Wave Interaction and Overwash with a Flexible Plate by Smoothed Particle Hydrodynamics

Round 1

Reviewer 1 Report

The paper “Wave Interaction and Overwash with a Flexible Plate by Smoothed Particle Hydrodynamics” focuses on the Overwash event in the thin plate using smoothed particle hydrodynamics (SPH). The numerical methodology of Incompressible SPH is well explained although there is no experiment result to compare wave profile however the author uses the analytic solution to compare amplitude and wavelength. Using thin plate theory, the elastic behavior of the thin plate was reproduced.

Overall the paper is of good quality and adds value to other literature studies centered on this subject. The reviewer feels the paper can be substantially improved before being accepted for publications, and therefore suggests the following revisions:

 

line 105 it is mentioned that L_bottom = 5m and L_beach= 4m however in Figure 2 it shows the end of the beach is 8m.

line 110 ‘’ Spatial resolution is set to be ∆x = 5m, does it means initial particle distance? Can you elaborate on this?

line 174 ‘’The pitch motion of the plate is also recorded and shown in Figure 7’’. I think this means Figure 6

Figure 1 there is no wave gauge in the schematic view of the water basin setup, please add the exact position wave gauge in the figure.

Figure 6 and Figure 10 shows only one legend for heave motion if the author wants to use the same legend, it’s better to put the legend at the end of the figure (below Figure).

Figure 7 and Figure 11. It’s very hard to differentiate between a_1, a_2, and a_3. Using a marker or different line type as well as Figure 6

Some questions

1. Does there is a correlation between initial particle distance with wave height or amplitude? Because you use only one initial particle distance, some ref. shows that initial particle distance has a significant effect on the accuracy of wave height. (Altomare et al., 2017)(Trimulyono and Hashimoto, 2019)
2. Only one wave condition i.e. intermediate wave, why the author does not consider others' conditions?
3. The wave basin is a short tank compare to simulated wavelength λ=2.35 m, there is only 2λ in a wave basin. Could you elaborate that there is no reflection wave on the beach?

 

Reference.

Altomare, C. et al. (2017) ‘Long-crested wave generation and absorption for SPH-based DualSPHysics model’, Coastal Engineering, 127(June), pp. 37–54. doi: 10.1016/j.coastaleng.2017.06.004.

Trimulyono, A. and Hashimoto, H. (2019) ‘Experimental Validation of Smoothed Particle Hydrodynamics on Generation and Propagation of Water Waves’, Journal of Marine Science and Engineering, 7(1), p. 17. doi: 10.3390/jmse7010017.

Author Response

The paper “Wave Interaction and Overwash with a Flexible Plate by Smoothed Particle Hydrodynamics” focuses on the Overwash event in the thin plate using smoothed particle hydrodynamics (SPH). The numerical methodology of Incompressible SPH is well explained although there is no experiment result to compare wave profile however the author uses the analytic solution to compare amplitude and wavelength. Using thin plate theory, the elastic behavior of the thin plate was reproduced.

Overall the paper is of good quality and adds value to other literature studies centered on this subject. The reviewer feels the paper can be substantially improved before being accepted for publications, and therefore suggests the following revisions:

1. line 105 it is mentioned that Lbottom = 5m and Lbeach= 4m however in Figure 2 it shows the end of the beach is 8m.

Response: The figures only show the region where the fluid phase occupies and the physical phenomena occurs.  No fluids extends beyond 8m.  We have explained this in the text.

2. line 110 ‘’ Spatial resolution is set to be ∆x = 5m, does it means initial particle distance? Can you elaborate on this?

Response: The typo is now corrected in the revised manuscript.

3. line 174 ‘’The pitch motion of the plate is also recorded and shown in Figure 7’’. I think this means Figure 6

Response: It was a mistake and it is corrected in the revised manuscript.

4. Figure 1 there is no wave gauge in the schematic view of the water basin setup, please add the exact position wave gauge in the figure.

Response: The setup is for numerical experiments and wave measurements are extracted from the numerical data obtained from the simulations, so there is no need for gauges.

5. Figure 6 and Figure 10 shows only one legend for heave motion if the author wants to use the same legend, it’s better to put the legend at the end of the figure (below Figure).

Response: Separate legends are now used for the figures.

