Analysis of Water-Surface Oscillations Upstream of a Double-Right-Angled Bend with Incoming Supercritical Flow
Round 1
Reviewer 1 Report
The manuscript aims to analyse the oscillation of free water surface in open channels where double-right angled junctions are present. This topic are surely interesting in facing several hydraulic issues of natural and anthropogenic drainage systems under global changes. The subject of the study is relevant with the scope of the journal and contains interesting data that can be published in Water after making the necessary major improvements.
The structure of the paper is not very good. The introduction must be improved explaining the practical problems of supercritical flow in open channel with some examples and relative references. Also the authors should provide in this paragraph the context in which high-velocity channels are designed. The introduction should contain a brief overview of the cross waves and system oscillation effects over the drainage and the issue of the computational fluid dinamic. Describing the previous studies, the authors should report the results obtained in the literature, such as those of Hager (1989). Also the previous experiments conducted by the authors must be detailed.
The objective of the study must be highlighted at the end of the introduction together with the questions that the paper addresses.
The paragraph of the methodology is very articulate and should be simplified giving a description of the experimental setup, methodologies and statistical approaches. Remind at the readers the meaning of Rn and Fn meaning at the first use
Paragraph 3 contain most of the results that are reported as description of the figures. Personally, I think this is not the correct approach in a scientific paper but it is the format for a project report. Moreover, it is not clear if the first part of the 3.2 paragraph “visual study” contains info from the experiments or are data from literature. In the latter case, please provide reference. In the section 3.3 the subparagraphs are redundant, please remove them and try to be more fluent in the description of the figures.
Paragraph 4 should contain the discussion, but unfortunately it is not very well developed and must be improved. My suggestion is to give the practical meaning of St. no and to include in this paragraph the limitation/outlook reported in paragraph 6 (so that it could be removed from the end of the manuscript).
The discussion should explain the advantage to test rectangular systems the meaning of the results in term of practical problem giving some examples or application in the hydraulic design and management of open channels.
The conclusions too should highlight the relevance to answer the questions posed in the article.
Minor comments:
Distances sometimes are in mm and sometimes in cm. Please, use the same units in all manuscript.
In paragraph 2.6 give unit for manning roughness
In paragraph 2.7 Appendix A does not exist.
Fig 4 y-axis does not have legend. It should be water depth, I suppose. Also fig 10 and 11 have the same lack. The meaning of the arrows must be indicate.
I suggest to analyse Fig 16 more in deep as it seems that there are two different trends.
Author Response
"Please see the attachment."
Author Response File: 
Author Response.docx
Reviewer 2 Report
I first note that line numbering in draft papers is a fundamental aspect to perform a review. The presence of line numbering should be checked by the editorial office before sending a paper to reviewers (this is the standard procedure for most journals).
The paper deals with an experimental study of supercritical open-channel flow approaching a double right-angle bend, with an analysis of the free-surface oscillations.
I have many serious concerns with the paper. The topic is not correctly identified, as a double bend is treated as a junction (but a junction is made of at least 3 branches, here we have only a single channel). The motivation and the interest of the study is not even presented. The quality of the English is unacceptably low. The figures are partly not clear. The presentation of the matter seems rather a collage of single parts than a well-organized, organic piece. The general goal and the usefulness of the study remain obscure.
Specific comments
Abstract
The Abstract should be more concise and in a single paragraph.
Section 1.1. Preface
The Preface has to be rewritten. Now it seems a set of sentences put in sparse order. For example, it is said that “the stability of flow is a crucial consideration…” but it is not said if, and why, stability is a particular matter for supercritical flows.
Sect. 1.2. Previous Research
I don’t understand why introducing previous literature studies dealing with channel junctions, which is not the focus of the present study. The double right-angle bend investigated in this study cannot be classified as a “junction”, because there is only one channel. Please refer to previous studies on supercritical flows and bends and/or obstacles (have a look at the additional references suggested below).
There is no word introducing the issue of water surface oscillations, which seems to be one of the main topics of the paper. How is it emerged? Is this a particular problem related to supercritical flows? Or to abrupt bends? Do oscillations represent a problem for open-channel flows? What is the interest of predicting the frequency, rather that the magnitude, of water surface oscillations?
Sect. 2
What is the “heading up (afflux)”? Is this the backwater effect?
