Numerical Simulation of 3D Flow Structure and Turbulence Characteristics near Permeable Spur Dike in Channels with Varying Sinuosities

Comments 3: Add all the assumptions for the mathematical modeling.

Response 3: Thank you for pointing that out. We agree with this comment. All assumptions for mathematical modeling have been added on lines 203 - 221.

Comments 4: In Figure 2, increase the font size of letters. (because it is hard to read).

Response 4: Thank you for pointing that out. We agree with this comment. The font size of Figure 2 has been increased at line 301.

Comments 5: Why the research conducted on bend with 45, 90 & 180 degrees only. What if for 60 deg. or 120 deg.? Explain?

Response 5: Thank you for pointing this out. We agree with this comment. Question 5 and Question 6 are similar, so the answer has been provided below Question 6.

Comments 6: If possible, include the results for other possible degrees of bend. It will strengthen the research and more useful.

Response 6: Thank you for pointing that out. We agree with this comment. This study aims to summarize the flow pattern variation law of three typical curves by studying typical curves, so as to provide reference for the study of other curves. Therefore, when selecting curve types in this study, we refer to previous research results, and we find that previous studies have focused on 90° curves or 180° curves, which indicates that the above two curves have certain representativeness. Therefore, when we select curve types, we determine 45°, 90° and 180° curves according to the gradual decrease of curvature. This prediction may have errors, but considering that the numerical simulation will occupy huge computational resources and the curvature of the laboratory flume can not be changed arbitrarily, this method still has certain practical value. At the same time, thank you very much for this question. In the follow-up research of our team, we will fully adopt your opinion and conduct numerical simulation research on other curves.

Comments 7: Are the equations (7) & (8) derived by authors or taken from other sources? If taken from others, give ref.

Response 7: Thank you for pointing that out. We agree with this comment. Equations (7) and (8) are derived from other people's research. In the article, 581 lines of equation (7) and 625 lines of equation (8) have been marked, and the source of the formula has been explained in detail. After changing, the number of equations becomes (8) and (9).

Comments 8: Add conclusion of the study.

Response 8: Thank you for pointing that out. We agree with this comment. Added discussion on lines 667- 733, modified conclusion on lines 738 - 743 and 760 - 767.

Comments 3: (1)For K- ξ, what are the boundaries of the fluid (obstacles or changing riverbanks) that explain the changes in fluid kinetic energy in various scenarios (such as inside embankments, inside, outside, etc.)? River bed, embankment? (2) What are the possible roles of SSF, TKE, and average flow characteristics in the design of embankment flood control and water resource scheduling?

Response 3: Thank you for pointing that out. We agree with this comment. Model boundaries include riverbed, riverbank, and groin. As a boundary condition of the calculation model, the spur dike has a strong interference effect on the flow direction between the two permeable spur dikes, which will lead to the enhancement of the transverse flow effect, so the turbulent kinetic energy between the two permeable spur dikes is obviously enhanced. As a boundary condition composed of riverbed and bank, river channel has little influence on normalized time-averaged turbulent kinetic energy upstream of spur dike, because there is no obstacle upstream, and the change of turbulent kinetic energy is only affected by curve curvature, while the influence of curve curvature on pulsating velocity is less than that of spur dike. Therefore, we observe in Figure 12 that normalized time-averaged turbulent kinetic energy is very small before 3.14m from curve entrance, and the intensity of turbulent kinetic energy in three kinds of curves is almost coincident. As the flow passes through the groin, the disturbance of the boundary condition of the groin to the flow is lost again, which leads to the gradual weakening of particle collision and separation motion in the fluid, so we see in Figure 12 that the normalized time-averaged turbulent kinetic energy begins to decrease.

(2) Thank you for pointing that out. We agree with this comment. SSF study can grasp the law of transverse sediment transport in bend, which has certain guiding significance for the study of sediment deposition and scouring effect in bend. NTKE can reflect the energy loss of water flow in bend, which has certain guiding significance for controlling water flow velocity. The three-dimensional flow motion is complex, and factors such as velocity and pressure fluctuate with time. Average flow characteristics reduce the complexity of the flow by averaging these fluctuations, making the problem easier to deal with. In river regulation, we tend to focus on the overall performance of the system rather than transient fluctuations. By studying the average flow characteristics, we can analyze the steady-state and periodic behavior of the fluid system.

Comments 4: I suggest the authors revise the introduction of the study per the comments raised. The authors can also use the following points below as a guideline to help them come up with an exciting introduction that is more scientific.

Background & Significance: (What general background does the reader need to understand the manuscript and how important is it in the context of scientific research).

