We study the problem of a thin liquid film falling down an inclined slope. We use a simplified model to study the evolution and morphology of the solitary waves on a thin film with a periodic forcing at the inlet. In recent work by Denner et al (2016 Phys. Rev. E 93 , 033121), the regime for high Re was studied and results obtained on the geometry and dispersion of the waves. We wish to establish whether similar results are observed in a regime of smaller Re and examine quantities which can be compared with experiment, such as the maximum and minimum film height as a function of a rescaled Reynolds number which accounts for the inclination of the substrate. Our results show some evidence that h min collapses onto a single curve when plotted as a function of Re*, and approaches the absolute value of h min / h N = 0.375 in agreement with results obtained at higher Re. We also obtain a curve for d

中文翻译：

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低雷诺数状态下下降的液膜上的孤波

我们研究了液体薄膜从倾斜的斜坡上掉下来的问题。我们使用简化的模型来研究薄膜的孤立波的演化和形态，并在入口处有周期性的强迫。在Denner等人的最新工作中（2016 Phys。Rev. E 93，033121），研究了高Re的范围，并获得了有关波的几何形状和色散的结果。我们希望确定在较小的Re范围内是否观察到相似的结果，并检查可以与实验进行比较的量，例如最大和最小膜高作为重新缩放的雷诺数的函数，雷诺数解释了基材的倾斜度。我们的结果表明，有一些证据表明，当h min作为Re *的函数绘制时，h min会折叠成一条曲线，并接近h min / h N = 0的绝对值。375与在较高Re下获得的结果一致。我们还获得了d的曲线