6. Figure 7 and Figure 11. It’s very hard to differentiate between a_1, a_2, and a_3. Using a marker or different line type as well as Figure 6

Response: The legend of the Figures 6, 7, 10, 11 is modified as suggested.

 

Some questions

 

1. Does there is a correlation between initial particle distance with wave height or amplitude? Because you use only one initial particle distance, some ref. shows that initial particle distance has a significant effect on the accuracy of wave height. (Altomare et al., 2017)(Trimulyono and Hashimoto, 2019)

Response: It is true that the particle size, or the initial particle distance, has certain impact to the wave height. In the simulations, the particle size is only about 3.2% and 2.6% of the wave amplitudes of 0.159m and 0.187m, respectively. Those resolutions are relatively fine for considered waves. Moreover, the authors compared parameters of the generated waves with those obtained from the theoretical estimation and it showed a very good agreement. It means that the resolution is high enough to achieve the numerical convergence. A statement on the issue is added in the revised manuscript with the suggested references.

2. Only one wave condition i.e. intermediate wave, why the author does not consider others' conditions?

Response: Overwash under mild shallow water waves was presented in many other works, such as Meylan et al. [7] and Zhang et al. [25], while the phenomenon for more extreme wave conditions has not been characterised well.  The SPH method is best suited to model extreme wave condition. Additionally, since the main purpose of the study is investigating how elastic deformations could affect the overwash, extreme wave conditions are more interesting. 

3. The wave basin is a short tank compare to simulated wavelength λ=2.35 m, there is only 2λ in a wave basin. Could you elaborate that there is no reflection wave on the beach?

 Response: The simulation domain is relatively short and wave reflections at the left and right boundary are unavoidable. However, as shown in Figure 2 and Figure 3 for the pressure field and the numerical data for the wave height and wavelength, the boundary effect is just minor.  

Reviewer 2 Report

In this study, by numerically solving the incompressible flow equations and thin plate equation, the motion of a flexible elastic plate under wave action is simulated with particular attention on the phenomena of overwash. This work belongs to the subject of two-phase transient mixed flow and coincides with the topics of the journal of Water. It is well organized. However, the following questions deserve further examination before being accepted for publication.

Questions:

1. The current work is based on Ref. [25]. Except for the difference in parameters: 1) wave conditions in this study are more severe with wave steepness up to 0.5, 2) plate stiffness varies in a wide range of values, from 25MPa to 2.5GPa, and 3) the ratio of the plate length to the wavelength is less than 11.0, do we have any new gradients in theoretical and numerical aspects?

 

2. As mentioned by the authors, the incompressible fluid equations are used to model the flow, but the continuity equation for compressible fluid Eq. (13) is used in the numerical model. Some clarification is needed here.

 

3. How is the equation of (16) derived? some explanation of the parameters in it should be introduced too.

 

4. Line 112, the viscosity of the fluid is set to be 1 Pa s. Is this a real value or just used in the numerical model? It is far larger than the real viscosity for water. In addition, only the viscosity for laminar flow is taken into account, and the viscosity for turbulence is neglected. For the intermediate water waves considered herein, is this reasonable?

 

5. Before numerical experiments, if the computer environment can be introduced, it will help the reader to better understand the numerical performance of the developed model.

 

6. The beach parameters are set according to the physical experiments or set arbitrarily? Have the effects of beach parameters on the numerical results been studied before? Do we have any common rules to set up a proper beach for sufficient wave absorption? 

 

7. The numerical performances of the current model for wave periods of T=1.2s and T=1.5s are largely different, comparing with the theoretical solutions. What are the possible reasons?

 

8. There are a few minor errors:

• Line 112, the particle spacing of dx = 5m is a typo?
• Line 116, in the other hand è on the other hand?
• Line 117, in the downside è under the downside?
• Line 177, the degree for angle should not be 0.
• Line 201, which is slightly smaller the previous wave condition?

Author Response

In this study, by numerically solving the incompressible flow equations and thin plate equation, the motion of a flexible elastic plate under wave action is simulated with particular attention on the phenomena of overwash. This work belongs to the subject of two-phase transient mixed flow and coincides with the topics of the journal of Water. It is well organized. However, the following questions deserve further examination before being accepted for publication.

