Assessment of Numerical Methods for Plunging Breaking Wave Predictions^†

Round 1

Reviewer 1 Report

1. The color contour in Figures 2, 3, and 7 should be enlarged.
2. In Figure 6, there is a great discrepancy between (i) and the others, please confirm the results.

Author Response

Comment #1. The color contour in Figures 2, 3, and 7 should be enlarged.

Response:  The contours legends have been enlarged.

Comment #2. In Figure 6, there is a great discrepancy between (i) and the others, please confirm the results.

Response: Yes, the RANS results show zagged shaped plunger tip. As discussed in lines 431- 438, this is because of large air flow velocity die to high turbulent eddy viscosity predictions. 

Reviewer 2 Report

The manuscript presents detailed assessment of several numerical approaches to modeling plunging breaking waves. The simulations are performed for four very different types of wave breaking generation scenarios. The results, while not really surprising, are obtained carefully and can serve as a basis for selection of adequate numerical method for various physical problems in which wave breaking is essential. I therefore recommend to accept the manuscript for publication in JMSE, after few relatively minor comments are addressed.

line 35: the authors probably mean 'wave peak velocity (u).

Section 2.3

The equations (11)-(14) that model solitary waves are not supported by any reference (a single ref. given later in Table 1 does not provide all necessary information) . The adopted assumptions, the governing equations and the the wave to obtain the analytical solutions presented in this section should be specified, at least in some detail.  

line 260. The ref. [4] is a PhD thesis. Were those experimental results published in a widely available journal? If not, more details on experiments should be provided.

Fig. 6. The bottom color bar has a title that is cropped. 

Author Response

The manuscript presents detailed assessment of several numerical approaches to modeling plunging breaking waves. The simulations are performed for four very different types of wave breaking generation scenarios. The results, while not really surprising, are obtained carefully and can serve as a basis for selection of adequate numerical method for various physical problems in which wave breaking is essential. I therefore recommend to accept the manuscript for publication in JMSE, after few relatively minor comments are addressed.

Response: Authors thank the reviewer for going through the paper in details and providing valuable feedback to improve our paper. The paper has been updated following reviewer’s comments, and the point-by-point response is provided below.

#1. line 35: the authors probably mean 'wave peak velocity (u).

Response: As suggested by the reviewer, “'wave peak velocity (u)” is used in lieu of “'wave peak (u).”

#2. The equations (11)-(14) that model solitary waves are not supported by any reference (a single ref. given later in Table 1 does not provide all necessary information) . The adopted assumptions, the governing equations and the the wave to obtain the analytical solutions presented in this section should be specified, at least in some detail. 

Response: It has been clarified that analytic equations of the solitary wave are based on first-order Boussinesq equations in shallow water. Reference [43] provides the original source of the equations. The readers are also referred to [37] for details of the derivation.

#3. line 260. The ref. [4] is a PhD thesis. Were those experimental results published in a widely available journal? If not, more details on experiments should be provided.

Response: The reference has been replaced by the journal publication as below:

Li, Y. and Raichlen, F. Non-Breaking and Breaking Solitary Wave Run-Up. J. Fluid Mech. 2002, vol. 456, pp. 295-318.

 

#4. Fig. 6. The bottom color bar has a title that is cropped.

Response: As suggested by the reviewer, the legend bar was corrected.

Reviewer 3 Report

The study presents the comparison of finite volume based VoF and finite element based CLSVoF methods to predict plunging breaking waves using test cases like dam break, solitary wave run-up over a slope and submerged obstacle and flow over submerged bumps. And experimental and literature results were also used for comparison. Within the scope of the paper the pros and cons associated with the adopted methods are well presented. Though the manuscript need minor corrections before it can be accepted for publication.

