| 快变海底和自由表面流共振生成的弱非线性Stokes波 |
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| 引用本文： | 黄虎,周锡.快变海底和自由表面流共振生成的弱非线性Stokes波[J].应用数学和力学,2001,22(6):651-660. |
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| 作者姓名： | 黄虎 周锡 |
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| 作者单位： | 1.天津大学建筑工程学院, 天津300072; |
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| 基金项目： | 国家教委博士点基金资助项目(940562)；国家高性能计算基金资助项目(96103) |
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| 摘 要： | 运用WKBJ型摄动逼近法,对环境流同沙纹海底共振产生的自由表面水波的非线性效应进行了研究。沙纹海底由缓变平均水深部分和快变海底部分叠加构成。根据对快变海底波长的不同选取,可以相应地激发环境流同非平整海底的同步共振、超谐波共振和次谐波共振,由此产生自由表面波运动。对次谐波共振进行了详细考察。对于定常流自治动力系统,对可能出现的非线性各种稳态及其稳定性进行了探讨。假如环境流具有一个小振动分量,动力系统成为非自治的,则将发生混沌现象。
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| 关 键 词： | 非线性共振 弱非线性Stokes波 自由表面流 沙纹海底 动力系统 |
| 文章编号： | 1000-0887(2001)06-0651-10 |
| 收稿时间： | 1999-09-03 |
| 修稿时间： | 1999年9月3日 |
On the Resonant Generation
of Weakly Nonlinear Stokes Waves in Regions With Fast Varying Topography and Free Surface
Current |
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| HUANG Hu ,ZHOU Xi_reng.On the Resonant Generation
of Weakly Nonlinear Stokes Waves in Regions With Fast Varying Topography and Free Surface
Current[J].Applied Mathematics and Mechanics,2001,22(6):651-660. |
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| Authors: | HUANG Hu ZHOU Xi_reng |
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| Institution: | 1.School of Civil Engineering, Tianjin University, Tianjin 300072, P R China;2.Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P R China |
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| Abstract: | The effect of nonlinearity on the free surface wave resonated by an incident flow over rippled beds, which consist of fast varying topography superimposed on an otherwise slowly varying mean depth, is studied using a WKBJ_type perturbation approach. Synchronous, superharmonic and in particular subharmonic resonance were selectively excited over the fast varying topography with corresponding wavelengths. For a steady current the dynamical system is autonomous and the possible nonlinear steady states and their stability were investigated. When the current has a small oscillatory component the dynamical system becomes non_autonomous, chaos is now possible. |
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| Keywords: | nonlinear resonance weakly nonlinear Stokes waves a free surface current rippled beds dynamical system |
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