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无穷多海洋表面波相互作用的能量守恒和共振条件

黄虎

黄虎. 无穷多海洋表面波相互作用的能量守恒和共振条件[J]. 应用数学和力学, 2014, 35(5): 565-571. doi: 10.3879/j.issn.1000-0887.2014.05.010
引用本文: 黄虎. 无穷多海洋表面波相互作用的能量守恒和共振条件[J]. 应用数学和力学, 2014, 35(5): 565-571. doi: 10.3879/j.issn.1000-0887.2014.05.010
HUANG Hu. Energy Conservation and Resonance Conditions for Interactions of an Infinite Number of Ocean Surface Waves[J]. Applied Mathematics and Mechanics, 2014, 35(5): 565-571. doi: 10.3879/j.issn.1000-0887.2014.05.010
Citation: HUANG Hu. Energy Conservation and Resonance Conditions for Interactions of an Infinite Number of Ocean Surface Waves[J]. Applied Mathematics and Mechanics, 2014, 35(5): 565-571. doi: 10.3879/j.issn.1000-0887.2014.05.010

无穷多海洋表面波相互作用的能量守恒和共振条件

doi: 10.3879/j.issn.1000-0887.2014.05.010
基金项目: 全国优秀博士学位论文作者专项资金(200428);国家自然科学基金(11172157);上海市浦江人才计划(12PJD001);上海高校创新团队建设资助项目
详细信息
    作者简介:

    黄虎(1964—),男,新疆石河子人,教授,博士,博士生导师(Tel: +86-21-56332947; E-mail: hhuang@shu.edu.cn)

  • 中图分类号: O353.2

Energy Conservation and Resonance Conditions for Interactions of an Infinite Number of Ocean Surface Waves

Funds: The National Natural Science Foundation of China (11172157)
  • 摘要: 依照能量守恒定律和业已证明的海洋表面波之波-波共振条件,通过将Hamilton能量泛函展开至一个7阶对称的积分幂级数,给出了一个典型的“3-4-5-6-7波相互作用系统的共振条件组”.进而归纳、推论出一个一般的“无穷多波相互作用系统的共振条件组”,据此可显著地改观目前的基本海洋波湍流理论格局.
  • [1] Phillips O M. On the dynamics of unsteady gravity waves of finite amplitude—part 1: the elementary interactions [J].Journal of Fluid Mechanics,1960,9(2): 193-217.
    [2] Hasselmann K. On the non-linear energy transfer in a gravity-wave spectrum—part 1: general theory[J].Journal of Fluid Mechanics,1962,12(4): 481-500.
    [3] Zakharov V E. Stability of periodic waves of finite amplitude on the surface of a deep fluid[J].Journal of Applied Mechanics and Technical Physics,1968,9(2): 190-194.
    [4] Dyachenko A I, Lvov Y V. On the Hasselmann and Zakharov approaches to the kinetic equations for gravity waves[J].Journal of Physical Oceanography,1995,25(12): 3237-3238.
    [5] Arnold V I.Mathematical Methods of Classical Mechanics [M]. Berlin: Springer, 1978.
    [6] Zakharov V E, L’Vov V S, Falkovich G.Kolmogorov Spectra of Turbulence I: Wave Turbulence [M]. Berlin: Springer, 1992.
    [7] HUANG Hu. Dynamics of Surface Waves in Coastal Waters: Wave-Current-Bottom Interactions [M]. Beijing-Berlin: Higher Education Press-Springer, 2009.
    [8] Kartashova E.Nonlinear Resonance Analysis: Theory, Computation, Applications [M]. Cambridge: Cambridge University, 2011.
    [9] 邓子辰, 钟万勰. 等式约束非线性控制系统的时程精细计算[J]. 应用数学和力学, 2002,23(1): 16-22.(DENG Zi-chen, ZHONG Wan-xie. Time precise integration method for constrained nonlinear control system[J].Applied Mathematics and Mechanics,2002, 23(1): 16-22.(in Chinese))
    [10] 黄虎, 丁平兴, 吕秀红. 广义缓坡方程[J]. 应用数学和力学, 2001,22(6): 645-650.(HUANG Hu, DING Ping-xing, L Xiu-hong. Extended mild-slope equation[J].Applied Mathematics and Mechanics,2001,22(6): 645-650.(in Chinese))
    [11] Feynman R P, Leighton R B, Sands M.The Feynman Lectures on Physics [M]. Beijing: Beijing World Publishing Corporation, 2004.
    [12] 杨振宁. 杨振宁文集[M]. 上海: 华东师范大学出版社,1998.(Yang C N.Chen Ning Yang’s Collection [M]. Shanghai: The East China Normal University Publishing Press, 1998.(in Chinese))
    [13] 郭奕玲, 沈慧君. 诺贝尔物理学奖1901-2010[M]. 北京: 清华大学出版社, 2012.(GUO Yi-ling, SHEN Hui-jun.The Nobel Prize in Physics 1901-2010 [M]. Beijing: Tsinghua University Press, 2012.(in Chinese))
    [14] Mcgoldrick L F. Resonant interactions among capillary-gravity waves[J].Journal of Fluid Mechanics,1965,21(2): 305-331.
    [15] McLean J W. Instabilities of finite-amplitude gravity waves on water of finite depth[J].Journal of Fluid Mechanics,1982,114: 331-341.
    [16] Krasitskii V P. On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves[J]. Journal of Fluid Mechanics,1994,272: 1-20.
    [17] 黄虎. 海洋表面波的3-4-5波共振守恒理论[J]. 物理学报, 2013,62(13): 139201.(HUANG Hu. A theory of 3-4-5-wave resonance and conservation for ocean surface waves[J]. Acta Physica Sinica,2013,62(13): 139201.(in Chinese))
    [18] Komen G J, Cavaleri L, Donelan M, Hasselmann K, Hasselmann S, Janssen P A E M.Dynamics and Modeling of Ocean Waves [M]. Cambridge: Cambridge University Press, 1994.
    [19] Janssen P A E M.The Interaction of Ocean Waves and Wind [M]. Cambridge: Cambridge University Press, 2004.
    [20] Newell A C, Rumpf B. Wave turbulence[J].Annu Rev Fluid Mech,2011,43: 59-78.
    [21] Nazarenko S.Wave Turbulence [M]. Berlin: Springer, 2011.
    [22] Goldstein H.Classical Mechanics [M]. Massachusetts: Addison-Wesley Publishing Company, 1980.
    [23] Kolmogorov A N. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers[J].Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences,1991,434(1890): 9-13.
    [24] Kolmogorov A N. Dissipation of energy in the locally isotropic turbulence[J].Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences,1991,434(1890): 15-17.
    [25] Obukhov A M. On the distribution of energy in the spectrum of turbulent flow[J]. Dokl Akad Nauk SSSR,1941,32(1): 22-24.
    [26] Zakharov V E. Weak turbulence in media with a decay spectrum[J]. Journal of Applied Mechanics and Technical Physics,1965,6(4): 22-24.
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出版历程
  • 收稿日期:  2013-10-16
  • 修回日期:  2014-03-01
  • 刊出日期:  2014-05-15

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