Minor comments:

1. The justification to the statement made in the abstract was not reflected with the same in the presented results and discussion  "CLSVoF performs much better than VoF". Please comment.
2. The types of wave breaking is a well known theory and widely available in the literature. The introduction part of the present version can be shortened and highlight the present study in light of current research (Line: 30 - 53).
3. Section 2.2 on VoF can be shortened. 
4. Section 3.2 it is better to mention the type of boundary conditions that they have used for the inlet, outlet, and top faces of the domain properly.
5. Fluid #1 and Fluid #2 are not defined?
6. Figure 3. It was very hard to see clearly the difference between the OpenFoam, Proteus and SPH results and same with the figure 11.  Can the author present the results by overlapping wave profiles alone?
7. Line 415: please justify why the discussion has been made based on laminar flow? Hope authors must have performed most of their results using OpenFoam by turbulent model? 
8. Please clarify that the presented results using Proteus are by CLSVoF?
9. As the present study do not involve any of LES method. Comments related to that can be avoided in the conclusion. 
10. Typo mistake line 162... "CLVoF".

 

 

Author Response

The study presents the comparison of finite volume based VoF and finite element based CLSVoF methods to predict plunging breaking waves using test cases like dam break, solitary wave run-up over a slope and submerged obstacle and flow over submerged bumps. And experimental and literature results were also used for comparison. Within the scope of the paper the pros and cons associated with the adopted methods are well presented. Though the manuscript need minor corrections before it can be accepted for publication.

Response: Authors thank the reviewer for going through the paper in details and providing valuable feedback to improve our paper. The paper has been updated following reviewer’s comments, and the point-by-point response is provided below.

#1. The justification to the statement made in the abstract was not reflected with the same in the presented results and discussion "CLSVoF performs much better than VoF". Please comment.

Response: Abstract is revised to clarify the pros and cons of the CLSVoF and VoF methods, as below:

“Both VoF and CLSVoF methods predict the large-scale plunging breaking characteristics well; however, they vary in the prediction of the finer details. The CLSVoF solver predicts the splash-up event and secondary plunger better than the VoF solver; however, the latter predicts the plunger shape better than the former for the solitary wave run-up on a slope case.”

#2. The types of wave breaking is a well known theory and widely available in the literature. The introduction part of the present version can be shortened and highlight the present study in light of current research (Line: 30 - 53).

Response: As suggested by the reviewer, the first paragraph has been shortened considerably.

#3. Section 2.2 on VoF can be shortened.

Response:  Section 2.2 has been re-written to provide a summary of the solvers and salient differences between VoF and CLSVoF methods.

#4. Section 3.2 it is better to mention the type of boundary conditions that they have used for the inlet, outlet, and top faces of the domain properly.

Response: Section 3 has been re-written to clearly provide the flow condition, boundary conditions, domain and grids and validation approach.  

#5. Fluid #1 and Fluid #2 are not defined?

Response: As suggested by the reviewer, Figure 1 was modified to specify the fluids used for the simulations.

#6. Figure 3. It was very hard to see clearly the difference between the OpenFoam, Proteus and SPH results and same with the figure 11.  Can the author present the results by overlapping wave profiles alone?

Response: Figure 3 provides a qualitative comparison between the OpenFoam, Proteus and SPH results, and the overlapping wave profiles for different times are shown in Fig. 4. Similarly, Fig. 11 provides a qualitative comparison, whereas Fig. 12 provides comparison using overlapping profiles.   

#7. Line 415: please justify why the discussion has been made based on laminar flow? Hope authors must have performed most of their results using OpenFoam by turbulent model?

Response: The choice of 2D simulations and laminar vs turbulent simulations is clarified in first paragraph of section 3, lines 261 – 269 as below:

“All the simulations were performed using a 2D domain. 2D domain simulation were performed as benchmark simulations available in the literature have used 2D simulations, and it has been reported in the literature that 2D simulations replicate most of the flow features predicted by three dimensional simulations [Alberello et al., 2017]. Effect of (RANS) turbulence modeling on the plunging wave breaking characteristics were studied for the solitary wave run-up case (discussed below), which showed that high turbulent eddy viscosity in the air flow deteriorated the breaking predictions. Further, Alberello et al., [2017] reported that for 2D simulations wave breaking predictions are not significantly affected by turbulence models. Thus, most of the simulations are performed using laminar flow conditions.”

