# Hydraulic Performance of Wave-Type Flow at a Sill-Controlled Stilling Basin
## 3 Results and Discussion  
### Flow Pattern  
In most practical cases, the stilling basin with a positive step or a sill (i.e., abrupt bottom rise) was constructed to grant a forced jump inside the basin [2]. Figure 5 illustrates the wave-type flow for both Case M31 and M32 at different inflow unit discharges. As the unit discharge increased, implying a decrease in \(F_{1}\), the beginning of the jump roller moved downstream. The wave type flow exhibited a significant wave height in the vicinity of the sill, a significant water drop downstream of the sill, and the resultant downstream supercritical flow (\(F_{2}>1\)), as listed in Table 1. In addition, air entrainment occurred at the toe of the jump, and entrained bubbles were transported into the downstream zone. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Cases** & \(l_{\mathbf{s}}\) **(m)** & \(s\) **(m)** & \(F_{1}\) & \(F_{2}\) & **Jump Type** \\ \hline M12-1 & 0.5 & 0.065 & 5.12 & 1.93 & SWTF \\ M12-2 & 0.5 & 0.065 & 4.21 & 1.65 & SWTF \\ M12-3 & 0.5 & 0.065 & 3.86 & 1.62 & SWTF \\ M12-4 & 0.5 & 0.065 & 3.77 & 1.72 & SWTF \\ M12-5 & 0.5 & 0.065 & 3.70 & 1.91 & SWTF \\ M22-1 & 0.6 & 0.065 & 5.18 & 1.66 & SWTF \\ M22-2 & 0.6 & 0.065 & 4.29 & 1.79 & SWTF \\ M22-3 & 0.6 & 0.065 & 4.13 & 1.87 & SWTF \\ M22-4 & 0.6 & 0.065 & 3.82 & 1.95 & SWTF \\ M22-5 & 0.6 & 0.065 & 3.74 & 1.77 & NSWTF \\ M32-1 & 0.7 & 0.065 & 5.31 & 1.97 & SWTF \\ M32-2 & 0.7 & 0.065 & 4.30 & 1.82 & SWTF \\ M32-3 & 0.7 & 0.065 & 4.08 & 1.76 & NSWTF \\ M32-4 & 0.7 & 0.065 & 3.93 & 2.79 & NSWTF \\ M32-5 & 0.7 & 0.065 & 3.74 & 2.96 & NSWTF \\ M31-1 & 0.7 & 0.050 & 5.26 & 1.44 & NSWTF \\ M31-2 & 0.7 & 0.050 & 4.43 & 2.89 & NSWTF \\ M31-3 & 0.7 & 0.050 & 4.08 & 3.10 & NSWTF \\ M31-4 & 0.7 & 0.050 & 3.93 & 3.19 & NSWTF \\ M31-5 & 0.7 & 0.050 & 3.74 & 3.13 & NSWTF \\ M33-1 & 0.7 & 0.080 & 4.96 & 2.07 & SWTF \\ M33-2 & 0.7 & 0.080 & 4.13 & 1.94 & SWTF \\ M33-3 & 0.7 & 0.080 & 3.77 & 1.95 & SWTF \\ M33-4 & 0.7 & 0.080 & 3.62 & 2.10 & SWTF \\ M33-5 & 0.7 & 0.080 & 3.47 & 1.99 & SWTF \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Hydraulic and geometrical parameters of the sill-controlled stilling basin. Figure 4: Layout of air concentration and pressure measurement points: (**a**) sideview; (**b**) plain view. For comparison purposes, the beginning of the jump roller in Case M32 moved downstream more clearly, presenting a distinct transition from the submerged jump to the non-submerged jump, especially when the unit discharge varied from 0.154 m\({}^{2}\)/s to 0.205 m\({}^{2}\)/s. Moreover, the visual observations suggested a more significant amount of air in the submerged jump in Case M32, and even the entrained air could reach the still basin bottom. Figure 5: Wave flow pattern at different inflow unit discharges (\(q_{\rm w}\) = 0.102, 0.154, 0.188, 0.205 and 0.230): (**a**) Case M31; (**b**) Case M32. In addition to the wave type flow, a jet flow may occur, and the curvature of the streamline approaching the sill became larger. The supercritical flow would splash over the sill and a cavity formed between the jet flow and the downstream depth [7]. Because the splash flow occurred when the relative sill height of \(s/y_{1}\) was larger than its critical value, the flow pattern was closely related to inflow conditions and the sill height. In Figure 6, the relative sill height \(S\) (i.e., \(S=s/y_{1}\)) is plotted against the upstream Froude number \(F_{1}\). The data for the critical splash flow conditions are also illustrated in this figure. The relative sill height, \(s/y_{1}\), in this study conformed to the wave-type flow conditions found in a previous study [7]. When wave-type flow occurred with a positive step, the flow zone behind the step could be classified into aerated or nonaerated flow. The main difference between these two wave types was that the aerated wave-type flows were associated with a better aeration effect and higher wave heights due to the subatmospheric pressure at the horizontal step surface [19].