A full-scale numerical study of interfacial instabilities in thin-film flows
A full-scale numerical study of interfacial instabilities in thin-film flows
复制标题
DOI：
10.1017/s0022112096008075
复制
发表时间：
1996-10
影响因子：
3.7
通讯作者：
B. Ramaswamy;S. Chippada;S. Joo
中科院分区：
文献类型：
--
作者：
B. Ramaswamy;S. Chippada;S. Joo
通过全非线性系统的直接数值模拟来研究二维薄排水膜中的表面波不稳定性。有限元方法与任意拉格朗日-欧拉公式一起使用来处理移动边界问题。对有限振幅非线性波态进行了时间和空间稳定性分析。当波数降低到线性截止波数以下时，如先前弱非线性分析和实验所报告的那样，会出现超临界正弦波。波数的进一步减少使得傅里叶谱变宽，从而产生孤立的驼峰。人们发现，从近正弦永久波形到孤立驼峰的这种转变经历了准周期状态。该准周期状态的相边界已通过广泛的数值参数搜索确定。讨论了复杂的波相互作用过程，例如波合并和波分裂。在本文进行的详尽数值模拟中，没有观察到波浪破裂趋势，推测是波合并和波分裂等复杂的波相互作用过程抑制了薄膜破裂的趋势。
Surface wave instabilities in a two-dimensional thin draining film are studied by a direct numerical simulation of the full nonlinear system. A finite element method is used with an arbitrary Lagrangian–Eulerian formulation to handle the moving boundary problem. Both temporal and spatial stability analysis of the finite-amplitude nonlinear wave regimes are done. As the wavenumber is decreased below the linear cut-off wavenumber, supercritical sinusoidal waves occur as reported earlier from weakly nonlinear analysis and experiments. Further reduction in wavenumber makes the Fourier spectrum broad-banded resulting in solitary humps. This transition from nearly sinusoidal permanent waveforms to solitary humps is found to go through a quasi-periodic regime. The phase boundaries for this quasi-periodic regime have been determined through extensive numerical parametric search. Complex wave interaction processes such as wave merging and wave splitting are discussed. In the exhaustive numerical simulations performed in this paper, no wave-breaking tendency was observed, and it is speculated that the complex wave-interaction processes such as wave merging and wave splitting curb the tendency of the film to break.