Modification of water continuity equation considering the exchange flux between sediment laden flow and bed

In the sediment mathematical model,three compossitions of the flow should be included in the continuity equation: the volume flow rate of a control volume,the volume flow rate in and out the control volume and the exchange flux between sediment laden flow and bed.Now,the exchange term between sediment laden flow and bed is not be considered in the flow continuity equation in most sediments mathematical models.One dimension-mathematical model is taken as an example to evaluate the importance of the exchange term with the numerical experiments.Based on the schematic model and the field data of the Weihe River,the research results show that the exchange term has obvious influence on discharge when sediment concentration is high.The phenomenon of the so-called‘change flow into bed material' or‘change bed material into flow',which often occurs in the sediment-laden river like the Yellow River,can be explained.The conclusion can be made when the sediment concentration is high.The three compositions of the equation of continuity of flow should be synthetically considered in the water and sediment mathematics model