# Influence of Right Triangular Prism Rough Beds on Hydraulic Jumps
## 3 Results and Analysis
### Effects of Right Triangular Prism Rough Bed on Total Entropy Generation Rate  
Recently, more and more researchers have reported that losses within internal flows often attributed to pressure losses are related to the local entropy production rate. The local energy dissipation rates could be figured out and integrated over the flow domain to obtain the losses. Therefore, to further clarify the influence of rough bed characteristics, in this section, we use the entropy production rate to analyze energy dissipation in hydraulic jumps. We used commercial software Tecplot (360 EX 2022R2 version 2022.2.0.18713) and the entropy determination formulas in Section 2.4 to display entropy distributions. Figure 21a,b shows the entropy production rate distribution in the case of the triangular rough bed with \(m_{1}=0\) (M_I8 (No. 38) test) and \(m_{2}=0\) (M_II8 (No. 83) test); for more detail see Table 7.  
As per the picture presentation, the flow is divided into three regions: Region 1 is the upstream hydraulic jump's beginning area; Region 2 is the hydraulic jump and Region 3 is the zone of stable flow after the hydraulic jump. The first region is the supercritical flow before the jump toe. There is a high entropy production region at the channel bottom surface, the incoming jet to the basin is fully developed, and the boundary layer is formed entirely in the incoming jet. The entropy production rate is higher because of the influence of the channel bottom. The second region is the hydraulic jump range. In this region, the flow suddenly changes from supercritical to subcritical, increasing water level depth  
Figure 21: Entropy production rate on the XZ-plane for two typical rough bed cases.  
downstream of the channel. The zone of the rough bed arrangement on the channel bottom, where the entropy production rate has a very high value of about 200 Wm\({}^{-3}\)K\({}^{-1}\), was concentrated in the rough bed zone at about \(L_{\rm j}/3\), and then gradually decreased towards the downstream hydraulic jumps for the M_18 model, No. 38 test (see Figure 21a). This region has a clear difference in entropy production distribution for the two cases of triangular prism elements. Figure 21a shows that the triangular prism elements have a shape that conflicts with the flow direction \(m_{1}=0\) (model No.38 test); the entropy production rate is higher near the jump toe and quickly tapers off after four to five rough rows.  
Meanwhile, with the triangular rough elements having a shape in the flow direction \(m_{2}=0\) (model No.83 test), the entropy production still has a significant value but is distributed along the jump length. The figure shows the flow close to the bottom slips on the crest of the triangular rough elements. Thus, the triangular rough elements shaped \(m_{1}=0\), which conflicts with the flow direction, have a better energy dissipation effect than the flow direction shape. Therefore, the character shape of a rough bed has a significant effect on reducing hydraulic jump length.  
The third region is the flow range behind hydraulic jumps. In this zone, the subcritical flow was formed. The entropy production is minimal (<30 Wm\({}^{-3}\)K\({}^{-1}\)), meaning the hydraulic jump had effective energy dissipation.