The stability of capillary waves on fluid sheets
The stability of capillary waves on fluid sheets
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DOI：
10.1017/jfm.2016.588
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发表时间：
2016-09
影响因子：
3.7
通讯作者：
M. Blyth;E. Părău
中科院分区：
文献类型：
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作者：
M. Blyth;E. Părău
研究了无粘流体面上有限振幅毛细波的线性稳定性。与Tiron和Choi（J. Fluid Mech.，第696卷，2012年，pp. 402-422），以确定在无限深的流体上的克拉珀波的稳定性，是通过扩展Dyachenko等人（Phys. Lett. A，vol. 221（1），1996 a，pp. 73-79）转换为能够在板的上表面和下表面上捕获一般周期波的形式，包括Kinnersley（J.FluidMech.，第77（02）卷，1976年，第100页。229-241）。主要的，令人惊讶的结果是，对称和反对称Kinnersley波是不稳定的小超谐扰动。波也是不稳定的亚谐扰动。针对Kinnersley族中的一系列稳定波以及沿着Blyth & Vanden-Broeck（J. Fluid Mech.，第507卷，2004年，第100页。255-264）。完全非线性非定常方程的时间积分证实了不稳定的结果。证据提出了超谐波不稳定性的非线性波通过碰撞的特征值的虚轴上出现具有相同的Krein签名。
The linear stability of finite-amplitude capillary waves on inviscid sheets of fluid is investigated. A method similar to that recently used by Tiron & Choi (J. Fluid Mech., vol. 696, 2012, pp. 402–422) to determine the stability of Crapper waves on fluid of infinite depth is developed by extending the conformal mapping technique of Dyachenko et al. (Phys. Lett. A, vol. 221 (1), 1996a, pp. 73–79) to a form capable of capturing general periodic waves on both the upper and the lower surface of the sheet, including the symmetric and antisymmetric waves studied by Kinnersley (J. Fluid Mech., vol. 77 (02), 1976, pp. 229–241). The primary, surprising result is that both symmetric and antisymmetric Kinnersley waves are unstable to small superharmonic disturbances. The waves are also unstable to subharmonic perturbations. Growth rates are computed for a range of steady waves in the Kinnersley family, and also waves found along the bifurcation branches identified by Blyth & Vanden-Broeck (J. Fluid Mech., vol. 507, 2004, pp. 255–264). The instability results are corroborated by time integration of the fully nonlinear unsteady equations. Evidence is presented for superharmonic instability of nonlinear waves via a collision of eigenvalues on the imaginary axis which appear to have the same Krein signature.