倾斜波浪形底部气膜流动的积分边界层方程
An integral boundary layer equation for film flow over inclined wavy bottoms
摘要：
本文研究不可压缩液体沿波浪形斜面的流动。本文将一种只有一个待定函数的Galerkin方法应用于斯托克斯方程，导出了一个二阶加权残差积分边界层方程，它特别适用于描述波浪形底槽中的旋涡。我们提出的数值结果表明，我们的模型是定性和定量准确的参数范围很广，我们使用该模型来研究一些新的现象，例如发生的短波不稳定性层流不存在平底。
英文摘要：
We study the flow of an incompressible liquid film down a wavy incline. Applying a Galerkin method with only one ansatz function to the Navier-Stokes equations we derive a second order weighted residual integral boundary layer equation, which in particular may be used to describe eddies in the troughs of the wavy bottom. We present numerical results which show that our model is qualitatively and quantitatively accurate in wide ranges of parameters, and we use the model to study some new phenomena, for instance the occurrence of a short wave instability for laminar flows which does not exist over flat bottom.
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