 

#8. Please clarify that the presented results using Proteus are by CLSVoF?

Response:  It is clarified both in section 3 and in the conclusions that Proteus results corresponds to the CLSVoF results.

#9. As the present study do not involve any of LES method. Comments related to that can be avoided in the conclusion.

Response: The future work discussions on lines 640 – 642 have be rewritten to exclude disvussions for LES. The revised discussuions reads:

“Future work will focus on extending the simulation to 3D flows. Alberello et al. [2017] reported that turbulence modeling becomes important for 3D simulations, and three-dimensional flow structures start to appear in the breaking region.”    

#10. Typo mistake line 162... "CLVoF".

Response: Thank you for pointing out the typo. It has been corrected.

 

Reviewer 4 Report

Assessment of numerical methods for plunging breaking wave predictions

The manuscript simulates the wave breaking processes using two different CFD solvers. Four different cases with known literature are used as a benchmark to assess simulation performances.

Overall the manuscript is satisfactorily presented, but I have few observations that need to be addressed.

• The authors analyse two models, the simulations and configurations are summarised in table 1. I do not understand why only OpenFoam is used for the solitary wave over an obstacle. Also why for the solitary wave on a slope OpenFoam has 5 various H/h ratio and Prometeus only one?
• Being a manuscript focussed on CFD I would expect a comparative table showing the computational cost for each simulation. In particular the authors should highlight which one of the code is more efficient.
• Authors mention that the Level Set (LS) approach does not provide the velocity field in the air. This is misleading. See for example Iafrati et al. 2013, Modulational Instability, wave breaking and formation of large scale dipoles in the Atmosphere, Physical Review Letters.
• Authors only analyse plunging of waves induced by the bottom, however waves can break in deep water as well (and with a plunger). Breaking is induced by either linear or nonlinear energy focussing. Numerical simulations and benchmark laboratory experiments have been discussed in the literature, see for example Alberello et al (2018) An experimental comparison of velocities underneath focussed breaking waves and Alberello & Iafrati (2019) The velocity underneath a breaking rogue wave: laboratory experiments versus numerical simulations.
• At line 167 the authors discuss experiments with turbulence closure scheme. Alberello et al (2017) Three dimensional velocity field underneath a breaking rogue wave demonstrated using VoF approach that the velocity field in a 2d and 3d setup differs if a turbulence closure scheme is introduced. In particular they showed variability in the cross section (y), which is not captured in 2d, and a reduction of the velocity at the crest of breaking waves.

As a general comment the presentation of the figures must be improved.

• Fig 2 the legend is too small to be read, also show with a thicker line the interface
• Fig 3 same as above
• Fig 4 I cannot distinguish in figure between LS and PR symbols. Also font in axis is small
• Fig 5 right panels, same as Fig 2
• Fig 6 is abcissa is x/h0 write in explicitly in the plot (like in Fig 8)
• Fig 7 same as Fig 2
• Fig 9 font in axis is small
• Fig 11 for middle and right column show legend
• Fig 13 legend top right too small, also font axis
• Fig 13, use same colormap for left and right plots. Also legend too small

Author Response

The manuscript simulates the wave breaking processes using two different CFD solvers. Four different cases with known literature are used as a benchmark to assess simulation performances.

Overall the manuscript is satisfactorily presented, but I have few observations that need to be addressed.

Response: Authors thank the reviewer for going through the paper in details and providing valuable feedback to improve our paper. The paper has been updated following reviewer’s comments, and the point-by-point response is provided below.

