运动波沟灌数学模型

运动波沟灌数学模型

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contributed at 2018-12-04

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Affiliation:  
岳天祥编著
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yue@lreis.ac.cn
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运动波沟灌数学模型

(1)          运动波沟灌数学结构模型的定界方程组:

                       1

式中,x为沿沟长方向的距离(m)t为灌水时间(min)Q为沟中流量();A为水流横断面面积();Z为单位沟长上的累计入渗量();R俄日水力半径(m)S0为沟底纵坡;C为谢才系数,可有曼宁公式求得,n为田间灌水沟的粗糙系数。

       将谢才系数带入均匀流方程中得:

                               2

       为便于计算,假设:

                           3

式中,均为经验常数。将(3)式代入(2)式后得:

                                                  4

                                     5

式中,可以用(3)式拟合田间灌溉沟断面求得。方程(1)和(4)即为运动波沟灌数学模型求解计算的定解方程组。

         沟灌条件下的入渗是二维非饱和土壤水分运动。通常沟灌数学模型中均采用经验式表示。本模型中采用具有稳定入渗项的考式入渗式。

                               6

式中,kαC均为经验常数;T为入渗时间(min);Z为单位沟长上的累计入渗量()。

(2)          应用积分法数值求解:

 内对连续方程(1)式积分:

        7

采用一阶尤拉积分,上式化为:

            8

式中,x+δx处在δt时段内的平均流量;x处在δt时段内的平均流量;t+δt时刻δx区间内的平均水流断面积;t时刻δx区间内的平均水流断面积;t+δt时刻δx区间内的平均单位沟长上的入渗量;t时刻δx区间内的平均单位沟长上的入渗量。

         很明显,上式反应了δt时段内δx区间的水量平衡关系式。对任一内单元LRJM,上式可写成:

                   9

式中,θΦ分别为时空加权平均系数。将均匀流公式(4)代入上式并化简整理可得:

                                                           10

                   11

参考文献;

   路京选等:地面灌溉节水结束研究――沟灌水流运动的数值模拟及其应用。自然资源学报,1989,44

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How to Cite

《资源环境数学模型手册》 (2018). 运动波沟灌数学模型, Model Item, OpenGMS, https://geomodeling.njnu.edu.cn/modelItem/4eebdb88-bc52-4118-ae3e-3e36a7ae7b6a
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Last modifier : 
tingxin
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Contributor(s)

initial contribute: 2018-12-04

Authorship

Affiliation:  
岳天祥编著
Email:  
yue@lreis.ac.cn
Homepage:  
View
Is authorship not correct? Feedback

History

Last modifier : 
tingxin
Last modify time : 
2020-12-22
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