the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 13 May 2024
Three-dimensional discrete element simulations on pressure ridge formation
Abstract. This study presents the first three-dimensional discrete element method simulations on pressure ridge formation. Pressure ridges are an important feature of the sea-ice cover, as they contribute to the mechanical thickening of ice and likely limit the strength of sea ice in large scale. We validate the simulations against laboratory-scale experiments, confirming their accuracy in predicting ridging forces and ridge geometries. Then we demonstrate that Cauchy-Froude scaling applies for translating laboratory-scale results on ridging to full-scale scenarios. We show that non-simultaneous failure, where an ice sheet fails at distinct locations across the ridge length, is required for an accurate representation of the ridging process. This process cannot be described by two-dimensional simulations. We also find a linear relationship between the ridging forces and the ice thickness, contrasting with earlier results in the literature obtained by two-dimensional simulations.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-831', Anonymous Referee #1, 15 Jun 2024
General Comments
Thanks for the opportunity. I enjoyed reading this manuscript.
This paper describes simulations conducted with a three-dimensional DEM-FEM sea ice model to study the dynamics of ridging. The study is grounded by a comparison of the model performance at laboratory scale with an experiment performed by Tuhkuri and Lensu (2002). The model simulations are then extended to a larger scale to see how the process scales. The authors draw conclusions about how the ridge force should scale with ice thickness in a three-dimensional setting, and about how ridge behavior might follow Cauchy-Froude scaling across scales. While I think the authors need to add some details, clarify some assumptions and couch some conclusions more carefully, their methodology is sound and the manuscript is well written and organized. Their conclusions are largely justified, in some ways provocative and worthy of publication
Science related questions (simply in the order in which they occured to me in reading the manuscript)
I think this experiment applies to unconsolidated ridges. If that is the case, it is worth noting somewhere near the top.
Line 35: Definition of Full-scale. My understanding is that ridges form over a variety of scales. So, I am not clear on what ‘full scale’ specifically means here. A reference would be useful here, if there is observational evidence for a particular ‘scale of a natural ice ridge’. From reading, it seems that for this manuscript's purposes full-scale is 10 times laboratory scale. But this should be stated upfront with some justification for the choice.
Line 51: DEM or FEM-DEM? I would not describe the FEM-DEM method being used here as ‘rather standard’, the beam component is more sophisticated than most that I am familiar with. Throughout the manuscript, the model is called a DEM. But I am not sure if DEM with FEM joints is referred to elsewhere in the literature as DEM.
Line 84: Do the authors think that the Tuhkuri and Lensu experiments captured 3-dimensional aspects of ridge formation? From the arguments later in the paper regarding the ridge force scaling linearly with h, it seems that 3-d behavior is already exhibited at the lab scale, if it is 3d behavior that leads to linear scaling of the force with h.
Line 93: It would be useful if the authors would comment on the implication of having one side of the ridge, being a thick unbreakable sheet as compared to two breakable sheets of equal thickness. I understand that with equal thicknesses the simulated ice rafted too much. I would like to know why that was the case. But also, this setup seems like an ice-structure interaction rather than a ridge formation between sheets of ice. For example, this setup does not allow a sail to form in addition to a keel. I imagine this might be a fair idealization as a first shot of handling this problem in 3D. I would just like to hear more justification for the setup.
Line 94: Can this be read to mean that you chose the aspect ratio of your elements to get simulated ice blocks in the rubble of the ridge that had the right characteristics compared to field observations?
Line 100: Please explain why an ice velocity of 0.05 m s-1 is used rather than 0.01 m s-1 Was it for computational efficiency or due to other considerations?
Line 112: Please clarify if 'l' in the Froude number is meant to be a vertical length scale, horizontal, or if they're considered comparable.
Line 126: From the earlier statements one would conclude that the thickness of the rigid floe affects the ridging force. In the LS it was chosen to be larger than the moving floe, because there was excessive rafting if it were not. So, this statement seems in conflict with other statements, unless I’m not interpreting it correctly. Intuitively it seems like the ‘l’ in the Froude number might be related to the thickness of the unbreakable sheet.
Line 142: I would not say that ‘F fluctuates around a mean value’ in the second phase of the experiment. To my eye it increases linearly in both the experiment and in the simulations (at a lesser slope). Given this, I’m not sure how the standard deviation is calculated for the figures, and if it is representative. By eye it looks like the simulations have notably greater standard deviation than the experiments unless you include the linear trend as part of the std.
Line 156: The plateau in W* is not visible to me.
Line 180. I think what has been demonstrated is that the model follows Cauchy-Froude scaling, but this does not necessarily mean that nature does. This conclusion should be stated a bit more carefully.
