Stability of steady gravity waves generated by a moving localised pressure disturbance in water of finite depth
Stability of steady gravity waves generated by a moving localised pressure disturbance in water of finite depth
复制标题
有限深度水中移动局部压力扰动产生的稳态重力波的稳定性
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
M. Maleewong
中科院分区：
文献类型：
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作者：
R. Grimshaw;M. Maleewong
研究了在有限水深的水中，由移动的局部压力扰动所强迫的定常波的稳定性。对于亚临界流动，定常波采取下游波列的形式，但对于超临界流，每个特定的强迫项都有一个解分支，每个弗劳德数有两个局域类孤子解，一个小幅度解和一个大幅度解。我们的主要目的是通过从适当的初始条件模拟非定常发展来数值研究这些定常波的稳定性。我们使用一个在跨临界区域适用于弱强迫的强迫Korteweg-de Vries模式和一个完全非线性的边界积分模拟。用强迫Korteweg-de Vries模式模拟的结果与完全非线性的模拟结果吻合较好，当小压力强迫的Froude数接近1时，如预期的那样。我们发现定常的亚临界下游波列是稳定的。对于超临界流体，小幅度固液两相流动具有较好的可比性。
We study the stability of the steady waves forced by a moving localised pressure disturbance in water of finite depth. The steady waves take the form of a downstream wavetrain for subcritical flow, but for supercritical flow there is a solution branch for each specified forcing term, which has two localised solitary-like solutions for each Froude number, a small-amplitude and a large-amplitude solution. Our main purpose is to numerically investigate the stability of these steady waves by simulating the unsteady development from appropriate initial conditions. We use a forced Korteweg-de Vries model valid in the transcritical regime for weak forcing, and a fully nonlinear boundary integral simulation. The simulations using the forced Korteweg-de Vries model are in good agreement with the fully nonlinear simulations when the Froude number is near unity for small pressure forcing, as expected. We find that the steady subcritical downstream wavetrain is stable. For supercritical flow, the small-amplitude soli...