基于连续性扩散流的湿地表面水流动力学模型

Mathematical model for continuous diffusion flow on wetland surface

受表面密生植被的影响,湿地表面流总是处于高阻力、低流速状态。湿地表面流的水流动力学方程中,其水流加速度项相对于地表高密度植被造成的高阻力项相比,可以忽略。由此,以水流连续性方程和忽略加速度项的水流动力学方程为基础,构建基于连续性扩散流的湿地表面流动力学模型。该模型是一个抛物型偏微分方程,相对于描述一般径流流态的圣维南双曲型偏微分方程组而言,其求解过程相对容易。模型中的表面流流量采用修正的曼宁方程描述,表面糙率采用已有经验公式,数值计算方法采用六点差分格式。模拟结果表明,该模型能够体现湿地表面流的高阻力、低流速特征。水深越浅,水流模式变化越慢,水深越大,表面流受植被阻力越小,水流模式变化越快。

As a result of dense vegetation the surface water flow in wetlands exhibits the characteristics of low velocity and high resistance. In consideration of these characteristics, the acceleration item in the flow equation of surface water flow in wetlands can be neglected. Thus, the mathematical model for continuous 2D-diffusion flow based on the Saint-Venant equations can be simplified as a parabolic partial differential equation, which is easy to be solved. In the model, the surface runoff is expressed by the amendatory Manning equation, the surface roughness is expressed by an empirical formula, and the numerical solution is solved by the six-point-difference algorithm. The application indicates that the model can reveal the surface flow characteristics of wetland, i.e. high resistance and low velocity. The variation of runoff flow depth in the flow process is mild, if the flow is shallow. Whereas, when the flow depth is great, the variation of the runoff flow depth in the process of flow become quickly.