Numerical Simulation of Radiatively Driven Convection in a Small Ice-Covered Lake with a Lateral Pressure Gradient

Round 1

Reviewer 1 Report

Reviewer comments

This manuscript uses numerical simulation to study small ice-covered lakes with a lateral pressure gradient under radially driven convection. Compared to previous articles, this study considered the lateral pressure gradient. Under the condition of zero pressure gradient, the dependence of CML temperature and depth increment on cumulative heating in the calculation of this model is in good agreement with experimental results. The results of the numerical simulation with a pressure gradient setting differed little from that of computations in the initial, zero-gradient variant. However, this simulation results shows that the calculations demonstrate that lateral transport has no obvious suppressive effect on the deepening of the CML is contrary to reality. In addition, there are a number of issues before this manuscript can be considered for acceptance.

#1. The authors of the lower 187 lines give the range of pressure gradients applied in the x-axis as 3.28·10^-6 Pa/m to 3.28·10^-4 Pa/m. What is the basis on which values in this range are chosen?

#2. The number and size of elements during numerical simulation is an important influence on the computation time and accuracy of the results. In line 202 of the manuscript the authors give the number of elements for the model of this study, but do not give a reason why 27 million cells are chosen.

#3. The results in Section 3.1 are those that have been widely reported in previous articles, and comparisons between the results of this study and those in previous articles are better to be given.

#4. The author mentions 'The upstream motion concentrates inside cells' in line 222, what are the cells?

#5. Why a point on the AIM is chosen to represent each state of turbulence?

#6. Why is the comparison between Figure 17 in the literature [33] and this study not shown in this manuscript?

#7. Why a fully developed CML has been formed over the previous three days (line 278)?

#8. The simulation results of this model were not compared with the experimental results, so how is the accuracy of the model ensured?

#9. The authors state that’ The structure and the cause of occurrence of the elongated rolls are very similar to those characteristic of the well-known Langmuir circulation’, so what exactly is the cause of this structure?

#10. What are the critical conditions for cell-to-roll?

Author Response

Answers to Reviewer 1 comments

We are very grateful to the Reviewer for carefully reading our manuscript and providing valuable comments, all of which we tried to take into account in a revised version. Below we provide our responses to the comments, indicating the corresponding changes in the text.

#0. The results of the numerical simulation with a pressure gradient setting differed little from that of computations in the initial, zero-gradient variant. However, this simulation results shows that the calculations demonstrate that lateral transport has no obvious suppressive effect on the deepening of the CML is contrary to reality.

Authors: We have added additional study concerning the case of largest pressure gradient (please see additional illustration of temperature profiles at Figure 9 and corresponding text). As our simulation shows, the dynamics of the CML changes significantly with a large pressure gradient. The relatively small effect of a smaller pressure gradient on the development of CML may be due to the insufficient duration of the simulation and therefore requires further research.

#1. The authors of the lower 187 lines give the range of pressure gradients applied in the x-axis as 3.28·10-6 Pa/m to 3.28·10-4 Pa/m. What is the basis on which values in this range are chosen?

Authors: The values of the pressure gradient was calculated by Darcy–Weisbach equation using well known experimental correlation for the friction coefficient (Darcy friction factor) according to the characteristic mean velocity of the horizontal flow in the fully established turbulent regime of the flow in 2D channel at the corresponding Reynolds number. In the section 2 “Problem definition and computational aspects” we have added corresponding explanations.

#2. The number and size of elements during numerical simulation is an important influence on the computation time and accuracy of the results. In line 202 of the manuscript the authors give the number of elements for the model of this study, but do not give a reason why 27 million cells are chosen.

Authors: The study of the grid sensitivity was presented in our previous papers. As our study showed, the grid with 27 mln cells is enough for obtaining grid-independent solution both for the mean flow and the parameters of velocity pulsations (intensities and stresses). In previous papers we also estimated the Kolmogorov turbulent length scale and showed that its typical values are of the same order as the cell size in most of the computational domain, so the grid is sufficient for Implicit LES. We have added corresponding text in the end of section 2.

#3. The results in Section 3.1 are those that have been widely reported in previous articles, and comparisons between the results of this study and those in previous articles are better to be given.

Authors: We have rewritten section 3.1 to reduce the description of already published results, and also added a paragraph describing the differences between this manuscript and our previous papers.

#4. The author mentions 'The upstream motion concentrates inside cells' in line 222, what are the cells?

Authors: We have removed this sentence and slightly changed the text to avoid misunderstanding.

#5. Why a point on the AIM is chosen to represent each state of turbulence?

Authors: We have added more detailed description of the AIM analysis (please see the paragraph below Figure 3) and improved the caption of Figure 3.

