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海洋通报  2010 

波浪在缓变海底上传播的一个简单数学模型

DOI: 10.11840/j.issn.1001-6392.2010.3.051

Keywords: 波浪传播,缓变海底,波形,摄动

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Abstract:

基于Liu和Shi(2008)的波浪势函数零阶、一阶近似解,采用四阶龙格-库塔法,对缓变海底上一维波浪传播理论模型进行了数值求解,并对波浪在定常坡度的斜坡地形、双曲正切地形为例的传播、变形进行了研究.为了更逼真地描述流体质点的波动特性,将在Euler坐标系下得到的解转换至Lagrange坐标下的解,并绘制Lagrange坐标下坡度为0.2的海滩上的一个波周期内临近破碎前的波形的详细变化过程.此外,计算得到了变水深区域波浪速度势以及自由面的分布,并与AthanassoulisandBelibassakis[34]的结果进行了对比,表明本文模型比保留了六个瞬息项的后者更有效.

References

[1]  Munk W H,Arthur R S,Wave intensity along a refracted ray,Gravity Waves U S National Bureau of Standards Circula,1952.
[2]  Berkhoff J C W,Computation of combined refraction-diffraction,Vancouver,ASCE,1977.
[3]  Ito Y,Tanimoto K,A method of numerical analysis of wave propagation:application to wave diffraction and refraction,Vancouver,ASCE,1972.
[4]  Radder A C,On the parabolic equation method for water-wave propagation,Journal of Fluid Mechanics,1979(1).
[5]  Kirby J T,Higher-order approximations in the parabolic equation method for water waves,Journal of Geophysical Research,1986.
[6]  Panchang V G,Wei G,Pearce B R,Briggs M J,Numerical simulation of irregular wave propagation over shoal,Journal of Waterway Port Coastal and Ocean Engineering,1990(3).
[7]  Li B,An evolution equation for water waves,Coastal Engineering,1994(3-4).
[8]  Li B,A generalized conjugate gradient model for the mild slope equation,Coastal Engineering,1994(3-4).
[9]  Eckart C,The propagation of gravity waves from deep to shallow water,1952.
[10]  Peters A S,Water waves over sloping beaches,Communications on Pure and Applied Mathematics,1952.
[11]  Roseau M,Contribution à la théorie des ondes liguides de gravité en profondeur variable,Paris,France,1958.
[12]  Biesel F,Study of wave progression in water of gradually varying depth,1952.
[13]  Battjes J A,Refraction of water waves,Journal of the Waterways Harbors and Coastal Engineering Division ASCE,1968.
[14]  Mei C C,LeMehaute B,Note on the equations of long waves over an uneven bottom,Journal of Geophysical Research,1968.
[15]  Mei C C,Tlapa G A,Eagleson P S,An asymptotic theory for water waves on beaches of mild slope,Journal of Geophysical Research,1968.
[16]  Chu V H,Mei C C,On slowly-varying Stokes waves,Journal of Fluid Mechanics,1970.
[17]  Liu P L F,Dingemans M W,Derivation of the third-order evolution equations for weakly nonlinear water waves propagating over uneven bottoms,WAVE MOTION,1989.
[18]  Massel S R,Extended refraction-diffraction equation for surface waves,Coastal Engineering,1993.
[19]  Chen Y Y,Yang B D,Ou S H,Hsu J R C,Transformation of progressive waves propagating obliquely on gentle slope,Journal of Waterway Port Coastal and Ocean Engineering,2004(4).
[20]  Chen Y-Y,Hwung H-H,Hsu H-C,Theoretical analysis of surface waves propagation on sloping bottoms:Part 1,WAVE MOTION,2005(4).
[21]  Hsu T W,Lin T Y,Wen C C,Ou S H,A complementary mild-slope equation derived using higher-order depth function for waves obliquely propagating on sloping bottom,Physics of Fluids,2006(8).
[22]  文圣常,余宙文,海浪理论与计算原理,北京:科学出版社,1984.
[23]  李德筠,沈国光,变深区浅水波的绕射和折射计算,海洋学报,1995(2).
[24]  黄虎 波-流相互作用的缓坡方程及其波作用量守恒 [J].-力学学报2005(5)
[25]  郑永红,夏进,近岸大区域水波数学模型及其数值求解,海洋学报,2000(5).
[26]  李孟国,时钟,李文丹,综合考虑多种变形因素的近岸多向不规则波传播数学模型_I_模型的建立,水动力学研究与进展,2006(4).
[27]  柳淑学,孙冰,考虑边界波浪方向的缓坡方程自适应求解模型,海洋工程,2007(1).
[28]  张洪生,赵红军,丁平兴,缪国平,非均匀水流水域波浪的传播变形,力学学报,2007(3).
[29]  Liu Y Z,Shi John Z,A theoretical formulation for wave propagations over uneven bottom,Ocean Engineering,2008(3-4).
[30]  Athanassoulis G A,Belibassakis K A,A consistent coupled-mode theory for the propagation of small-amplitude water waves over variable bathymetry regions,Journal of Fluid Mechanics,1999.
[31]  Mason M A,A study of progressive oscillatory waves in water[Technical Report No.1,1941],U.S.Army Corps of Engineers,Beach Erosion Board,.
[32]  Dean R G,Dalrymple R A,Water Wave Mechanics for Engineers and Scientists,World Scientific Publishing Co.,Pte,Ltd,1984.
[33]  Penny W G,Price A T,Diffraction of sea waves by breakwaters,Philosophical Transactions of the Royal Society London,1944.
[34]  Sommerfeld A,Mathematische Theorie der Diffraction,Mathematische Annalen,1896.
[35]  Lewy H,Water waves on sloping beaches,BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY,1946(9).
[36]  Arthur R S,Refraction of water waves by islands and shoals with circular bottom contours,Transactions American Geophysical Union,1946(2).

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