## Laboratory Experiments
### Experimental Procedures  
In order to characterize accurately the properties of unsteady flow and compare the influence of different velocity skewness on the mass transfer, we define the velocity skew characteristic value as:  
\[a=\frac{2\big{(}U_{p}-U_{b}\big{)}}{t-t_{0}} \tag{1}\]  
where \(a\) is the unsteady flow velocity skewness characteristic value, \(U_{b}\) is the base flow velocity, \(U_{p}\) is the peak flow velocity, \(t_{0}\) is the unsteady flow start time, and \(t\) is the end time of the process. The \(Q\)-\(t\) curve was used to generate the unsteady flow. The flow increased from 90 m\({}^{3}\)/h to 260 m\({}^{3}\)/h, followed by the decrease to 90 m\({}^{3}\)/h, and the time interval \(\Delta t\) between flows was changed to produce different unsteady flow patterns. The ensemble mean of the flow velocity \(u_{b}\) was obtained by the \"rlowess\" smoothing algorithm based on linear fitting in Matlab, which belongs to the instantaneous and the mean point velocity at \(z=2\) mm above the bed, as shown in Figure 2a under \(a=1.08\times 10^{-3}\) m/s\({}^{2}\). The method was used to generate five different periods of \(Q\)-\(t\) curves, as illustrated in Figure 2b. Five different skewed unsteady flows were generated, and the water level changes have been accompanied by this process. Figure 1: Experimental setup. Five kinds of non-cohesive uniform sand were used in the experiment, and the particle diameters \(d\) were 0.296 mm, 0.664, 1.333, 2.639, and 3.741 mm, respectively. The non-uniform sand was obtained according to the equal mass ratio, such as \(\varphi_{0.296}\):\(\varphi_{0.664}\):\(\varphi_{1.333}\)=1:1:1, \(\varphi_{0.664}\):\(\varphi_{1.333}\):\(\varphi_{2.639}\) = 1:1:1, \(\varphi_{1.333}\):\(\varphi_{2.63}\):\(\varphi_{3.741}\) = 1:1:1, and \(\varphi_{0.296}\):\(\varphi_{1.333}\):\(\varphi_{3.741}\) = 1:1:1 Table 1. Four non-cohesive non-uniform sands A, B, C, and D, corresponding to the median diameter \(d_{50}\) of 0.664, 1.333, 2.639, and 1.333 mm, respectively. The \(\varphi_{d}\) represents the mass of particle diameter \(d\). The smoothed unsteady flow hydrographs and equivalent steady flow conditions will be considered in this study. It should be noted that a steady flow process has the same total water volume as an unsteady flow hydrograph, which is referred to as the equivalent steady flow [37; 38]. The method is that the \(u_{b}\)\(\sim\)\(t\) curve of the unsteady flow is converted into the steady flow \(u_{b}\)\(\sim\)\(t\) curve by the equivalent area integration, namely \(\int_{0}^{t}u_{1}dt=u_{2}t\), as shown in Figure 3. The corresponding sediment transport rate was measured. Otherwise, different steady flows were generated in the flume, which will make same sediment transport rate as the unsteady flow. A constant head pump was applied to re-circulate water in the flume. The control of flow was achieved with the discharge through changing of the pump rotational speed. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{2}{c}{**Sediment Composition**} \\ \cline{2-3}  & **Uniform Sand, \(d\)/mm** & **Non-Uniform Sand** \\ \hline
1 & 0.296 & \(\varphi_{0.296}\):\(\varphi_{0.664}\):\(\varphi_{1.333}\) = 1:1:1, A \\
2 & 0.664 & \(\varphi_{0.664}\):\(\varphi_{1.333}\):\(\varphi_{2.639}\) = 1:1:1, B \\
3 & 1.333 & \(\varphi_{1.333}\):\(\varphi_{2.639}\):\(\varphi_{3.741}\) = 1:1:1, C \\
4 & 2.639 & \(\varphi_{0.296}\):\(\varphi_{1.333}\):\(\varphi_{3.741}\) = 1:1:1, D \\
5 & 3.741 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The sediment composition. Figure 2: Unsteady flow rate curve under \(d=0.296\) mm (\(a\) is the velocity skewness, \(d\) is the particle diameter). (**a**) Ensemble mean of the flow velocity and (**b**) Variation of flow velocity in different (continuous lines). Many researchers use unsteady parameters to describe the hydrodynamic characteristics of the unsteady flow in detail. The stronger the unsteadiness effects, the greater influence on the bed surface sediment movement [20,22].