In the long‐wave approximation, a theoretical model is developed to describe waves in a rivulet flowing down the lower surface of an inclined cylinder. The model equations are derived by the weighted residual method by projecting the Navier–Stokes equations onto the constructed system of basic orthogonal polynomials. The simplest case of quasi‐two‐dimensional waves is studied in detail. The stability of the rivulet flow is analyzed and dispersion dependences for linear waves are obtained. The characteristics of nonlinear steady‐state traveling waves have been obtained by numerical method for the first time, and the spatial development of forced waves has been studied. The results of calculations are in good agreement with the available experimental data for various liquids in a wide range of parameters.

中文翻译：

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小溪中的波浪从倾斜的圆柱体上掉下来

在长波近似中，建立了一个理论模型来描述在倾斜圆柱体下表面向下流动的小溪中的波浪。通过将Navier–Stokes方程投影到构造的基本正交多项式系统上，通过加权残差法导出模型方程。详细研究了最简单的准二维波情况。分析了小溪流的稳定性，并获得了线性波的色散依赖性。首次通过数值方法获得了非线性稳态行波的特性，并对强迫波的空间发展进行了研究。计算结果与各种参数下各种液体的可用实验数据高度吻合。