Stability of a liquid film with respect to initially finite three‐dimensional disturbances
Stability of a liquid film with respect to initially finite three‐dimensional disturbances
复制标题
液膜相对于初始有限三维扰动的稳定性
DOI：
10.1063/1.861832
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发表时间：
1977
影响因子：
4.6
通讯作者：
M. Krishna
中科院分区：
文献类型：
--
作者：
S. P. Lin;M. Krishna
在相平面内研究了沿斜面稳定流动的粘性液膜的非线性稳定性。得到了控制微分系统临界点的显式表达式。临界点的性质和积分曲线对应于各种流动参数，初始条件和扰动特性的数值确定。基于相平面分析和数值计算结果，得到以下结论：对于有限三维扰动，如果初始振幅和边带宽度足够小，则根据线性理论不稳定的薄膜可能是稳定的。初始振幅和边带宽度的特定值取决于相关的流动参数，超过该值，膜变得不稳定。根据线性理论是稳定的膜也被证明是稳定的，相对于具有有限带宽的三维小的有限振幅扰动。
The nonlinear stability of a viscous liquid film flowing steadily down an inclined plane is studied in the phase plane. Explicit expressions of the critical points of the governing differential system are obtained. The nature of the critical points and the integral curves corresponding to various flow parameters, initial conditions, and disturbance characteristics are determined numerically. Based on the phase plane analysis and the numerical results, the following conclusions are reached: The film which is unstable according to linear theory may be stable with respect to a finite three‐dimensional disturbance if the initial amplitude and the side‐band width are sufficiently small. The particular values of the initial amplitude and the side‐band width beyond which the film becomes unstable depend on the relevant flow parameters. The film which is stable according to linear theory is also shown to be stable with respect to three‐dimensional small finite amplitude disturbances with finite bandwidths.