Boussinesq Equations and Other Systems for Small-Amplitude Long Waves in Nonlinear Dispersive Media. I: Derivation and Linear Theory
Boussinesq Equations and Other Systems for Small-Amplitude Long Waves in Nonlinear Dispersive Media. I: Derivation and Linear Theory
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DOI：
10.1007/s00332-002-0466-4
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发表时间：
2002-08
影响因子：
3
通讯作者：
J. Bona;Min Chen;J. Saut
中科院分区：
文献类型：
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作者：
J. Bona;Min Chen;J. Saut
本文考虑的是经典 Boussinesq 系统的许多变体及其高阶概括。这些方程首先由 Boussinesq 导出，用于描述小振幅、长波长的重力波在运河水面上的双向传播。当对大型湖泊或海洋以及其他环境中的长波峰传播进行建模时，也会出现这些系统。根据色散建模，所得系统可能具有也可能不具有关于适定的静止状态的线性化。即使在适当的情况下，线性化系统也可能表现出缺乏能量守恒，这与其作为欧拉方程的近似状态相矛盾。在本脚本中，我们从自由表面流的二维欧拉方程导出了布辛涅斯克系统的四参数族，并制定了标准来帮助决定在给定的建模情况下可以选择这些方程中的哪一个。根据这些标准开始对系统进行分析。
Considered herein are a number of variants of the classical Boussinesq system and their higher-order generalizations. Such equations were first derived by Boussinesq to describe the two-way propagation of small-amplitude, long wavelength, gravity waves on the surface of water in a canal. These systems arise also when modeling the propagation of long-crested waves on large lakes or the ocean and in other contexts. Depending on the modeling of dispersion, the resulting system may or may not have a linearization about the rest state which is well posed. Even when well posed, the linearized system may exhibit a lack of conservation of energy that is at odds with its status as an approximation to the Euler equations. In the present script, we derive a four-parameter family of Boussinesq systems from the two-dimensional Euler equations for free-surface flow and formulate criteria to help decide which of these equations one might choose in a given modeling situation. The analysis of the systems according to these criteria is initiated.