地转效应对非线性表面波的影响
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摘要
从包含完整地转效应的无粘、不可压缩流体控制方程出发,利用摄动展开法求得了地转条件下线性和非线性表面波的谐波解,并给出了频散关系式.结果表明,与仅考虑地转垂向分量相比较,在各个波速上增加了随深度增大的相位延迟因子einz.此外,地转水平分量将导致水中波动压强的增加,其物理意义是地转水平分量对海水混合起重要作用.
Considering the earth's rotation included in the governing equations of the inviscid、imcompressible fluids, the harmonic wave solutions and dispersion relations of the linear and nonlinear surface waves are obtained by using the perturbation method. The results show that the phase de-layed factor einz which is increased with the depth is added on the every wave speeds compare with the traditional approximation (only the vertical component of the earth's rotation is included in the governing equations). Moreover, the wave pressure is increased by the horizonal component of the earth's rotation, physical meaning of which is that the horizonal component of the earth's rotation react on seawater admixture.
Considering the earth's rotation included in the governing equations of the inviscid、imcompressible fluids, the harmonic wave solutions and dispersion relations of the linear and nonlinear surface waves are obtained by using the perturbation method. The results show that the phase de-layed factor einz which is increased with the depth is added on the every wave speeds compare with the traditional approximation (only the vertical component of the earth's rotation is included in the governing equations). Moreover, the wave pressure is increased by the horizonal component of the earth's rotation, physical meaning of which is that the horizonal component of the earth's rotation react on seawater admixture.
引文
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[30]孙孚,钱成春,王伟,高山.海浪波生切应力及其对流驱动作用的估计.2003,33(8)：791-798.
[31]赵强,刘式适.地球旋转水平分量对Rossby波的影响.2004,28(1)：146-150.
[32]刘永军.地转对海洋内波影响的研究：[博士学位论文].中国科学院青岛海洋研究所,2009.
[2]Boussinesq J. Theorie de 1'intumescence liquide appelee onde solitaire ou de translation, se propageant dans un canal rectangulaire. Acad.Sci.Paris Comptes Rengus.1871,72:755-759.
[3]Rayleigh J W S, Lord. The form of standing waves on the surface of running water. Proc.London Math. Soc.1883,15:69-78.
[4]Korteweg D J, de Vries G. on the change of form of long waves advancing in a rectangular canal and on a new type of long stationary waves. Phil.Mag.1895,39:422-443.
[5]Whitham G B. Linear and nonlinear waves. Wilry.1974.
[6]Kadomtsev B B, Petviashvili V I. On the stability of solitary waves in weakly dispersing media. Sov.Phys.Dokl.1970,15:539-541.
[7]Kakutani T. Effect of an uneven bottom on gravity waves. J.Phys.Soc.Japan. 1971,30(1):272-276.
[8]Matsuno Y. Nonlinear evolutions of surface gravity gravity waves of fluid of finite depth. Phys.Rev.Lett.1992,69:609-611.
[9]Matsuno Y. Two-dimensional evolution of surface gravity waves on a fluid of arbitrary depth. Phys. Rev. E.1993,47:4593-4596.
[10]Matsuno Y. Nonlinear evolution of surface gravity waves over an uneven bottom. Journal of Fluid Mechanics.1993,249:121-133.
[11]Choi W. Nonlinear evolution equations for two-dimensional surface waves in a fluid of finite depth. Journal of Fluid Mechanics.1995,295:381-394.
[12]Dyachenko A I, Kuznetsov E A, Spector M D, Zakharov V E. Analytical description of the free surface dynamics of an ideal fluid (canonical formalism and conformal mapping). Phys.Lett.A.1996,221:73-79.
[13]Dyachenko A I, Zakharov V E, Kuznetsov E A. Nonlinear dynamics of the free surface of an ideal fluid. Plasma Phys. Rep.1996,22:829-840.
[14]Choi W, Camassa R. Exact evolution Equations for surface waves. Journal of Engineering Mechanics.1999,7:756-760.
[15]Byatt-Smith J G. An exact internal equation for steady surface waves. Proc.Royal Soc. of London.1970315:405-418.
[16]Schwartz L W. Computer extension and analytic continuation of Stokes' expansion for gravity waves. Journal of Fluid Mehanics.1974,62:553-578.
[17]Cokelet E D. Steep gravity waves in water of arbitrary uniform depth. Philosophical Trans. Royal Soc. of London.1977,286:183-230.
[18]Vanden-Broeck J M, Miloh T. Computations of steep gravity waves by a refinement of Davies-Tulin approximation. SIAM J. Appl. Mathematics.1995,55:892-903.
[19]陈小刚.N层密度分层流体界面波的研究：[博士学位论文].中国科学院青岛海洋研究所,2005.
[20]Song Jinbao, Hou Yijun, He Yijun. Statistical distribution of wave-surface elevation for second-order random directional ocean waves in finite water depth. Coastal Engineering. 2002,46:51-60.
[21]Song Jinbao, Wei Enbo, Hou Yijun. Joint statistical distribution of two-point sea surface elevations in finite water depth. Coastal Engineering.2004,50:169-179.
[22]吴望一,流体力学.北京大学出版社,2000.
[23]王斌,地球物理流体动力学导论[编译],海洋出版社,1981.
[24]Chiang C.Mei, Michael Stiassnie, Dick K.-P.Yue. Theory and applications of ocean surface waves. World Scientific Publishing Co. Pte. Ltd.2005.
[25]Phillips N A. The equations of motion for a shallow rotating atmosphere and the'traditional approximation'. J.Atmos. Sci.,1966,23:626-628.
[26]Phillips N A. Reply to G. Veronis's comments on Phillips(1966). J.Atmos. Sci.,1968, 25:1155-1157.
[27]Veronis G. Comments on Phillips's (1966) proposed simplification of the equations fo motion for a shallow rotating atmosphere. J. Atmos. Sci.,1968,25:1154-1155.
[28]Wangsness R K. Comments on "The equations of motion for a shallow rotating atmosphere and the'traditional approximation'". J. Atmos. Sci.,1970,27:504-506.
[29]White A A, Bromley R A. Dynamically consistent, quasi-hydrostatic equations for global models with a complete representation of the Coriolis force. Quart. J. Roy. Meteor. Soc., 1995,121:399-418.
[30]孙孚,钱成春,王伟,高山.海浪波生切应力及其对流驱动作用的估计.2003,33(8)：791-798.
[31]赵强,刘式适.地球旋转水平分量对Rossby波的影响.2004,28(1)：146-150.
[32]刘永军.地转对海洋内波影响的研究：[博士学位论文].中国科学院青岛海洋研究所,2009.