黄河下游动床阻力变化及其计算方法

动床阻力在冲积河道洪水演进与河床冲淤计算中具有十分重要的作用。黄河下游不同水沙条件下的床面形态变化较大，动床阻力变化规律十分复杂，因此需要研究动床阻力的计算方法。利用黄河下游花园口、高村、利津等7个水文站1958—1990年的686组实测数据，确定了影响动床阻力变化的关键水沙因子——水流弗劳德数（Fr）与相对水深（h/D₅₀），前者表示水流强度，后者表示床面相对粗糙度；建立了基于水流能态分区的动床阻力计算公式，并采用这些实测数据率定了公式中的相关参数；利用黄河下游各水文站1991—2016年的2 288组实测资料，进一步验证了公式的计算精度。计算结果表明:动床阻力的大小随弗劳德数或相对水深的增加而减小；基于水流能态分区动床阻力公式的计算精度明显高于未分区的公式及其他4个动床阻力公式，且决定系数（R2）总体接近0.80，说明水流强度与床面相对粗糙度对动床阻力影响十分显著。

Variation characteristics and formula of movable bed roughness for the Lower Yellow River

The calculation of movable bed roughness plays an important role in modelling of flood routing and bed deformation in alluvial rivers. Bedforms in the Lower Yellow River (LYR) vary greatly under different flow and sediment regimes,which cause complicated variation characteristics of movable bed roughness. Therefore,it is necessary to propose a formula of movable bed roughness,in order to improve the predictive accuracy of morphodynamic models for the LYR. Based on 686 runs of measurements at seven hydrometric stations such as Huayuankou,Gaocun and Lijin in the LYR during the period 1958-1990,Froude number (Fr) and relative water depth (h/D₅₀) were selected as the representative factors influencing the magnitude of movable bed roughness in the LYR,and then a formula of movable bed roughness based on the flow regime partition was proposed and calibrated by these measurements. Finally,the accuracy of the proposed formula was verified against 2 288 runs of measurements at these stations during the period 1991-2016. Main results obtained from this study indicate that the magnitude of movable bed roughness decreases with an increase in Froude number or relative water depth;the calculation accuracy of the proposed formula of movable bed roughness based on the flow regime partition is obviously higher than the formula without considering the flow regime partition and the existing four formulae proposed by other researchers,with the determination coefficient between the calculated and measured data at each station generally greater than 0.80. Therefore,flow-sediment conditions and bedforms play an important role in the variation of movable bed roughness in the LYR.