What is the meaning of determining an equivalent Manning n? How was this achieved?
Figure 6 and 7
I cannot identify the channel in the upper panels of these figures.
Figure 8
The edge of the downstream channel is incorrectly identified.
Sect. 3.3
Do not use additional subsections.
Additional References
Abdo, K., Riahi-Nezhad, C. K., and Imran, J., “Steady supercritical flow in a straight-wall open-channel contraction”, Journal of Hydraulic Research 57(5), 647–661 (2019).
Akers, B., and Bokhove, O., “Hydraulic flow through a channel contraction: Multiple steady states”, Physics of Fluids 20(5), 056601 (2008).
Beltrami, G. M., Del Guzzo, A., and Repetto, R., “A simple method to regularize supercritical flow profiles in bends”, Journal of Hydraulic Research 45(6), 773–786 (2007).
Binder, B. J., “Steady two-dimensional free-surface flow past disturbances in an open channel: solutions of the Korteweg–De Vries equation and analysis of the weakly nonlinear phase space”, Fluids 4(1), 24 (2019).
Cui, X., “Strong oblique shock waves in granular free-surface flows”, Physics of Fluids 33(8), 083302 (2021).
Defina, A., Susin, F. M., and Viero, D. P., “Numerical study of the Guderley and Vasilev reflections in steady two-dimensional shallow water flow”, Physics of Fluids 20(9), 097102 (2008).
Defina, A., and Viero, D. P., “Open channel flow through a linear contraction”, Physics of Fluids 22(3), 036602 (2010).
Defina, A., Viero, D. P., and Susin, F. M., “Numerical simulation of the Vasilev reflection”, Shock Waves 18(3), 235–242 (2008).
Dey, S., “No‐Choke Flow in Trapezoidal Channels”, Journal of Engineering Mechanics 120(10), 2224–2231 (1994).
Engelen, L., Perrot-Minot, C., Mignot, E., Riviere, N., & De Mulder, T., “Experimental study of bidirectional seiching in an open-channel, lateral cavity in the time and frequency domain” Physical Review Fluids 5(10), 104801 (2020).
Hager, W. H., “Supercritical Flow in Channel Junctions”, Journal of Hydraulic Engineering 115(5), 595–616 (1989).
Hager, W. H., Schwalt, M., Jimenez, O., and Hanif Chaudhry, M., “Supercritical flow near an abrupt wall deflection”, Journal of Hydraulic Research 32(1), 103–118 (1994).
Hager, W. H., “History of roll waves”, L’Acqua (2002).
Horoshenkov, K. V., Nichols, A., Tait, S. J., & Maximov, G. A., “The pattern of surface waves in a shallow free surface flow”, Journal of Geophysical Research: Earth Surface 118(3), 1864-1876 (2013).
Hsu, M.-H., Su, T.-H., and Chang, T.-J., “Optimal channel contraction for supercritical flows”, Journal of Hydraulic Research 42(6), 639–644 (2004).
Ippen, A. T., “An analytical and experimental study of high velocity flow in curved sections of open channels”, California Polytechnic University, Ca (1936).
Ippen, A. T., “High-Velocity Flow in Open Channels: A Symposium: Mechanics of Supercritical Flow”, Transactions of the American Society of Civil Engineers 116(1), 268–295 (1951).
Ippen, A. T., and Dawson, J. H., “High-Velocity Flow in Open Channels: A Symposium: Design of Channel Contractions”, Transactions of the American Society of Civil Engineers 116(1), 326–346 (1951).
Ippen, A. T., and Harleman, D. R. F., “Verification of Theory for Oblique Standing Waves”, Transactions of the American Society of Civil Engineers 121(1), 678–694 (1956).
Kidanemariam, A. & Marusic, I., “On the turbulence-generated free-surface waves in open-channel flows”, 22nd Australasian Fluid Mechanics Conference AFMC2020, doi:10.14264/0912f75.
Lazzarin, T., Viero, D. P., Defina, A., and Cozzolino, L., “Flow under vertical sluice gates: Flow stability at large gate opening and disambiguation of partial dam-break multiple solutions”, Physics of Fluids 35(2), (2023).
Muskatirovic, D., and Batinic, D., “The influence of abrupt change of channel geometry on hydraulic regime characteristics”, Proceedings of the 17th IAHR Congress 397–404 (1977).
