## 留言板

 引用本文: 马晨明. 圆柱形容器中自由表面波的三波内共振相互作用[J]. 应用数学和力学, 2003, 24(12): 1249-1257.
MA Chen-ming. Internal Resonant Interactions of Three Free Surface-Waves in a Circular Cylindrical Basin[J]. Applied Mathematics and Mechanics, 2003, 24(12): 1249-1257.
 Citation: MA Chen-ming. Internal Resonant Interactions of Three Free Surface-Waves in a Circular Cylindrical Basin[J]. Applied Mathematics and Mechanics, 2003, 24(12): 1249-1257.

## 圆柱形容器中自由表面波的三波内共振相互作用

###### 作者简介:马晨明(1977- ),女,山东菏泽人,博士生(E-mail:chenmingma@sina.com).
• 中图分类号: O353.2

## Internal Resonant Interactions of Three Free Surface-Waves in a Circular Cylindrical Basin

• 摘要: 由Luke变分原理导出了圆柱形容器中自由毛细重力表面波的基本方程.首先对速度势和自由面波高作Galerkin展开,用多重尺度法导出了控制方程前二阶摄动方程,在此基础上讨论了三个波二阶内共振的非线性相互作用,导出了三波内共振的非线性耦合作用方程和守恒律.针对非退化的作用方程,分析了相平面上平衡点的位置,研究了参数对应共振与非共振的各种情况,在不同参数情况下求出二阶作用方程的稳态解并分析了解的稳定性态,还讨论了只在有限时间内有效的解.分析表明,在非退化情况下,由于初始条件不同,3个波之间能量传递的模式不尽相同,有可能能量在3波之间周期性传递,亦可能单波的能量有衰减或增长.
•  [1] Mc Goldrick L F.Resonant interactions among capillary-gravity waves[J].J Fluid Mech,1965,21:305-331. [2] Hasselmann K.On the nonlinear energy transfer in a gravity wave spectrum-Part 1:General theory[J].J Fluid Mech,1962,12:481-500. [3] Annenkov S Yu,Shrira V I.Physical mechanisms for sporadic wind wave horse-shoe patterns[J].Eur J Mech B/Fluids,1999,18(3):463-474. [4] Miles J W.Nonlinear surface waves in closed basins[J].J Fluid Mech,1976,75:419-448. [5] Miles J W.Internally resonant surface waves in a circular cylin der[J].J Fluid Mech,1984,149:1-14. [6] Hammack J L,Henderson D M.Resonant interactions among surface water waves[J].Annu Rev Fluid Mech,1993,25:55-97. [7] Benielli D,Sommeria J.Excitation and breaking of internal gravity waves by parametric instability[J].J Fluid Mech,1998,374:117-144. [8] Shivamoggi B K.Non-linear resonant three-wave interactions of sound waves[J].J Sound Vib,1994,176(2):271-277. [9] MA Chen-ming.Resonant interactions of free and forced capillary-gravity surface waves in a circular cylindrical basin[D].the dissertation submitted for the Master's Degree.Shanghai:Shanghai University,2002.

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##### 出版历程
• 收稿日期:  2002-05-13
• 修回日期:  2003-07-02
• 刊出日期:  2003-12-15

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