Response 4:Thank you for pointing that out. We agree with this comment. Background and significance added on lines 28 - 42

The background and significance of comparing time-averaged flow fields in curved channels with different curvatures mainly include the following aspects:

Firstly, it helps us to understand the influence of curvature on river flow, so as to help us evaluate the hydrodynamic characteristics such as velocity, discharge, water surface line and sediment transport, which is of great significance for river regulation, river reconstruction and flood prevention. Meanwhile, the time-averaged flow field characteristics in different curvature rivers are helpful for hydraulic engineers to predict the velocity distribution and sediment movement, which is of certain value for reasonable design of river regulation buildings. Secondly, the curvature variation will lead to flow instability, such as vortex and turbulence. Studying the characteristics of flow field in different curvature channels can help us understand the development trend of flow in curved channels and predict river bed deformation and channel erosion. Finally, the difference of turbulence and velocity in curved river channel will affect the habitat and migration of aquatic organisms. Comparing the time-averaged flow field in different curved river channel can provide basis for the protection and restoration of river ecosystem.

Problem definition: (What are the research questions to fill in the gaps of the existing knowledge body or methodology )?

Response 4:Thank you for pointing that out. We agree with this comment. Problem definition added on lines 181 – 195.

This study supplements existing knowledge bodies and methods as follows: Most of the previous researches are based on a curvature river as background, so they ignore the reality that the curvature of natural river is complex, and the study of a curvature river can not reflect the influence of river curvature change on the time-averaged flow field. Therefore, the research first uses the physical experiment and numerical simulation method to verify the turbulence model, and then uses the turbulence model to simulate the time-averaged flow field in various bends. Finally, the time-averaged flow field in different curvature river channels is compared, which provides reference for river management and ecological restoration with different curvature. This method firstly ensures the reliability of turbulence model, and secondly makes up for the defect that the laboratory can not provide multiple curves by numerical simulation, which effectively expands the research scope and makes the research no longer stick to one curve.

Motivations & Objectives: (Why are you conducting the study and what are the goals to achieve?)

Response 4:Thank you for pointing that out. We agree with this comment. Motives and goals have been added on lines 195 - 200.

Objective of this study: This study was conducted because previous studies of curves were limited by experimental conditions and could not compare the effect of curve curvature on the flow field, which is crucial. The goal of this study is to verify the RNG k-e turbulence model and prove the reliability of the turbulence model. Secondly, the time-averaged flow field variation law in three typical curved channels is studied and summarized, and then the flow field variation in other types of curved channels is predicted, which provides reference for natural river management and river ecological restoration.

Comments 5: Section 2 needs a more notable reedit below.

The meaning and purpose of each equation need to be explained. It is recommended to write a paragraph in the equation set, and then describe the meanings of each term and physical quantity separately.

Response 5: Thank you for pointing that out. We agree with this comment. The meaning and purpose of each equation has been explained and labeled on lines 223 - 231, 240 - 246, and 257 - 263. Each term and physical quantity has been described and labeled on lines 234 - 237, 252 - 254, and 270 - 272.

In Lines 165-174, What is the reason for choosing these numbers? It needs to be clarified whether such small embankments and rivers are related to the goals and models of this study itself.

Response 5: Thank you for pointing that out. We agree with this comment. These values have been explained in lines 275 - 292 and clarified in lines 292 - 294 as relevant to the objectives and models of the study itself.

These values represent the flume parameters used in the physical test and the model parameters used in the numerical simulation. 45°, 90° and 180° represent the curve types used in the numerical simulation, and 8m,4m and 2m represent the curve radii of the above three types respectively. Because the purpose of the study is to compare the time-averaged flow field changes in typical curves, after reading the existing research results, we found that 90° and 180° curves have attracted many people's attention, which indicates that the above two curves have certain representativeness. Therefore, this study finally decided to choose 45°, 90° and 180° curves according to the decreasing curvature. The upstream length of laboratory flume and numerical model is 6.28m, which is 42 times of spur dike length, which is beneficial to the full development of upstream flow. The width of the laboratory flume was 0.8 m, so the numerical model width was kept consistent with the physical model for model validation. By consulting the existing research results, it is found that the ratio of spur dike length to flume width is about 0.2, and the ratio of spur dike length to water depth is about 1.5. Therefore, the ratio of spur dike length to flume width designed in this study is 0.19, and the ratio of spur dike length to water depth is 1.25. Finally, the length, thickness and height of spur dike are determined as 0.15m, 0.02m and 0.17m. Previous studies have given an optimal water permeability of 20%-30%, so this study uses a water permeability of 20%. The ratio parameters between spur and flume used in the test were determined strictly according to the recommended values of previous studies, and the model validation was carried out at the beginning of the study, so this kind of spur and river is relevant to the objectives and models of this study.

