中文摘要：

以Reynolds平均的Navier—Stokes紊流方程为基础，提出了河渠恒定非均匀流的水深平均流速横向分布的准二维模型，该模型包括了河渠流动的一些关键三维紊流因素。研究了用数值有限差分将它转换为一组三对角线性方程并用追赶法求解，然后，研究了用该模型推算水面线的迭代计算，最后以实测数据检验了所提模型的准确性，结果表明计算流量与实测流量的偏差相对值小于4％，而计算水深与实测水深偏差相对值小于1％。

英文摘要：

Based on Reynolds averaged Navier-Stokes equations, a quasi-2D model of the steady non-uni- form flows is presented. The model includes some of the key 3D flow structures that occur in rivers and compound channels and can be used to estimate the lateral distributions of depth-averaged velocity. With a finite differential method, the quasi-2D model is converted to a group of linear equations with a tridiagonal coefficient matrix, and then a double sweeping method is used to solve it. On that basis, it is studied how to apply the quasi-2D model to determining the water surface profile of a river or channel. At last, taking the measured data of the flows and water depths as examples, it is verified that the model is of high accu- racy in computation of flow and water depth. The results show that the relative deviations between the mea- sured flows and the computed ones are less than 4 %, and that those between the measured water depths and the computed ones are less than 1%.