Abstract—

The methods and results of the mathematical simulation of nonlinear waves generated by hydrodynamic instability in traveling capillary films of a viscous liquid are discussed. Two model systems of differential equations for the local values of the layer thickness h and the fluid flow rate q are considered. The single-parameter (h–q) Kapitsa–Shkadov model that ensures the effective simulation of low-viscosity liquid film flows has received wide acceptance in world literature devoted to film hydrodynamics. The two-parameter (h–q)₁ model extends the possibilities for direct calculation of nonlinear waves in the higher viscosity liquid films. A succession of the systems of model equations is given, the scenarios of instability and bifurcation are discussed, and the results of calculations of wave structures in comparison with the experimental data are given.

中文翻译：

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任意 Kapitsa 数下薄膜粘性液体流动中的非线性波

摘要-

讨论了在粘性液体的移动毛细管膜中由流体动力学不稳定性产生的非线性波的数学模拟方法和结果。考虑了层厚度h和流体流速q的局部值的两个微分方程模型系统。确保有效模拟低粘度液膜流动的单参数 ( h – q ) Kapitsa-Shkadov 模型已在致力于膜流体动力学的世界文献中得到广泛接受。两个参数 ( h–q ) ₁模型扩展了在较高粘度液膜中直接计算非线性波的可能性。给出了一系列模型方程组，讨论了不稳定和分叉的情况，并给出了与实验数据相比较的波浪结构计算结果。