Reply to the discussion by H. Chanson and L. Toombes on "Characteristics of free overfall for supercritical flows"

Abstract

We thank the discussers for their interest in our paper. It is stated in our paper that the downstream position of the drop for a supercritical flow has not been investigated. Chanson and Toombes (1998) published a paper entitled “Supercritical flow at an abrupt drop: flow patterns and aeration”, and we are sorry that we missed this paper when conducting our literature review. However, after reviewing their study, it was found that there are major differences between the present study and the study of the discussers. The discussers state that “the supercritical flow at an abrupt drop is strongly three-dimensional and unsteady, and this aspect has direct implications for engineering designs.” In several sections of our paper, it is emphasized that the flow at an abrupt drop is strongly three-dimensional (see p. 163). However, as long as the inflow discharge remains constant, the average behavior of flow should be steady. In our case the flow was steady. Another difference is the upstream boundary condition. In our study, the supercritical flow before the drop was generated by a sluice gate. In the discussers’ study, however, the supercritical flow was generated by an elliptical convergent nozzle. Chanson and Toombes (1998) claim that the approach flow and the free-falling nappe were basically twodimensional, and at the downstream of the nappe impact the flow became three-dimensional. In our case, as explained on p. 164 under the subtitle “Characteristics of the base of the free overfall”, it was observed that the jet leaving the drop showed a horizontal and vertical spread due to variation of velocity across the cross section of the channel. The streamlines near the center had higher velocities than those near the sidewalls, therefore the streamlines leaving the drop near the sidewalls hit the base channel at a distance shorter than those near the centerline, resulting in a three-dimensional jet. The discussers claim that “for all experiments, nappe ventilation was provided at the first drop by sidewall splitters.” In their paper (Chanson and Toombes 1998), however, they stated that “the study presents new experimental data obtained in a 0.5 m wide stepped flume with an unventilated nappe”, which is a contradiction to the statement in their discussion. Another claim of the discussers is that “At the nappe impact, the change in flow direction on the invert resulted in the formation of sidewall standing waves and shockwaves in the downstream supercritical flow.” In our study, we never observed a sidewall standing wave. It was observed that at the base of the supercritical free overfall, a heavy splash of water takes place at a small Froude number and vigorous mixing and turbulence takes place at the end of the jet. As the Froude number of the upstream flow increases, this heavy splash takes the form of a standing wave that has a maximum height at the centerline of the channel. The discussers relate the properties they have observed at the base of the free overfall to a downstream ideal flow Froude number, Fr. However, a supercritical flow is subject to an upstream control. This seems to be a significant contradiction to the nature of the supercritical flow. If Chanson and Toombes (1998) used side splitters to aerate the nappe, it may have caused the sidewall standing waves. Yet, they claim that the falling jet is a two-dimensional jet; this may also cause a sidewall standing wave. In our case, the falling jet was a three-dimensional jet. Experimental observations showed that water accumulates behind the jet as in the case of subcritical flow free fall. They do not mention the phenomenon of standing water behind the jet. It seems to us that the sidewall standing wave generated in the discussers’ study is a type of standing water behind the jet that was influenced by upstream conditions. The discussers also state that “Downstream of the nappe impact, flow was characterized by a highly fragmented spray. The spray and splashing appeared to be concentrated towards the centerline of the channel”, which was also discussed in our paper in the subsection entitled “Characteristics of the base of the free overfall”. As expressed in subsection “Depth of flow y2” of our paper, the flow was also supercritical in the downstream channel. It is the nature of supercritical flow that cross waves occur because of changes in direction, and this is also mentioned in several places in the text.