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

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．

For shallow water flow,the depth-averagod governing equations are derived by depth-ayeraging of the mean cquations for three-dimensional turbulent flows.The influences of free water surface and toptography of river bed are taken into account.The depth-averaged squat ions 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.The obtained equations can be applieddirectly to numerical computation of practical problems.