A Strongly-Nonlinear Model for Water Waves in Water of Variable Depth—The Irrotational Green-Naghdi Model
A Strongly-Nonlinear Model for Water Waves in Water of Variable Depth—The Irrotational Green-Naghdi Model
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DOI：
10.1115/1.1537722
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发表时间：
2003-02
影响因子：
1.6
通讯作者：
J. W. Kim;K. Bai;R. Ertekin;W. Webster
中科院分区：
文献类型：
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作者：
J. W. Kim;K. Bai;R. Ertekin;W. Webster
总结和结论无旋Green-Naghdi方程是在有限水深条件下导出的，并通过数值试验证明了其自收敛性和准确性。IGN方程的行波解的线性和非线性色散随方程级数的增加而收敛到已知的精确解。对于孤立波爬高和倾斜海滩上非线性浅滩等非定常问题，IGN方程的数值解也是收敛的。看来IGN Level 3方程可以为大多数工程问题提供非常精确的解。IGN Level2方程组的精度与最优WKGS方程组相当，而WKGS方程组被认为是最精确的Boussinesq型模型，一旦IGN Level2方程组在每一层的精度得到提高，在将来应用模型求解各种水波问题时就可以选择最优的方程组。致谢JWK和RCE已得到ONR的支持，批准号N 000114 -98-1-0800;项目经理是C博士。林伍德文森特。JWK还得到了韩国科学和工程基金会的支持，用于目前工作的初始阶段。KJB得到韩国科学和工程基金会的R 01 -2000-00321号资助。这些赠款在此表示感谢~索斯特第6056号！
Summary and Conclusions The Irrotational Green-Naghdi equations are derived for finitewater-depth conditions, and tested numerically to show their self-convergence and accuracy. The linear and nonlinear dispersion ofthe permanent progressive wave solutions of the IGN equationsconverged to known exact solutions as the Level of the equationsincreases. The numerical solution of the IGN equations for un-steady problems, such as the run-up of solitary waves and nonlin-ear shoaling over a sloping beach, also converged. It appears thatthe IGN Level 3 equations can provide very accurate solutions formost engineering problems. The IGN Level 2 equations showedcomparable accuracy with the optimal WKGS equation set, whichis known to be the most accurate Boussinesq-type model.Once the accuracy of the IGN equations at each level is iden-tified, the level can be optimally chosen in future application ofthe model to various water-wave problems. Acknowledgment JWK and RCE have been supported by the ONR, Grant No.N000114-98-1-0800; the Program Manager was Dr. C. LinwoodVincent. JWK was also supported by Korea Science and Engi-neering Foundation for an initial stage of the present work. KJBwas supported by Grant No. R01-2000-00321 from the KoreaScience and Engineering Foundation. These grants are gratefullyacknowledged ~SOEST No. 6056!.