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    沙波形态及运动特征的概化数学模型研究

    Study on a Generalized Mathematical Model of Sand Wave Morphology and Migration Characteristics

    • 摘要: 水库修建后坝下游水沙条件发生显著变化, 推移质补给大量减少, 悬移质占输沙量的主要部分. 在河床持续冲刷过程中, 沙波运动从以推移质为主逐渐转变为推移质与悬移质共同输移. 建立了一维沙波形态及运动特征的概化数学模型, 对比了基于推移质和悬移质输移的沙波运动特征, 采用已有公式对基于推移质运动的沙波形态变化和运动速度进行了验证, 并讨论了不同参数对沙波运动的影响. 模拟结果表明:(1)基于推移质运动的沙波向下游运动, 沙波上各点的运动速度与其高程正相关, 迎流面冲刷, 背流面淤积, 沙波形态逐渐向不对称发展, 沙波运动临界时间为31.78h, 与已有解析解误差仅为1.5%; 基于悬移质运动的沙波未向下游运动, 以垂向冲刷为主, 沙波上各点冲刷强度与其高程正相关, 波高逐渐减小, 沙波形态基本对称且趋于消亡; (2)基于推移质运动的沙波波峰和波谷的运动速度计算值分别为51m/d和17m/d, 与已有公式的最大相对误差小于26%, 形态曲线的平均相对误差小于19%, 故计算结果能较好地反映沙波运动特征; (3)水沙参数对沙波的影响比沙波初始形态参数更显著, 增大单宽流量和减小水深均能使沙波运动增强, 且对水深变化的响应更加敏感.

       

      Abstract: Upstream damming can alter significantly the flow and sediment regime in the reach downstream. The bed load discharge would decrease greatly, and the suspended load discharge would account for the main part of sediment transport. During the continuous channel degradation, the sand wave migration gradually changes from a predominantly transport of bed load to the combined transport of bed load and suspended load. In this study, a one-dimensional generalized mathematical model of sand wave morphology and migration characteristics was established, and the migration characteristics based on bed load and suspended load were compared based on the model predictions. Then the sand wave morphology and migration rate were verified by comparing the results of bed load model with the existing formulas. The effects of different parameters on the sand wave migration were finally discussed. Simulative results indicate that:(1)Sand wave based on the bed load transport migrates downstream while the rate is positively correlated with the bed elevation. Sediment erodes on the stoss side and deposits on the lee side, which leads to an asymmetrical morphology. The critical time for the sand wave migration is 31.78h and the relative error with the existing analytical solution is only 1.5%. Sand wave based on the suspended load transport does not migrate downstream. Sediment erodes vertically mainly while the erosion intensity is positively correlated with the bed elevation and the wave height decreases gradually. The sand wave morphology is basically symmetrical and tends to wash out; (2)The calculated migration rate of crest and trough based on the bed load transport is 51m/d and 17m/d respectively, and the maximum relative errors are less than 26% compared with the calculated values of existing three formulas. The average relative errors of morphology curve calculated by this model and existing three formulas are less than 19%. Therefore, the calculated results can generally reflect the characteristics of sand wave migration; (3)Effects of flow and sediment parameters on sand wave are more significant than initial morphological parameters. The migration intensity of sand wave can be enhanced by increasing the discharge per width or decreasing the flow depth, while it is more sensitive to the variation of flow depth.

       

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