1. The current work is based on Ref. [25]. Except for the difference in parameters: 1) wave conditions in this study are more severe with wave steepness up to 0.5, 2) plate stiffness varies in a wide range of values, from 25MPa to 2.5GPa, and 3) the ratio of the plate length to the wavelength is less than 11.0, do we have any new gradients in theoretical and numerical aspects?

Response: The aims of the current study is understanding how elastic deformations of a floating plate affect the overwash under severe wave conditions and the numerical results reveal that the deformations absorb the wave energy and therefore reduce the overwash. This was not the point in the Ref. [25]. The methodology is different here, as we use thin plate theory.

1. As mentioned by the authors, the incompressible fluid equations are used to model the flow, but the continuity equation for compressible fluid Eq. (13) is used in the numerical model. Some clarification is needed here.

Response: The authors would like to dictate that the fluid is incompressible. However, in the prediction-correction algorithm used in the current study, the density is slightly varied in the prediction step and it is then corrected in the correction step. In other words, the fluid density equals to the physical density of the fluid after the correction step. This is standard in SPH.

1. How is the equation of (16) derived? some explanation of the parameters in it should be introduced too.

Response: Equation (16) is the common form of the discretisation of the viscous stress used in many works, such as in Ref. [34-35]. Explanations for the notations have been added in the revised manuscript.

1. Line 112, the viscosity of the fluid is set to be 1 Pa s. Is this a real value or just used in the numerical model? It is far larger than the real viscosity for water. In addition, only the viscosity for laminar flow is taken into account, and the viscosity for turbulence is neglected. For the intermediate water waves considered herein, is this reasonable?

Response: At this length scale, hydrodynamic force acting on the floating plate is mainly contributed from the dynamic pressure, not the viscous factor. Therefore, adopting a high value for the fluid viscosity in the simulations is just for simplicity, instead of applying a turbulent model. It is known that all the turbulent models are not perfect and have pros and cons, and adequate validations are always necessary for every investigated problems.

1. Before numerical experiments, if the computer environment can be introduced, it will help the reader to better understand the numerical performance of the developed model.

Response: Information for the computer environment used for the simulations has been added in the revised manuscript.

1. The beach parameters are set according to the physical experiments or set arbitrarily? Have the effects of beach parameters on the numerical results been studied before? Do we have any common rules to set up a proper beach for sufficient wave absorption?

Response: Beach is a common setup in wave basin experimental setups to absorb wave energy and reduce wave reflections. The smaller beach angle is, the better wave absorption the beach performs. In the current study, the beach angle is set as 22 degrees and its efficiency for the wave absorption is examined and presented in Figures 2 and 3 and their corresponding discussions. We note that the configuration is designed to be small enough to be computationally feasible without having too much reflection.

1. The numerical performances of the current model for wave periods of T=1.2s and T=1.5s are largely different, comparing with the theoretical solutions. What are the possible reasons?

Response: As presented in the manuscript, by just reducing the period from 1.5s down to 1.2s, the wave steepness increases by 70%, leading the much stronger overwash.

1. There are a few minor errors:

Line 112, the particle spacing of dx = 5m is a typo?

Line 116, in the other hand è on the other hand?

Line 117, in the downside è under the downside?

Line 177, the degree for angle should not be 0.

Line 201, which is slightly smaller the previous wave condition?

Response: All the typos have been corrected.

Reviewer 3 Report

The manuscript describes the implementation of smoothed particle hydrodynamics (SPH) method to simulate the phenomena of overwash for the floating thin plane by water waves. The manuscript is well written and has a good structure, simulations are well described, included SPH details are reasonable and the results are clearly presented. But, in my opinion, the manuscript needs some additional efforts in Introduction and Conclusion sections.

My comments:

1. Introduction needs diversity. The majority of the references are from the same authors. For example, out of the first 18 references used to describe the state of the field in floating plate modeling, Michael Meylan is the coauthor for 12. I get that he is an expert in the field but nobody else is not doing anything anywhere in the world?

2. The introduction covers the efforts performed in the field to the current times, but barely says anything about the reason for the research. The first sentence of Introduction is “The interaction of a flexible floating plate with wave forcing has been the subject of extensive research due to the application in offshore engineering, polar engineering, and geophysics.” And then just sends the reader to read examples somewhere else. By the way, there should be references at the end of this sentence. I suggest the authors to add some examples of the applications and elaborate more on the importance of their research. Also the first sentence of Conclutions is exactly the same “The dynamics of flexible floating structures interacting with ocean waves has been a subject of extensive research due to its application in offshore engineering, polar engineering, and geophysics.”