Line 191-197. I think this is an interesting point, potentially deserving of a figure if the supplementary simulations could supply one.
Line 222-225. Related to my previous (Line 191) comment. I do not fully understand the basis for the statement starting on line 225. I take it to mean that the ridge length was varied in FS experiments, and at a 30:1 L/h ratio, non-simultaneous failure behavior was observed. But would the non-simultaneous failure behavior differ at 100:1 or 1000:1? The author’s again use the term full-scale here, but might not things change at floe scales larger than the ‘full-scale’ considered here. For that matter the simulated LS scale gave results quite similar to the FS, which returns to my earlier comment (Line 84). It would be good if the authors could disentangle their conclusions a bit better here with regards to scale and 3d vs 2d behavior.
Technical corrections
Line 3: suggestion: ‘at’ large scale
Line 6: suggestion: ‘along the contact interface’ rather than ‘across the ridge length’.
Line 13: no need for ‘Thus’
Line 21: ‘The’ first
Line 24: ambiguous phrase. What are the different processes involved and how do they differ from ‘the process itself’?
Line 81 possibly replace ‘of the amount of ice pushed’, with ‘the distance the ice was pushed’?
Line 82: Were the 3 experiments in each of the four sets (S1..S4), replicates of each other?
Line 145: At what point in the experiment and simulation are the profiles taken delta=4m? 10m? Line 158 suggests it’s ‘at the end of the experiment’ but should probably say that here.
Line 173: ‘conducted at different scales’
Figure 6, etc. The terminology ‘LS simulations to FS’ isn’t explained anywhere. Although I’m guessing it means that the LS variables are CF scaled (Force is multiplied by lambda^3 for example).
Citation: https://doi.org/10.5194/egusphere-2024-831-RC1 -
AC1: 'Reply on RC1', Marek Muchow, 01 Aug 2024
We sincerely thank the reviewers for their insightful comments and constructive feedback. Their suggestions have significantly improved the quality of our manuscript. We appreciate their time and effort in reviewing our work. All the answers to the reviewers comments are in the attached document.
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AC1: 'Reply on RC1', Marek Muchow, 01 Aug 2024
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RC2: 'Comment on egusphere-2024-831', Anonymous Referee #2, 26 Jun 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-831/egusphere-2024-831-RC2-supplement.pdf
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AC2: 'Reply on RC2', Marek Muchow, 01 Aug 2024
We sincerely thank the reviewers for their insightful comments and constructive feedback. Their suggestions have significantly improved the quality of our manuscript. We appreciate their time and effort in reviewing our work. All the answers to the reviewers comments are in the attached document.
-
AC2: 'Reply on RC2', Marek Muchow, 01 Aug 2024
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2024-831', Anonymous Referee #1, 15 Jun 2024
General Comments
Thanks for the opportunity. I enjoyed reading this manuscript.
This paper describes simulations conducted with a three-dimensional DEM-FEM sea ice model to study the dynamics of ridging. The study is grounded by a comparison of the model performance at laboratory scale with an experiment performed by Tuhkuri and Lensu (2002). The model simulations are then extended to a larger scale to see how the process scales. The authors draw conclusions about how the ridge force should scale with ice thickness in a three-dimensional setting, and about how ridge behavior might follow Cauchy-Froude scaling across scales. While I think the authors need to add some details, clarify some assumptions and couch some conclusions more carefully, their methodology is sound and the manuscript is well written and organized. Their conclusions are largely justified, in some ways provocative and worthy of publication
Science related questions (simply in the order in which they occured to me in reading the manuscript)
I think this experiment applies to unconsolidated ridges. If that is the case, it is worth noting somewhere near the top.
Line 35: Definition of Full-scale. My understanding is that ridges form over a variety of scales. So, I am not clear on what ‘full scale’ specifically means here. A reference would be useful here, if there is observational evidence for a particular ‘scale of a natural ice ridge’. From reading, it seems that for this manuscript's purposes full-scale is 10 times laboratory scale. But this should be stated upfront with some justification for the choice.
Line 51: DEM or FEM-DEM? I would not describe the FEM-DEM method being used here as ‘rather standard’, the beam component is more sophisticated than most that I am familiar with. Throughout the manuscript, the model is called a DEM. But I am not sure if DEM with FEM joints is referred to elsewhere in the literature as DEM.
Line 84: Do the authors think that the Tuhkuri and Lensu experiments captured 3-dimensional aspects of ridge formation? From the arguments later in the paper regarding the ridge force scaling linearly with h, it seems that 3-d behavior is already exhibited at the lab scale, if it is 3d behavior that leads to linear scaling of the force with h.
