正变坐标系下完全深度平均湍流方程组

The Equations of Complete Depth-Averaged Turbulence Model in General Orthogonal Coordinates

摘要: 本文针对宽浅型水域,对三维湍流时均方程组逐项进行深度平均,推导出包含自由水面和地形影响的深度平均流动控制方程组。本文还同时获得了深度平均形式的k-ε湍流模型方程组。因计入了水流的三维效应,该模型称为完全深度平均模型。考虑到天然水域几何边界复杂,本文运用较简便的方法,将上述模型方程组交换至正交坐标系下。所得控制方程组可以直接运用于对实际问题的数值模拟。
- 湍流 /
- 数学模型 /
- 深度平均 /
- 正交坐标系
Abstract: For shallow water flow, the depth-averaged governing equations are derived by depth-averaging of the mean equations for three-dimensional turbulent flows. The influences of free water surface and of topography of river bed are taken into account.The depth-averaged equations of k-turbulence model are also obtained. Because it Accounts for the three-dimensional effect, this model is named as the complete Depth-averaged model.The boundaries of natural water bodies are usually curved.In this work, the derived equations in Cartesian coordinates are transformed into orthogonal coordinates. The obtained equations can be applied directly to numerical computation of practical problems.
- turbulent flow /
- mathematical model /
- depth-average /
- general orthogonal coordinates

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