mech, 1984, 141:265～274

Dalrymple R A, Kirby J T. Models for very wide-angle water waves and wave diffraction. J Fluid Mech, 1988, 192:33～50.

林刚,邱大洪.新抛物型缓底坡波动方程.水利学报,1999,(3):59～63

陶建华,韩光,龙文.浅水区大面积波浪场数值计算方法的研究.第九届全国海岸工程学术讨论会北京:海洋出版社,1999.17～24

Kirby J T. A general wave equation for waves over rippled beds. J Fluid Mech, 1986, 162:171～186

Liu P L-F, Dingemans M W. Derivation of the third-order evolution equatons for weakly nonlinear water propagating over uneven bottoms. Wave Motion, 1989, 11:41～64

Chandrasekera C N, Cheung K F. Extended linear refraction-diffraction model. J Wtrwy, Port, Coast, and Oc Engr, 1997, 123(5):280～286

Mei C C, Benmousa C. Long waves induced by short wave groups over an uneven bottom. J Fluid Mech, 1984, 139:219～350

Wu J K, Liu P L-F. Harbor excitations by incident wave groups. J Fluid Mech, 1990, 217:595～613

Roelvink J K, Stive MJ F. Bar-generating cross-shore flow mechanism on a beach. J Geophys Res, 1989, 94:4 785～4 800

Berkhoff J C W, Booij N, Radder A C. Verification of numerical wave propagation models for simple harmonic linear waves.Coastal Eng, 1982, 6:255～279

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文章访问数: 744
HTML全文浏览量: 8
PDF下载量: 569
被引次数: 0

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