Line 93: It would be useful if the authors would comment on the implication of having one side of the ridge, being a thick unbreakable sheet as compared to two breakable sheets of equal thickness. I understand that with equal thicknesses the simulated ice rafted too much. I would like to know why that was the case. But also, this setup seems like an ice-structure interaction rather than a ridge formation between sheets of ice. For example, this setup does not allow a sail to form in addition to a keel. I imagine this might be a fair idealization as a first shot of handling this problem in 3D. I would just like to hear more justification for the setup.
Line 94: Can this be read to mean that you chose the aspect ratio of your elements to get simulated ice blocks in the rubble of the ridge that had the right characteristics compared to field observations?
Line 100: Please explain why an ice velocity of 0.05 m s-1 is used rather than 0.01 m s-1 Was it for computational efficiency or due to other considerations?
Line 112: Please clarify if 'l' in the Froude number is meant to be a vertical length scale, horizontal, or if they're considered comparable.
Line 126: From the earlier statements one would conclude that the thickness of the rigid floe affects the ridging force. In the LS it was chosen to be larger than the moving floe, because there was excessive rafting if it were not. So, this statement seems in conflict with other statements, unless I’m not interpreting it correctly. Intuitively it seems like the ‘l’ in the Froude number might be related to the thickness of the unbreakable sheet.
Line 142: I would not say that ‘F fluctuates around a mean value’ in the second phase of the experiment. To my eye it increases linearly in both the experiment and in the simulations (at a lesser slope). Given this, I’m not sure how the standard deviation is calculated for the figures, and if it is representative. By eye it looks like the simulations have notably greater standard deviation than the experiments unless you include the linear trend as part of the std.
Line 156: The plateau in W* is not visible to me.
Line 180. I think what has been demonstrated is that the model follows Cauchy-Froude scaling, but this does not necessarily mean that nature does. This conclusion should be stated a bit more carefully.
Line 191-197. I think this is an interesting point, potentially deserving of a figure if the supplementary simulations could supply one.
Line 222-225. Related to my previous (Line 191) comment. I do not fully understand the basis for the statement starting on line 225. I take it to mean that the ridge length was varied in FS experiments, and at a 30:1 L/h ratio, non-simultaneous failure behavior was observed. But would the non-simultaneous failure behavior differ at 100:1 or 1000:1? The author’s again use the term full-scale here, but might not things change at floe scales larger than the ‘full-scale’ considered here. For that matter the simulated LS scale gave results quite similar to the FS, which returns to my earlier comment (Line 84). It would be good if the authors could disentangle their conclusions a bit better here with regards to scale and 3d vs 2d behavior.
Technical corrections
Line 3: suggestion: ‘at’ large scale
Line 6: suggestion: ‘along the contact interface’ rather than ‘across the ridge length’.
Line 13: no need for ‘Thus’
Line 21: ‘The’ first
Line 24: ambiguous phrase. What are the different processes involved and how do they differ from ‘the process itself’?
Line 81 possibly replace ‘of the amount of ice pushed’, with ‘the distance the ice was pushed’?
Line 82: Were the 3 experiments in each of the four sets (S1..S4), replicates of each other?
Line 145: At what point in the experiment and simulation are the profiles taken delta=4m? 10m? Line 158 suggests it’s ‘at the end of the experiment’ but should probably say that here.
Line 173: ‘conducted at different scales’
Figure 6, etc. The terminology ‘LS simulations to FS’ isn’t explained anywhere. Although I’m guessing it means that the LS variables are CF scaled (Force is multiplied by lambda^3 for example).
Citation: https://doi.org/10.5194/egusphere-2024-831-RC1 -
AC1: 'Reply on RC1', Marek Muchow, 01 Aug 2024
We sincerely thank the reviewers for their insightful comments and constructive feedback. Their suggestions have significantly improved the quality of our manuscript. We appreciate their time and effort in reviewing our work. All the answers to the reviewers comments are in the attached document.
-
AC1: 'Reply on RC1', Marek Muchow, 01 Aug 2024
-
RC2: 'Comment on egusphere-2024-831', Anonymous Referee #2, 26 Jun 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-831/egusphere-2024-831-RC2-supplement.pdf
-
AC2: 'Reply on RC2', Marek Muchow, 01 Aug 2024
We sincerely thank the reviewers for their insightful comments and constructive feedback. Their suggestions have significantly improved the quality of our manuscript. We appreciate their time and effort in reviewing our work. All the answers to the reviewers comments are in the attached document.
-
AC2: 'Reply on RC2', Marek Muchow, 01 Aug 2024
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Arttu Polojärvi
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(2225 KB) - Metadata XML