#1. The authors analyse two models, the simulations and configurations are summarised in table 1. I do not understand why only OpenFoam is used for the solitary wave over an obstacle. Also why for the solitary wave on a slope OpenFoam has 5 various H/h ratio and Prometeus only one?

Response: It is clarified in Section 3 that for the Solitary wave over an obstacle case, Proetus simulations were performed only for H₀/h₀= 0.45, which involves Plunging breaking. Several H₀/h₀ were used for OpenFOAM simulations to explore the predictability of CFD methods in general for range of wave breaking events spanning from no-breaking to surging to plunging breaking. 

It has also been clarified that only OpenFOAM simulations were performed for the flow over an obstacle case (case #4). The objective of this case was to evaluate how CFD methods perform for the prediction of wave breaking due to flow recirculation induced by vortices. 

The objective and approach on pg. 4, section 1.3 has been revised to accurately reflect what has been done in the paper. The “Conclusions” section has been revised accordingly.

#2. Being a manuscript focussed on CFD I would expect a comparative table showing the computational cost for each simulation. In particular the authors should highlight which one of the code is more efficient.

Response: A discussion regarding the computational cost for each case, and OpenFOAM bs Proteus computational cost is provided on lines 324 – 332 as below:

“The computational cost for each test depends almost linearly with the grid size requirements. Thus, the case#4 is the most computationally extensive followed by cases 2 and 3, and case #1 is the least expensive. In general, for similar grid size the Proteus simulations required 2 times more memory and CPU time compared to OpenFOAM. However, a direct comparison between Proteus and OpenFOAM computational cost does not reflect the computational cost associated with VoF vs CLVoF. The two solvers use very different solution convergence, in particular finite-element Proteus requires much lower convergence tolerance compared to finite-volume OpenFOAM. In addition, the large memory requirement for Proteus is perhaps because the solver is Python based, whereas OpenFOAM is C++ based.”

#3. Authors mention that the Level Set (LS) approach does not provide the velocity field in the air. This is misleading. See for example Iafrati et al. 2013, Modulational Instability, wave breaking and formation of large scale dipoles in the Atmosphere, Physical Review Letters.

Response: We believe the reviewer is referring to the statement:

“The level-set approach is more common in ship hydrodynamics solvers, which focus on single phase flows, whereas VoF is used for two-phase solvers.”

Authors acknowledge that the above statement can be misconstrued as “Level Set (LS) approach does not provide the velocity field in the air.”

Authors would also like to that the reviewer for pointing out the reference Iafrati et al. 2013. This reference has been cites in the paper.

Refer to revides discussions on lines 114 -121 as below:

“The level-set approach is more common in ship hydrodynamics solvers, wherein the focus is on single phase (water) flows [Bhushan et al. 2019]. However, they can also predict two-phase flow, e.g., Iafrati et al. [2013] used level-set approach to predict large-scale dipole structures in the air for steep waves (expected for wave-breaking). However, VoF is the method of choice for two-phase solvers which may involve mixing of fluids and breaking waves. Level-set method requires additional modeling to predict breaking waves, such as additional pressure on the surface in the breaking region to mimic the momentum dissipation [30-32].”

 

#4. Authors only analyse plunging of waves induced by the bottom, however waves can break in deep water as well (and with a plunger). Breaking is induced by either linear or nonlinear energy focussing. Numerical simulations and benchmark laboratory experiments have been discussed in the literature, see for example Alberello et al (2018) An experimental comparison of velocities underneath focussed breaking waves and Alberello & Iafrati (2019) The velocity underneath a breaking rogue wave: laboratory experiments versus numerical simulations.

Response: Reviwer is correct in pointing out that the literature review regarding the wave breaking focused mostly on the wave breaking in presence of the surface and/or obstacle. Breaking can occur in deep water as doe the rogue waves.

