Harmonic stability of standing water waves
Harmonic stability of standing water waves
复制标题
驻水波的谐波稳定性
DOI：
10.1090/qam/1552
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发表时间：
2020
影响因子：
0.8
通讯作者：
Wilkening, Jon
中科院分区：
文献类型：
--
作者：
Wilkening, Jon
使用 Floquet 理论开发了一种数值方法来研究驻水波的稳定性和自由表面欧拉方程的其他时间周期解。单向算子的傅里叶截断是通过求解关于驻波的线性化欧拉方程来计算的，初始条件范围涵盖所有傅里叶模式直至给定波数。截断单峰算子的特征值通过相应特征函数的平均波数进行计算和排序，我们将其引入作为仅保留精确计算的 Floquet 乘子的方法。平均波数与零振幅驻波的分析结果相匹配，有助于识别哪些 Floquet 乘数发生碰撞并离开单位圆以形成不稳定的本征模式或重新加入单位圆以恢复稳定。对于深水中的驻波，大多数波峰加速度低于的波对于谐波扰动是线性稳定的；然而，我们发现在较低值下存在一些不稳定的气泡，这些气泡在以前的文献中没有报道过。我们还研究了深水或浅水中几种新的或最近发现的时间周期重力毛细管波或重力波的稳定性，发现了一些对谐波扰动稳定的大振幅波的例子，而其他则不稳定。还提出了一种通过解决线性分配问题来匹配两个附近驻波的 Floquet 乘数的新方法，以通过从零振幅状态到大振幅驻波的同伦来跟踪各个特征值。
A numerical method is developed to study the stability of standing water waves and other time-periodic solutions of the free-surface Euler equations using Floquet theory. A Fourier truncation of the monodromy operator is computed by solving the linearized Euler equations about the standing wave with initial conditions ranging over all Fourier modes up to a given wave number. The eigenvalues of the truncated monodromy operator are computed and ordered by the mean wave number of the corresponding eigenfunctions, which we introduce as a method of retaining only accurately computed Floquet multipliers. The mean wave number matches up with analytical results for the zero-amplitude standing wave and is helpful in identifying which Floquet multipliers collide and leave the unit circle to form unstable eigenmodes or rejoin the unit circle to regain stability. For standing waves in deep water, most waves with crest acceleration beloware found to be linearly stable to harmonic perturbations; however, we find several bubbles of instability at lower values ofthat have not been reported previously in the literature. We also study the stability of several new or recently discovered time-periodic gravity-capillary or gravity waves in deep or shallow water, finding several examples of large-amplitude waves that are stable to harmonic perturbations and others that are not. A new method of matching the Floquet multipliers of two nearby standing waves by solving a linear assignment problem is also proposed to track individual eigenvalues via homotopy from the zero-amplitude state to large-amplitude standing waves.
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大振幅驻水波波峰处的自相似性破裂。
影响因子：
8.6
作者：
J. Wilkening
通讯作者：
J. Wilkening
威尔顿波纹的不稳定性
DOI：
--
发表时间：
2015
期刊：
影响因子：
--
作者：
O. Trichtchenko;B. Deconinck;J. Wilkening
通讯作者：
J. Wilkening
影响因子：
3.7
作者：
P. J. Bryant;M. Stiassnie
通讯作者：
M. Stiassnie
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影响因子：
3.7
作者：
D. Henderson;J. Miles
通讯作者：
J. Miles
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影响因子：
3.7
作者：
P. Concus
通讯作者：
P. Concus