3. Conclusion section is thin and together with very descriptive Results section lacks in scientific discussion. How and where the new findings can be used? What could be the next steps in research?

4. In the Introduction the authors mention the differences in lab-scale and real-world observations of the phenomena. The simulations were done for a lab-scale problem. I’d like the authors to elaborate some on how could this “peculiar paradox” be solved. For example, if overwash leads to rapid ice melting, is it possible to observe it in lab-scale modeling with SPH, etc.

Author Response

The manuscript describes the implementation of smoothed particle hydrodynamics (SPH) method to simulate the phenomena of overwash for the floating thin plane by water waves. The manuscript is well written and has a good structure, simulations are well described, included SPH details are reasonable and the results are clearly presented. But, in my opinion, the manuscript needs some additional efforts in Introduction and Conclusion sections.

My comments:

1. Introduction needs diversity. The majority of the references are from the same authors. For example, out of the first 18 references used to describe the state of the field in floating plate modeling, Michael Meylan is the coauthor for 12. I get that he is an expert in the field but nobody else is not doing anything anywhere in the world?

Response: We have added some further references.

1. The introduction covers the efforts performed in the field to the current times, but barely says anything about the reason for the research. The first sentence of Introduction is “The interaction of a flexible floating plate with wave forcing has been the subject of extensive research due to the application in offshore engineering, polar engineering, and geophysics.” And then just sends the reader to read examples somewhere else. By the way, there should be references at the end of this sentence. I suggest the authors to add some examples of the applications and elaborate more on the importance of their research. Also the first sentence of Conclutions is exactly the same “The dynamics of flexible floating structures interacting with ocean waves has been a subject of extensive research due to its application in offshore engineering, polar engineering, and geophysics.”

Response:

We have explained the motivation of very large floating structures and wave propagation in the frozen ocean. We have included references the end of the first sentence. We have extended the discussion of the problems of interest and tried to place our work in context more..

• Conclusion section is thin and together with very descriptive Results section lacks in scientific discussion. How and where the new findings can be used? What could be the next steps in research?

Response: We have extensively rewritten the conclusions. The main finding of the current study is that elastic deformations reduce overwash caused by the water waves. We have also discussed future work.

1. In the Introduction the authors mention the differences in lab-scale and real-world observations of the phenomena. The simulations were done for a lab-scale problem. I’d like the authors to elaborate some on how could this “peculiar paradox” be solved. For example, if overwash leads to rapid ice melting, is it possible to observe it in lab-scale modeling with SPH, etc.

Response: It is true that lab-scale experiments, in many cases, cannot be carried out in the same real-world conditions and scaling rules are not always working. However, lab-scale experiments can be used to validate mathematical models that are useful to answer physics and mechanisms behind the real-world problems. Basically, rapid ice melting caused by overwash can be incorporated into the current SPH model via a mathematical model for the melting process. We have mentioned in the conclusions about simulating the melting process.

Reviewer 4 Report

Overall, this is an interesting work, written in good quality, and extensive analyses were presented. It developed a novel model coupling SPH with a linear thin plate theory to model wave-plate interactions. Particularly, the elastic deformation of the plate has been considered to simulate the scenario of a large-thin ice floe in waves. 

Previous work considering the deformations mostly used the potential flow theory for fluid solutions, which however excludes overwash (except the work of [17] using CFD). This work, by using SPH, also allows overwash to be included in the hydroelastic interaction. Overwash is of high scientific value in the field, which highlights the merits of this work.

Therefore, I recommend this work to be accepted after addressing several comments:

1. The numerical wave tank looks very short. Can you explain the particular reason for that? It might cause some issue when there is a plate floating inside: as the plate would disturb the surrounding water, a short tank could affect the wave radiation (reflection and transmission). 
2. The consideration of Young modulus from 25MPa to 2.5GPa. The upper value is ok, but 25MPa seems to be way too low to be ice? Please clarify this in the manuscript, because some conclusions might be applicable for flexible plates but might not for ice. It would be helpful if you identify the materials of different Young modulus and describe corresponding practical applications.
3. Some future work should be recommended. For example, the use of linear thin plate theory is only valid with small strain problems. It seems like (in Figure 8) the deformation is already nonlinear? I think this is something that could be improved in future work - I recommend you to consider the St. Venant Kirchhoff solid model in [17].
   