#6. Why is the comparison between Figure 17 in the literature [33] and this study not shown in this manuscript?

Authors: We did not show Figure 17 from [33], because, firstly, this could be regarded as a repetition of already published results, and secondly, the curves in Figure 17 from [33] and Figure 4 from this manuscript overlap, which would complicate their analysis. We have added more detailed description of Figure 4 in the text.

#7. Why a fully developed CML has been formed over the previous three days (line 278)?

Authors: We have rewritten the above text to more clearly indicate that in our calculations, three days are sufficient for CML to form.

#8. The simulation results of this model were not compared with the experimental results, so how is the accuracy of the model ensured?

Authors: In Figure 14, as in our previous papers, we show a comparison of simulation results and observational data, which are in good agreement. In the text, both in the introduction and in the last section, we have added several phrases about comparing our computational model with observational data.

#9. The authors state that’ The structure and the cause of occurrence of the elongated rolls are very similar to those characteristic of the well-known Langmuir circulation’, so what exactly is the cause of this structure?

Authors: We are grateful to the reviewer for this valuable comment. Indeed, our study does not indicate the reasons for the transition from convective cells to rolls because we currently have no information about the exact reasons for the transition. In the text, we tried to more clearly describe the possible reasons for the appearance of two-dimensional rolls in our calculations.

#10. What are the critical conditions for cell-to-roll?

Authors: Unfortunately, we currently have no information about the critical conditions for the transition from cells to rolls. But, as we noted in the revised text, the imposed pressure gradient leads to the appearance of a selected direction, according to which the flow self-organizes. Thus, in our simulations we expect a transition to two-dimensional rolls even at a very small applied pressure gradient. In real conditions, there should be a critical value of the pressure gradient, below which the transition is not observed.

Author Response File: Author Response.pdf

Reviewer 2 Report

The manuscript “Numerical simulation of radiatively driven convection in a small ice-covered lake with a lateral pressure gradient” by smirnov et al. demonstrated existence of CML in a small ice-covered lake used Implicit large Eddy Simulation based on CFD-code_SINF/Flag-2.  It is good written and organzaition. Thus, I would suggest it should be accepted.

Author Response

Answers to Reviewer 2 comments

Authors: We kindly thank the Reviewer for reading our manuscript and recommending it for publication. In the revised version, we tried to improve the text and add more information about the study.

Author Response File: Author Response.pdf

Reviewer 3 Report

This paper reported a numerical investigation on a radiatively driven convection (RDC) in a small ice-covered lake with a lateral pressure gradient. So far, the main contribution of this paper is the reproduction of the evolution of CML in a small ice-covered lake with a lateral pressure gradient over several days using Implicit Large Eddy Simulation. They reported that after a few days of lateral pressure gradient occurrence, convective cells are replaced by rolls oriented toward the lateral transport, and the change in CML’s turbulence patterns under lateral pressure gradient is confirmed by Anisotropic Invariant Map analysis. However, the novelty and originality of this paper should clearly be stated; only a line like "Until now, little is known about how the structure of CML changes in lakes with lateral transport." shouldn't be the novelty.  Although the paper is well-documented and well-presented, some very minor issues (typographical and editing issues) should be resolved, and a few of them are listed below as examples:

1. Page 2, line 54: "by 2001 is given in [7]"  should be rewritten.

2. Page 3, line 142~143: "<<unstructured>>" should be avoided; the sentence should be rewritten. 

3. Page 4: equation numbers should be indented on the right margin.

4. Fig 3 & 10: Requested to provide sub-captions for top and bottom figures. 

Finally, the authors are requested to take a thorough and careful review of other typographical mistakes. 

A minor editing of the English language is required; it will improve the quality of the paper. 

Author Response

Answers to Reviewer 3 comments

Authors: We are very grateful to the Reviewer for carefully reading our manuscript and pointing out some inaccuracies in the text, which we corrected in the revised version. We also read the text and corrected other typos and mistakes found, as well as performed editing of the English language. We also rewrote the last part of the introduction to clearly highlight the novelty and originality of our manuscript. Below we provide our responses to the comments, indicating the corresponding changes in the text.

1. Page 2, line 54: "by 2001 is given in [7]"  should be rewritten.

Authors: We have rewritten the sentence.

2. Page 3, line 142~143: "<<unstructured>>" should be avoided; the sentence should be rewritten.

Authors: We have rewritten the sentence to avoid inappropriate use of the term “unstructured”.

3. Page 4: equation numbers should be indented on the right margin.

Authors: We have corrected equation numbers.

4. Fig 3 & 10: Requested to provide sub-captions for top and bottom figures.

Authors: We have corrected the captions of the figures.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

N/A.

N/A.