Knowledge Management System of Institue of Mechanics, CAS
| 非传播孤立波的数值模拟 | |
| 芮炎炎 | |
| Thesis Advisor | 周显初 |
| 1999 | |
| Degree Grantor | 中国科学院研究生院 |
| Place of Conferral | 北京 |
| Subtype | 硕士 |
| Degree Discipline | 流体力学 |
| Keyword | 孤立波 非传播孤立波 立方schrodinger方程 数值模拟 Solitary Waves Non-propagating Solitary Waves Cubic Schrodinger Equation Numerical Simulation |
| Other Abstract | 非传播孤立波是近年来由中国学者发现的一种独特的孤立水波。本文通过数值求解非传播孤立波目前公认的控制方程-Miles导出的一个带共轭项的非线性立方Schrodinger方程，对非传播孤立波进行数值模拟。本文针对非传播孤立波的各种性质，作了大量的数值计算工作，并与实验观察的现象及人们对非传播孤立波的理论研究结果进行了比较和分析。为了得到稳定的非传播孤立波，本文讨论了Miles方程中的线性阻尼系数a的值，计算表明，线性阻尼a对能否形成稳定的非传播孤立波影响很大，在某些情况下，Laedke等人提出的Miles方程的非传播孤立波解的稳定性条件与我们对Miles方程的数值模拟的结果相当一致，a可在满足稳定性条件的区间内取值，但也发现在某些情况下Laedke等人的稳定性条件与我们的数值模拟不完全符合，证明Laedke等人关于非传播孤立波的稳定性条件只是一个必要条件，而不是充分条件。本文研究了两个非传播孤立波的相互作用，数值模拟表明，两个波的作用模式依赖于系统的参数，只有适当大小的外驱动频率和振幅及线性阻尼a可算出两个非传播孤立波周而复始的相互作用现象来，参数不合适时，两个波可能最终合并为一个非传播孤立波而不再分离，也可能彼此不发生作用，保持各自的独立。对不同的初始扰动及其演化的计算表明，要形成单个稳定的非传播孤立波，则初始扰动必须适当，否则扰动可能消失或发展成多个孤立波。关于形成非传播孤立波所需的外驱动条件，计算结果表明，只有适当大小的外驱动频率和振幅可形成稳定的非传播孤立波，数值结果可以描述驱动频率的上限和驱动振幅的上下限，但无法描述驱动频率的下限。我们的数值模拟工作说明Miles方程确实较好的描述了非传播孤立波的物理模型，该方程可以解释许多关于非传播孤立波的物理特性。但Miles方程无法对非传播孤立波的某些实验现象作出解释，因而有待于进一步研究改进。; Found by a Chinese visiting scholar in 1984, the non-propagating solitary wave is a kind of unique soliton in the field of Fluid Dynamics. The present thesis tried to simulate the non-propagating solitary wave by solving the Miles' nonlinear cubic Schrodinger equation with complex conjugate term numerically, which is the accepted governing equation of the non-propagating solitary wave at present. Through the present numerical model, many characters of the non-propagating solitary wave were investigated, and the numerical results were carefully compared with the experimental and theoretical results. The value of the linear damping a of Mile's equation to get a stable non-propagating solitary wave was discussed in the thesis. The computations showed that the linear damping a is the key to obtain a stable non-propagating solitary wave in the numerical simulation. In some cases, Laedke's stability condition of the non-propagating solitary wave highly agrees with our numerical simulation of Miles' equation. To produce and maintain a stable non-propagating solitary wave the linear damping a can adopt values in the region, which satisfies the stability condition. Yet there existed some situations that Laedke's stability analysis was in conflict with our numerical results. It elucidated that Laedke's stability condition of the non-propagating solitary wave is not a sufficient condition but a necessary condition. The interaction of two non-propagating solitary waves was studied in the thesis. Our numerical results indicated that the pattern of the interaction of two solitary waves depends on the parameters of the system. To obtain a typical interaction of two solitary waves, the frequency and amplitude of the external vibration and the linear damping a must be strictly appropriate. Otherwise the two solitary waves will combine to a single and never separated non-propagating solitary wave or both of them maintain independent development without any interaction. The numerical simulation of initial disturbances and their developments proved that to form a single stable non-propagating solitary wave requires a appropriate initial disturbance, otherwise the initial disturbance will possibly develop to several solitary waves or vanish at last. About the requirement of the external drives in the water trough to obtain a non-propagating solitary wave, the numerical results indicated that only suitable external drives can inspire a non-propagating solitary wave. Our numerical simulation described the upper and lower limits of the amplitude and the upper limits of the frequency, but no lower limits of the frequency were found in our computation. In brief, it was proved that Miles's equation well describes the physics model of the non-propagating solitary wave. The equation can explain many properties of the non-propagating solitary wave. However, it is unable to explicate some other experimental results regarding the non-propagating solitary wave. So, Miles equation should be studied and improved further. |
| Call Number | 29856 |
| Language | 中文 |
| Document Type | 学位论文 |
| Identifier | http://dspace.imech.ac.cn/handle/311007/23676 |
| Collection | 力学所知识产出(1956-2008) |
| Recommended Citation GB/T 7714 | 芮炎炎. 非传播孤立波的数值模拟[D]. 北京. 中国科学院研究生院,1999. |
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| 非传播孤立波的数值模拟.pdf（11193KB） | 开放获取 | -- | Application Full Text | |||
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