4. Your conclusion "less overwash is observed for a more flexible plate
   " agrees well with this reference: HUANG, L., BENNETTS, L., CARDIFF, P., JASAK, H., TUKOVIC, Z. and THOMAS, G., 2020, June. THE IMPLICATION OF ELASTIC DEFORMATION IN WAVE-ICE INTERACTION. In The 15th OpenFOAM Workshop.They found the same trend, so I suggest you cite the work, which would provide a sort of verification for your simulations.

Author Response

Overall, this is an interesting work, written in good quality, and extensive analyses were presented. It developed a novel model coupling SPH with a linear thin plate theory to model wave-plate interactions. Particularly, the elastic deformation of the plate has been considered to simulate the scenario of a large-thin ice floe in waves.

Previous work considering the deformations mostly used the potential flow theory for fluid solutions, which however excludes overwash (except the work of [17] using CFD). This work, by using SPH, also allows overwash to be included in the hydroelastic interaction. Overwash is of high scientific value in the field, which highlights the merits of this work.

Therefore, I recommend this work to be accepted after addressing several comments:

 

1. The numerical wave tank looks very short. Can you explain the particular reason for that? It might cause some issue when there is a plate floating inside: as the plate would disturb the surrounding water, a short tank could affect the wave radiation (reflection and transmission).

Response: The finite-size tank definitely has boundary effects to the wave radiation with the presence of the floating plate. However, because the current study is more focusing how elastic deformations could affect the overwash under the extreme wave conditions, in which the wave radiation just has minor effects. We have included a sentence explaining that our computational domain is chosen to be the minimal size because of the high computational cost of the SPH method.

1. The consideration of Young modulus from 25MPa to 2.5GPa. The upper value is ok, but 25MPa seems to be way too low to be ice? Please clarify this in the manuscript, because some conclusions might be applicable for flexible plates but might not for ice. It would be helpful if you identify the materials of different Young modulus and describe corresponding practical applications.

Response: Although the value of 25MPa is relatively low compared to that the ice floes, it is used for demonstrate how the plate with highly deformable ability is able to reduce the overwash. We note that the geophysical scale requires dimensional scaling so that a direct comparison of Young’s modulus is not necessarily appropriate.  We have added text to this affect.

1. Some future work should be recommended. For example, the use of linear thin plate theory is only valid with small strain problems. It seems like (in Figure 8) the deformation is already nonlinear? I think this is something that could be improved in future work - I recommend you to consider the St. Venant Kirchhoff solid model in [17].

Response: Future works are mentioned in the conclusions of the revised manuscript. However,

1. Your conclusion "less overwash is observed for a more flexible plate " agrees well with this reference: HUANG, L., BENNETTS, L., CARDIFF, P., JASAK, H., TUKOVIC, Z. and THOMAS, G., 2020, June. THE IMPLICATION OF ELASTIC DEFORMATION IN WAVE-ICE INTERACTION. In The 15th OpenFOAM Workshop.They found the same trend, so I suggest you cite the work, which would provide a sort of verification for your simulations.

Response: The reference is cited in the revised manuscript as a verification for the current findings.

Round 2

Reviewer 2 Report

1. Line 54-55, to avoid any misunderstanding, the sentence "the extension of the SPH method to elastic bodies was considered by Zhang et al. [35]" can be changed into "the extension of the SPH method to floating elastic bodies on see surface was considered by Zhang et al. [35]", because the extension of the SPH method to elastic bodies has been long studied.
2. Line 72-74, it is suggested the sentences "Our study has application to the storm damage of very large floating structures and the melting and breakup of sea ice. However, our focus here is on simulating at the laboratory scale where extensive experiments have been conducted" had better move to line 70, just before "The rest of the paper is organised as follows ...
3. Although T_mw (period of the moving boundary) is explained later on, it is better to introduce it just after Eq. (2). 
4. Some typos: 1) line 90, Equation (12)-(13) == Equations (12)-(13)；2）Line 106, Poisson equation 18 == Poisson's equation (18).  

Author Response

Thanks for spotting these.  We have made all the changes, but only marked the major ones in red.