Authors would also like to that the reviewer for pointing out the references. The reference Alberello and Iafrati [2019] is now added to the Introduction, lines 68-79 as below:

“Plunging wave breaking can also occur in deep water, i.e., breaking rogue waves. As discussed by Alberello and Iafrati [2019] growth and eventual breaking of rogue waves are due to nonlinear interaction between the monochromatic carrier wave and the infinitesimal sidebands perturbations, wherein results in energy transfer from the former to latter resulting in growth of the perturbations. They performed simulations using a hybrid level-set/high order spectral method solver to predict the rogue wave breaking and associate velocities, and the results were validated using complimentary experiments. The simulations showed a qualitatively accurate wave evolution and breaking shape, except for discrepancies for the jet shape. It was reported that shape of the jet highly depends on the choice of the physical parameters, i.e., surface tension and viscosity. The velocity filed was also predicted well, except for 10% underprediction at the wave crest. The errors were attributed to grid resolution. They concluded that accurate velocity predictions require finer grid resolutions compared to those required for the accurate air-water interface predictions.”

 

#5. At line 167 the authors discuss experiments with turbulence closure scheme. Alberello et al (2017) Three dimensional velocity field underneath a breaking rogue wave demonstrated using VoF approach that the velocity field in a 2d and 3d setup differs if a turbulence closure scheme is introduced. In particular they showed variability in the cross section (y), which is not captured in 2d, and a reduction of the velocity at the crest of breaking waves.

Response: Authors again thank the reviewer for referring the paper to us. The paper provided valuable insight on the effect of turbulence model on the 2D and 3D predictions. The above reference has been cited on lines 261 to 269, to discuss the implications of the choice of simulation dimensionality and turbulence model, as below:  

“All the simulations were performed using a 2D domain. 2D domain simulation were performed as benchmark simulations available in the literature have used 2D simulations, and it has been reported in the literature that 2D simulations replicate most of the flow features predicted by three dimensional simulations [Alberello et al., 2017]. Effect of (RANS) turbulence modeling on the plunging wave breaking characteristics were studied for the solitary wave run-up case (discussed below), which showed that high turbulent eddy viscosity in the air flow deteriorated the breaking predictions. Alberello et al., [2017] reported that for 2D simulations wave breaking predictions are not significantly affected by turbulence models. Thus, most of the simulations are performed using laminar flow conditions.”  

The reference is also discussed for the future work discussions on lines 640 – 642, as below:

“Future work will focus on extending the simulation to 3D flows. Alberello et al. [2017] reported that turbulence modeling becomes important for 3D simulations, and three-dimensional flow structures start to appear in the breaking region.”

#6. Fig 2 the legend is too small to be read, also show with a thicker line the interface

Response: As suggested by the reviewer, the size of the legend was increased.

#7. Fig 3 same as above

Response: As suggested by the reviewer, the size of the legend was increased.

#8. Fig 4 I cannot distinguish in figure between LS and PR symbols. Also font in axis is small

Response: As suggested by the reviewer, the legend colors for LS were changed and the size of the axis font was increased.

#9. Fig 5 right panels, same as Fig 2

Response: As suggested by the reviewer, the size of the legend was increased.

#10. Fig 6 is abcissa is x/h0 write in explicitly in the plot (like in Fig 8)

Response: As suggested by the reviewer, the axis titles were changed from “x” to “x/h₀”

#11. Fig 7 same as Fig 2

Response: As suggested by the reviewer, the size of the legend was increased.

#12. Fig 9 font in axis is small

Response: As suggested by the reviewer, the size of the axis font was increased.

#13. Fig 11 for middle and right column show legend

Response: As suggested by the reviewer, the legend was added.

#14. Fig 13 legend top right too small, also font axis

Response: As suggested by the reviewer, the legend and font size where increased.

#15. Fig 13, use same colormap for left and right plots. Also legend too small

Response: As suggested by the reviewer, the figure has been modified to use same colormap as the experiment, and the legend font size has been increased.