Nasif, G., Balachandar, R., and Barron, R. M., “Supercritical flow characteristics in smooth open channels with different aspect ratios”, Physics of Fluids 32(10), 105102 (2020).
Reinauer, R., and Hager, W. H., “Supercritical Flow in Chute Contraction”, Journal of Hydraulic Engineering 124(1), 55–64 (1998).
Rouse, H., Bhoota, B. V., and Hsu, E.-Y., “High-Velocity Flow in Open Channels: A Symposium: Design of Channel Expansion”, Transactions of the American Society of Civil Engineers 116(1), 347–363 (1951).
Schwalt, M., and Hager, W. H., “Shock‐Wave Reduction by Bottom Drop”, Journal of Hydraulic Engineering 120(10), 1222–1227 (1994).
Sturm, T. W., “Simplified Design of Contractions in Supercritical Flow”, Journal of Hydraulic Engineering 111(5), 871–875 (1985).
Tian, Z., Ding, C., Wang, W., and Zhang, C. N., “Supercritical flow in bend with variable curvature radius”, Journal of Hydraulic Research 57(5), 724–732 (2019).
Viero, D. P., and Defina, A., “Extended Theory of Hydraulic Hysteresis in Open-Channel Flow”, Journal of Hydraulic Engineering 143(9), 06017014 (2017).
Viero, D. P., and Defina, A., “Consideration of the Mechanisms for Tidal Bore Formation in an Idealized Planform Geometry”, Water Resources Research (2018).
Viero D.P., Lazzarin T., Peruzzo P., Defina A., “Supercritical flow overpassing forward- or backward-facing steps non-orthogonal to the flow direction”, Physics of Fluids 36, 036604 (2023).
Viero, D. P., Peruzzo, P., and Defina, A., “Positive surge propagation in sloping channels”, Water (Switzerland) 9(7), 1–13 (2017).
Viero, D. P., Susin, F. M., and Defina, A., “A note on weak shock wave reflection”, Shock Waves 23(5), 505–511 (2013).
Zhao, K., Cheng, N. S., & Huang, Z., “Experimental study of free-surface fluctuations in open-channel flow in the presence of periodic cylinder arrays”, Journal of Hydraulic Research 52(4), 465-475 (2014).
See the comments above.
Author Response
"Please see the attachment."
Author Response File: Author Response.docx
Reviewer 3 Report
The paper covers the highlights and graphical abstract as well as it reports interesting data. The methods of investigation are well structured and the discussions are organized consecuely very well.
Good
Author Response
"Please see the attachment."
Author Response File: Author Response.docx
Round 2
Reviewer 2 Report
I reviewed the revised version of the paper, initially submitted to the Hydrology journal.
The paper has been partially improved, but is still far from being publishable.
I put a lot of corrections and comments in the Word file, up to Section 3.
I stopped when I found a fundamental flaw in the theoretical interpretation of the investigated phenomena. According to the Authors, the backwater effect (i.e., the rise in water level upstream of the double bend) is made of two components: the energy needed by the flow to go through the double bend, and the hydraulic jump that turn the upstream supercritical flow into subcritical flow.
This contradicts fundamental principles of free-surface flow hydraulics. The flow through the double bend is subcritical, hence the water level just upstream of the first bend is controlled only by the downstream conditions, i.e., the flow pattern and the energy loss through the double bend. The location of the upstream hydraulic jump is a matter of energy and momentum balance between the subcritical flow just upstream of the first bend, and of the upstream undisturbed uniform (supercritical) flow.
Accordingly, the water level upstream of the first bend (say YU) only depends on the geometry of the double bends and on the flowrate. The location of the hydraulic jump depends on YU and on the characteristics of the upstream undisturbed flow. So, I’m expecting to see a relationship between water level upstream of the DRAB and the discharge, and a check that the experimental location of the hydraulic jump agrees with theoretical calculations.
The experimental results have to be interpreted according to these principles. Section 4 has to be re-thought in this view. For example, I have doubts on scaling YU with the upstream supercritical uniform flow, as done in the current Figure 18.
Comments for author File: Comments.docx
Substantial improvements are needed. I gave a lot of advices and corrections in the attached docx file.
Author Response
"Please see the attachment."
Author Response File: Author Response.docx
