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Approximate solution of nonlinear triad interactions of acoustic–gravity waves in cylindrical coordinates
Communications in Nonlinear Science and Numerical Simulation ( IF 3.9 ) Pub Date : 2020-09-06 , DOI: 10.1016/j.cnsns.2020.105514
Usama Kadri , Zhan Wang

The three-dimensional radial propagation of wave disturbances over a slightly compressible fluid of constant depth is discussed. We focus on resonant triads comprising two gravity modes and one acoustic mode. The derivation of the evolution equations in a non-integral form is made possible by approximating the radial solution by cosine functions in two regions, inner and outer, that are matched at a location where all relevant derivatives are in agreement with the exact Bessel solution. When the interaction takes place in the inner region of all modes, the amplitude evolution equations are found to be similar to the two-dimensional case. However, focusing of one gravity mode and de-focusing of the other is observed when the interaction involves an inner region of the acoustic mode, and outer regions of the gravity modes.



中文翻译:

圆柱坐标系中重力波的非线性三重相互作用的近似解

讨论了波扰动在恒定深度的可压缩流体上的三维径向传播。我们专注于包括两个重力模式和一个声学模式的共振三重轴。通过用两个区域(内部和外部)中的余弦函数逼近径向解,可以以非整数形式推导演化方程,这两个区域在所有相关导数与精确的Bessel解一致的位置匹配。当相互作用发生在所有模式的内部区域时,发现振幅演化方程类似于二维情况。然而,当相互作用涉及声学模式的内部区域和重力模式的外部区域时,观察到一种重力模式的聚焦和另一种重力模式的散焦。

更新日期:2020-09-06
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