Stokes波高阶谐波系数递推的数值计算*
Numerical Calculation For The Coefficients of Stokes Harmonic Waves of High Order
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摘要: 本文用W.H.Hui提出的方法,在半物理平面内重新表述了Stokes波的数学模型和边界条件,提出了两种更有效的数值计算方法来获得Stokes波高阶谐波系数,并可递推至无穷.通过小参数转换,重新得到了Cokelet(1977)的波速和半波高的摄动展开式.Abstract: This paper has reformulated the mathematical model and boundary conditions in the semi-physical plan (x,ψ)by using W.H.Hui's method and suggested two new ways of numerical calculation for the coefficients of Stokes harmonic waves of high order. By transforming the perturbation parameter into a new one, we refind Cokelet's results (1977) of phase speed and semi-waveheight expressions.
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[1] 李家春,深水波理论的新进展,力学进展,16,(1986),175-184. [2] Schwartz, L.W., Computer extension and analytic continuation of Stokes cxpansion for gravity waves, J.F.M., 62 (1974), 553-578. [3] Cokelet, E.D., Steep gravity waves on water of arbitrary umform depth, Phil. Trans. Roy. Soc., A 286 (1977), 183-230. [4] Hui, W.H., A new approach to steady flows with free surfaces, J. of Appl. Math. and Phys. (Z.A.M.P) 33, September (1982), 569-589. [5] Dubren Jacotin, M.L., Sur la determination rigoureuse des ondes permanants periodiques d'ampleur finie, J. Math. Pure et Appl., 13 (1934). [6] Longuet-Higgins, M.S., Integral properties of periodic gravity waves of finite amplitude, Proc. Roy. Soc. Lond., A 342. (1975), 157-174. [7] 李家春,摄动级数收敛性的改进及其应用,《摄动法及其在力学中的应用》(钱伟长主编),科学出版社(1981), 263-309. -
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