Hamiltonian Formulation of Free Surface and Interface Motions in a Tank (N-Wave Resonant Interaction Caused by Nonlinearity of System)
Hamiltonian Formulation of Free Surface and Interface Motions in a Tank (N-Wave Resonant Interaction Caused by Nonlinearity of System)
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储罐中自由表面和界面运动的哈密顿公式（系统非线性引起的 N 波共振相互作用）
DOI：
10.1299/jsdd.2.1218
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
H. Takahara
中科院分区：
文献类型：
--
作者：
K. Hara;H. Takahara
本文研究了含有两种不同密度的不可压缩无旋流体的贮箱中的非线性液面和界面波动。为了研究时程响应和非线性特性，我们将正则方程（哈密顿方程）应用于该问题。通过求解该系统的正则方程，给出了表面波和界面波运动的时间历程和转变。本研究的目的是澄清该系统的非线性耦合特性。我们重点研究了N波共振相互作用（NWRI），并研究了NWRI的发生条件。特别是，三波共振相互作用（3WRI）引起的共振状态的时程响应的矩形和圆柱形储罐进行了讨论。另一方面，通过实验验证了理论分析的有效性。这些结果彼此吻合得很好。
This paper deals with nonlinear liquid surface and interfacial wave motions in a tank containing two incompressible irrotational fluids of different densities. In order to investigate time history responses and nonlinear characteristics, we apply canonical equations (Hamiltonian equations) to this problem. The time histories and the transitions of surface and interfacial wave motions are given by solving the canonical equations of this system. This study is intended to clarify the nonlinear coupling characteristics for this system. We have focused on the N-Wave Resonant Interaction (NWRI) and investigated occurrence conditions of the NWRI. In particular, the time history responses on the resonant state caused by the Three-Wave Resonant Interaction (3WRI) are discussed for the rectangular and the circular cylindrical tanks. On the other hand, the validly of the theoretical analysis is verified through the experiments. These results are in good agreement with each other.