In Lines 179-185, what are the criteria for selecting FLUENT mode parameters?

Response 5: Thank you for pointing that out. We agree with this comment. Criteria for selecting model parameters have been added on lines 306 - 313.

High Reynolds number flow conditions are designed in this study, and curved river channels are involved. The moderate turbulence intensity ranges from 5% to 10%, and the turbulent viscosity ratio ranges from 10 to 100. Considering that the boundary conditions of the flume in this study are not complicated, the inlet velocity is 0.52m/s, and the Reynolds number is 6.9. By consulting FLUENT operation manual and referring to the recommended values of relevant studies, the final turbulence intensity is taken as 5%, and the turbulent viscosity ratio is taken as 10. When the inlet velocity is 0.52m/s, the tailgate depth measurement is 0.12m.

In Lines 190-198, the source of the method needs to be cited and its description needs to be simplified, as it is not the focus of this article.

Response 5: Thank you for pointing that out. We agree with this comment. Lines 190 - 198 have been deleted.

In Lines 200-203, why did you choose the case 4 experiment? What is the significance of distinguishing it from case 3 and its impact on the conclusion of this article?

Response 5: Thank you for pointing that out. We agree with this comment. Added on lines 320-332.

Since there is only a 180° bend model in the laboratory, the size of the laboratory tank model used in Case 4, as well as the spur dike model and inlet velocity and tailgate depth, remain the same as the numerical tank model used in Case 3. Therefore, Case 4 is selected to compare with Case 3 in this study to ensure the reliability of turbulence model. The significance of separating Case 3 and Case 4 is to compare the time-averaged velocity in the same bend by numerical simulation and physical test respectively, and to analyze the correlation between simulated velocity and measured velocity. The final results show that the correlation coefficient of the inner bank velocity is 0.94 and the correlation coefficient of the outer bank velocity is 0.88 in Case 3 and Case 4.

In Lines 208-211, for parameters of significant importance in this article, it is recommended to highlight and standardize their mathematical expressions and clarify their meanings.

Response 5: Thank you for pointing that out. We agree with this comment. Modified on lines 347 - 351.

In Lines 211-212, repeat the statement in Table 1.

Response 5: Thank you for pointing that out. We agree with this comment. The statements in Table 1 have been repeated at lines 337 - 344.

In Lines 213-238, the connection between the expression and the image is not clear. It is recommended to express this part in the form of a table for easy review.

Response 5: Thank you for pointing that out. We agree with this comment. Table redrawn at line 383.

Figure 3, the points and markers in Figure 3 are almost indistinguishable, so it is recommended to delete them or display them in the subgraph of Figure 2

Response 5: Thank you for pointing that out. We agree with this comment. Deleted Figure 3

Section 2.3, What about the citation for the experimental method? I suggest experimental setup is displayed in the form of a table. The corresponding relationship with section 2.2 needs to be specifically explained here.

Response 5: Thank you for pointing that out. We agree with this comment. The relationship between Section 2.2 and Section 2.3 has been described in lines 400 - 407. The physical test (Case4) settings are consistent with those of the numerical simulation test (Case3). The physical test settings are shown in Case 4 in Table 1. A total of four sets of tests are designed. The first three sets of tests (Case1,Case2,Case3) are numerical simulation tests conducted in 45°, 90°, 180° curves. The fourth set of tests (Case4) is physical tests conducted in 180° curves. The reliability of turbulence model is verified by comparing Case3 and Case4. Section 2.3 mainly describes Condition 4 in Table 1. This section is the repeatability physical test for Condition 3 in Section 2.2.

Section 2.4, This section is recommended to be explained separately in the Section result.

Response 5: Thank you for pointing that out. We agree with this comment. Section 2.4 has been summarized in lines 738 - 743.

Generally, Suggest that Section 2 should highlight the experimental process and its corresponding relationship with Sections 3 and 4 of this article.

Response 5: Thank you for pointing that out. We agree with this comment. The test conditions have been restated in lines 320 - 332, and lines 428 - 431 emphasize that the numerical model described in Section 2 can be used for subsequent studies, and that the results of Section 3 are based on the turbulence model validated in Section 2, strengthening the correspondence between Section 2 and Section 3 and Section 4.

Comments 6: In Section 3, What are the selection criteria for sections, and why are there such significant differences in the selected sections among different bending degrees? In Line 294, the images cannot indicate, whether can they be data and/or phenomena. Also, Line 349, Line 417, Line 471, and many others should be revised. In addition, equations 7 and 8, Lines 392-395, and Lines 437-440 are suggested to be reorganized in Section 2 (method/model section).

