This paper validates the theory of linear stability as applied to a fluid flowing down a vertically inclined plane using experimental comparison. The theoretically predicted mode 1 instability, corresponding to a surface wave oscillating at half the forcing frequency, is found to exist alongside the mode 2 instability, corresponding to a surface wave oscillating at the forcing frequency. Instability onset amplitude and frequency were compared, and an investigation of wavenumber with forcing amplitude at several distinct frequencies further confirmed the validity of the theory. A study of the wavenumber trend revealed distinct differences in the stability and development of the surface wave with increasing forcing amplitude. An analysis of the Womersley number, which expresses the ratio of the oscillatory inertia force to the viscous shear force, provides a physical indication of the differences in the wavenumber trend observed.

中文翻译：

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沿垂直倾斜面流动的流体膜的振动引起的不稳定性：实验和理论比较

本文通过实验比较验证了线性稳定性理论适用于沿垂直倾斜平面向下流动的流体。理论预测的模式 1 不稳定性，对应于以强迫频率的一半振荡的表面波，被发现与模式 2 不稳定性并存，对应于以强迫频率振荡的表面波。比较了不稳定起始幅度和频率，并且在几个不同频率下对波数与强迫幅度的研究进一步证实了该理论的有效性。对波数趋势的研究表明，随着强迫振幅的增加，表面波的稳定性和发展存在明显差异。对表示振荡惯性力与粘性剪切力之比的沃默斯利数进行分析，