Weakly nonlinear internal waves in a two-fluid system
Weakly nonlinear internal waves in a two-fluid system
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DOI：
10.1017/s0022112096002133
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发表时间：
1996-04
影响因子：
3.7
通讯作者：
W. Choi;R. Camassa
中科院分区：
文献类型：
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作者：
W. Choi;R. Camassa
本文导出了两种不同密度流体系统中自由表面上二维弱非线性波的一般演化方程。上流体层的厚度被假定为与特征波长相比是小的，但是对下层的厚度没有限制。我们考虑的情况下，一个自由的上边界的海洋动力学问题的应用程序中的相关性和一个非均匀的刚性上边界的情况下，应用到大气问题。对于浅水的特殊情况，新的方程组简化为二维内波的Boussinesq方程，而对于大的和无限的下层深度，我们可以恢复著名的中长波和Benjamin-Ono模型，分别为一维单向波传播。给出了该模型在深水中一维波浪的一些数值解，并与已知的单向模型的解进行了比较。最后，有限振幅缓慢变化的海底地形的影响包括在一个模型中，适合的情况下，当依赖于一个水平坐标是弱的。
We derive general evolution equations for two-dimensional weakly nonlinear waves at the free surface in a system of two fluids of different densities. The thickness of the upper fluid layer is assumed to be small compared with the characteristic wavelength, but no restrictions are imposed on the thickness of the lower layer. We consider the case of a free upper boundary for its relevance in applications to ocean dynamics problems and the case of a non-uniform rigid upper boundary for applications to atmospheric problems. For the special case of shallow water, the new set of equations reduces to the Boussinesq equations for two-dimensional internal waves, whilst, for great and infinite lower-layer depth, we can recover the well-known Intermediate Long Wave and Benjamin–Ono models, respectively, for one-dimensional uni-directional wave propagation. Some numerical solutions of the model for one-dimensional waves in deep water are presented and compared with the known solutions of the uni-directional model. Finally, the effects of finite-amplitude slowly varying bottom topography are included in a model appropriate to the situation when the dependence on one of the horizontal coordinates is weak.