Response 6: Thank you for pointing that out. We agree with this comment. Position of Vertical Section in Section 3 (Figures 4, 5 and 6) It is related to the length of spur dike. It is found that the way of selecting sections according to the length of spur dike is common in previous studies, which can well reflect the velocity distribution at representative positions near spur dike. By referring to previous studies, the flow field changes in the range of 1-3 times the length of spur dike upstream and downstream, and the turbulence intensity and secondary flow intensity are relatively high. The velocity on sections in this range is representative. Therefore, section a is selected at the position of twice the length of spur dike upstream, section b is selected at the position between two spur dikes, the distance between section b and two spur dikes is exactly one time the length of spur dike, and section c is selected at the position of twice the length of spur dike downstream. In the same kind of bend, sections a,b and c are located upstream, downstream and between spur dikes respectively, and the velocity distribution at these three positions is quite different, which is due to the vortex generated between spur dikes and the high turbulence intensity. The velocity distributions at the locations of sections a, b and c are different in curves with different curvatures, which is caused by the curvature increasing from 0.125 to 0.5. The horizontal section position (Figure 7, 8 and 9) is related to water depth. It is found that section a is selected at the position of 10% water depth, and section a is close to the river bed, so that the influence of river bed on velocity can be observed; section b is selected at the position of 90% water depth, and section b is close to water surface, so that the velocity distribution far away from river bed plane can be reflected. The difference of velocity distribution between the two sections is due to the lower velocity near the bed and the higher velocity near the water surface.

Line 294, line 349, cloud response and velocity distribution, which is composed of data, calculation formula has been added to line 441, line 445, line 448, line 497, line 500, line 503. Figure 10 and Figure 11 are composed of data to modify Figure 10 and Figure 11. The modified pictures are numbered (11) and (12). Formula (7)(8) has been explained in Section II, added in lines 378 - 383, modified formula numbers are (8),(9).

Comments 7: Section 4 is more like a conclusion than a discussion, thus, it needs re-editing.

Response 7: Thank you for pointing that out. We agree with this comment. Discussion re-added on lines 667 - 733.

Comments 8: What are the application prospects of each Finding in this study, which needs to be emphasized for discussion? The weaknesses or shortcomings in each finding, as well as the similarities and differences with relevant research and the reasons behind them, need to be discussed. 

Response 8: Thank you for pointing that out. We agree with this comment. The application prospects of the study and the strengths and weaknesses of each finding, as well as the comparison with related studies, have been added in the discussion section.

In lines 671 - 683, 691 - 704, and 715 - 732 of the discussion section, the prospects for application of the study, as well as each finding and the reasons behind it, have been analyzed.

Comments 3: The governing equations is inaccurate for incompressible flows. The density of the fluid shall be constant. 

Response 3: Thank you for pointing that out. We agree with this comment. The equation has been changed at lines 233, 237, and 251.

Comments 3: Introduction: The literature review covers previous related work but could be expanded with some more discussion on recent advances in numerical modeling of flows past hydraulic structures. The objectives and significance of the study are well described.

Response 1: Thank you for pointing that out. We agree with this comment. Added on lines 163 - 166 and 175 - 176.

Comments 4: Methodology: Sufficient details are provided to reproduce the simulations, including mesh properties, boundary conditions, and solution methods. Providing some sample simulation convergence data could further validate the adequacy of the numerical model.

Response 1: Thank you for pointing that out. We agree with this comment. The correlation analysis of velocity was performed in this study, and the convergence accuracy of numerical simulation was set to 0.00001. Thank you very much for your suggestion, and our team will pay attention to this in future studies.

Comments 5: Results and Discussion: The presentation of results is satisfactory with sufficient graphs and visualizations of flow patterns and turbulence parameters. Relating the results to practical implications such as spur dike design or sediment management would further improve this section. The limitations of the numerical modeling approach are noted e.g. the limitations of RANS modeling for turbulence are not mentioned. The implications for applied engineering could be expanded on.

Response 1: Thank you for pointing that out. We agree with this comment. Results have been linked to practical impacts such as spur dike design and sediment management at lines 695, 760 - 766, 714 – 720.

Thank you for pointing that out. We agree with this comment. Limitations of RANS simulation are added on lines 728 - 733. RANS simulation is difficult to capture the small-scale structure in turbulence, which depends on turbulence model. However, different turbulence models may have different applicability to different flow situations. RANS simulation depends on mesh greatly, and mesh quality will affect simulation accuracy. Therefore, it is necessary to pay attention to this point when using RANS model.

Comments 6: Conclusions: Suggestions for future work could be expanded, for example, comparing numerical simulations with physical model data.

Response 1: Thank you for pointing that out. We agree with this comment. A comparison of the numerical simulation with the physical model has been added in lines 738 - 744 of the results section.