Abstract Utilizing the geometrical characteristics of a simple smooth curve embedded in an orientable surface of arbitrary shape, expressions are derived in boundary-fitted curvilinear coordinates, for the normal and tangential strain rate of a fluid which contacts the surface. The derived expressions can be applied to stream-surfaces, solid walls with hydrodynamic slippage and two-fluid interfaces. The use of the expressions is discussed with specific examples and critical examination of the literature.

中文翻译：

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曲面上的应变率：微分几何方法

摘要 利用嵌入任意形状的可定向曲面的简单光滑曲线的几何特征，推导出与曲面接触的流体的法向和切向应变率的边界拟合曲线坐标表达式。导出的表达式可以应用于流表面、具有流体动力滑移的实体壁和两流体界面。用具体的例子和对文献的批判性检查来讨论这些表达的使用。