Linear stability of a viscoelastic liquid flow on an oscillating plane
Linear stability of a viscoelastic liquid flow on an oscillating plane
复制标题
DOI：
10.1017/jfm.2017.275
复制
发表时间：
2017-05
影响因子：
3.7
通讯作者：
A. Samanta
中科院分区：
文献类型：
--
作者：
A. Samanta
研究了任意波数扰动下粘弹性液体在振荡平面上的线性稳定性。主要目的是将 Dandapat 和 Gupta 的早期研究（J. Fluid Mech.，第 72 卷，1975 年，第 425-432 页）扩展到有限波数范围，迄今为止文献中尚未尝试过。奥尔-索末菲边值问题针对非定常基流制定，并基于切比雪夫谱配置法和 Floquet 理论进行数值求解。解析解预测，在施加频率的分离带宽中会出现 U 形不稳定区域，并且在存在粘弹性参数的情况下，长波不稳定的主模态会加剧。数值解表明，倾斜中性曲线从有限波数处的U形中性曲线的分支点出来，并以施加的频率继续，直到曲线与下一条U形中性曲线相交。因此，在有限波数范围内，长波长分析无法预测所施加频率的稳定带宽。此外，在某些频率范围内，有限波数不稳定性比长波不稳定性更危险。
Linear stability of a viscoelastic liquid on an oscillating plane is studied for disturbances of arbitrary wavenumbers. The main aim is to extend the earlier study of Dandapat & Gupta (J. Fluid Mech., vol. 72, 1975, pp. 425–432) to the finite wavenumber regime, which has not been attempted so far in the literature. The Orr–Sommerfeld boundary value problem is formulated for an unsteady base flow, and it is resolved numerically based on the Chebyshev spectral collocation method along with the Floquet theory. The analytical solution predicts that U-shaped unstable regions appear in the separated bandwidths of the imposed frequency, and the dominant mode of the long-wave instability intensifies in the presence of the viscoelastic parameter. The numerical solution shows that oblique neutral curves come out from the branch points of the U-shaped neutral curves at finite wavenumber and continue with the imposed frequency until the curves cross the next U-shaped neutral curve. As a consequence, in the finite wavenumber regime, no stable bandwidth of the imposed frequency is predicted by the long-wavelength analysis. Further, in some frequency ranges, the finite wavenumber instability is more dangerous than the long-wave instability.