Band gaps and the Kelvin-Helmholtz instability.
Band gaps and the Kelvin-Helmholtz instability.
复制标题
带隙和开尔文-亥姆霍兹不稳定性。
DOI：
10.1103/physreve.75.016315
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Chou,Tom
中科院分区：
文献类型：
--
作者：
Chou,Tom
我们考虑两种无粘性流体在重力存在下相互剪切并被柔性板分开的线性稳定性。速度扰动指数增长的条件被发现为板的弯曲刚度和剪切速率的函数。然后，在具有空间周期性（有周期）弯曲刚度的板存在的情况下分析这种开尔文-亥姆霍兹不稳定性，例如，由于周期性材料变化而产生的弯曲刚度。该周期系统的特征值是使用布洛赫定理（Floquet 理论）计算的，该定理对速度势和板块变形进行特定的傅立叶分解。我们推导了非埃尔米特矩阵，其特征值决定了色散关系。我们的色散关系表明，与具有相同平均弯曲刚度的均匀板相比，板周期性通常会破坏流动稳定性。然而，对于波长接近板周期偶数倍的扰动，可能会发生增强的不稳定和稳定。具有此类波长的流的敏感性源自通过板处的边界条件耦合到板周期性的非传播“布拉格反射”模式。
We consider the linear stability of two inviscid fluids, in the presence of gravity, sheared past each other and separated by a flexible plate. Conditions for exponential growth of velocity perturbations are found as functions of the flexural rigidity of the plate and the shear rate. This Kelvin-Helmholtz instability is then analyzed in the presence of plates with spatially periodic (with period) flexural rigidity arising from, for example, a periodic material variation. The eigenvalues of this periodic system are computed using Bloch’s theorem (Floquet theory) that imposes specific Fourier decompositions of the velocity potential and plate deformations. We derive the non-Hermitian matrix whose eigenvalues determine the dispersion relation. Our dispersion relation shows that plate periodicity generally destabilizes the flow, compared to a uniform plate with the same mean flexural rigidity. However, enhanced destabilization and stabilization can occur for disturbances with wavelengths near an even multiple of the plate periodicity. The sensitivity of flows with such wavelengths arises from the nonpropagating, “Bragg reflected” modes coupled to the plate periodicity through the boundary condition at the plate.