Introduction
Scouring downstream of weirs, due to high velocity and turbulence of the flow, has always been one of the major challenges in the design and operation of these hydraulic structures. Previous studies have shown that various factors, including jet velocity, water drop height, flow rate, and weir plan, affect the amount and pattern of scouring. Labyrinth weirs are used in places that have width limitations and are used to increase the crest length. If a proper foundation is not built, there is a possibility of destruction of these weirs due to downstream scouring. On the other hand, excessive increase in the depth of the weir foundation will entail high costs. Therefore, the aim of this study is to carefully investigate the amount, pattern, and trend of scour changes downstream of triangular and arched convoluted weirs in two single-cycle and two-cycle modes in uniform sediments.
Materials and Methods
The experiments were conducted in a laboratory flume 12 m long and 80 cm wide. The discharge was measured using an ultrasonic flowmeter with an accuracy of ±0.01 lit/s, and the water level was measured with a point gauge. Four types of labyrinth weirs, including single-cycle triangular, double-cycle triangular, single-cycle arched and double-cycle arched with a crest length of 1.26 m and a magnification ratio of 1.58, were installed at a distance of 6 m from the beginning of the channel. The weirs were made of iron with a thickness of 4 mm and a height of 35 cm. Coarse-grained sediments were used up to a height of 20 cm upstream of the weirs, and uniform sediments with a median diameter of 3 mm were used downstream with a length of 70 cm and a height of 20 cm. 15 cm of the weir height was placed above the sediments and 20 cm of it was placed as a foundation under the sediments. The depth of the tailwater was set to 10 cm in all experiments. Experiments were conducted at three discharges of 5, 10, and 15 lit/s. The topography was measured with a 3x3 cm grid and the data were analyzed in Sigma Plot software to draw a three-dimensional scour shape.
3Results and Discussion
The results of the experiments showed that the greatest scour depth always occurs at the junction of the weir with the channel wall. The presence of severe transverse curvature of flow and nappe interference lead to increased turbulence and, as a result, more scour on the sides. In single-cycle weirs, the second maximum scour point was observed near the weir apex. In double-cycle weirs, the second maximum scour point occurs at the intersection of the two cycles and then at the weir apex. This is due to the nappe interference and the transverse curvature of the flow at the intersection of the cycles, which, similar to near the channel wall, creates more turbulence. A comparison of single-cycle and double-cycle weirs showed that with an increase in discharge and water head ratio, the discharge coefficient in single-cycle weirs decreases faster. This faster decrease in the efficiency of single-cycle weirs leads to a faster increase in the scour rate in them compared to double-cycle weirs. So that in the curved single-cycle weir, the increase in scour from a discharge of 5 to 15 lit/s was 101%, while in the curved double-cycle weir this increase was 27%. For triangular weirs, these values were 53% for single-cycle and 39% for double-cycle, respectively. This difference in the scour increase trend shows that despite the better initial hydraulic performance of single-cycle weirs at low discharges, with increasing discharge, two-cycle weirs are more stable in terms of scour. Therefore, despite the lower discharge coefficient, two-cycle weirs are structurally more resistant to scour.

4Conclusion
The studies showed that the maximum scour location always occurs at the junction of the weir with the channel wall. In single-cycle weirs, the second maximum scour is near the weir apex; but in two-cycle weirs, this phenomenon is observed at the intersection of the two cycles and then near the weir apex. This is due to the increased turbulence caused by the transverse curvature of the flow and the nappe interference at low angles of flow exit from the weir. The studies showed that increasing discharge leads to an increase in scour depth. This increase is more significant in single-cycle weirs than in double-cycle weirs due to the faster decrease in discharge coefficient. The Froude number study showed that although a higher Froude number usually means more scour, in conditions where different of Froude number in two weirs are insignificant, the nappe interference and discharge coefficient play a major role in the scour rate. Finally, it was found that double-cycle weirs, although hydraulically less efficient than single-cycle weirs, are structurally more suitable due to the lower scour depth.