Using low-dimensional numerical simulations, we investigate the characteristics of complex and three-dimensional surface waves in a liquid film flowing over a rotating disk, focusing on large flow rates from a nozzle. Existing integral boundary layer (IBL) models, which are based on spatially averaged variables along the direction normal to the disk surface, have primarily focused on the formation of axisymmetric waves under relatively small flow rates. In this study, an extended IBL model that accounts for both laminar and turbulent regimes is developed by considering the non-uniformity of the local flow rate in the spreading film flow and incorporating closure models dependent on the local Reynolds number. Our numerical results successfully capture the generation of concentric waves by an impinging circular liquid jet and their transition into three-dimensional solitary waves. These findings are in good agreement with visualization images and time-series data of free-surface fluctuations from a displacement sensor. The backscattering of small-scale three-dimensional turbulence into large-scale horizontal turbulence inside the film plays a critical role in determining the transition of wave modes and the nonlinear dynamics of the waves in the turbulent regime. Furthermore, the behaviour of three-dimensional waves in the downstream region, including frequent wave coalescence in the transition region and the breakup of small-scale solitons, is distinct from that of gravity-driven falling film flows. The amplitude of the three-dimensional waves is inversely related to the generalized Reynolds number defined for rotating films.

中文翻译：

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旋转盘上液膜流三维表面波的低阶建模

使用低维数值模拟，我们研究了在旋转盘上流动的液膜中复杂的三维表面波的特征，重点关注喷嘴的大流量。现有的积分边界层（IBL）模型基于沿盘表面法线方向的空间平均变量，主要关注相对较小流量下轴对称波的形成。在本研究中，通过考虑扩散膜流中局部流速的不均匀性并结合依赖于局部雷诺数的闭合模型，开发了一种同时考虑层流和湍流状态的扩展 IBL 模型。我们的数值结果成功地捕获了撞击圆形液体射流产生的同心波及其向三维孤立波的转变。这些发现与位移传感器的自由表面波动的可视化图像和时间序列数据非常吻合。膜内小尺度三维湍流向大尺度水平湍流的后向散射在确定湍流状态下波模的转变和波的非线性动力学方面起着至关重要的作用。此外，下游区域三维波的行为，包括过渡区域频繁的波合并和小尺度孤子的破碎，与重力驱动的降膜流的行为不同。三维波的振幅与为旋转薄膜定义的广义雷诺数成反比。