Numerical Generation of Solitary Wave and Its Propagation Characteristics in a Step-Type Flume
Round 1
Reviewer 1 Report
see attachment
Comments for author File: 
Comments.pdf
Author Response
We feel so sorry to response so late, due to the damage of the hard disks and COVID-19. We have spent a lot time and money to recovery the data, but failed.
Response to Reviewer 1 Comments
Point 1: The rationale behind the chosen motion protocol would however need to be better motivated. Apparently, it takes the vertically-integrated continuity equation, assumes that the response can still be described as having a definite wave length and phase speed, and then applies it at the moving piston boundary Still the manner in which phase speed and effective wave number are obtained need further explanation.
Response 1: The relationship between the linear motion of the paddle and the resulting profile of solitary wave are determined by means of the method according to Goring (1979). Yes, it integrates the continuity equation to obtain the relationship. However, the solution of motion stroke is just asymptotic solution, see Eq. (7). Theoretically, the paddle is always moving without stopping during the wave generation. This means the wave length tends to infinite (not a definite wave length), that is consistent with theory.
Point 2: The paper also needs to better explain why the Goring (1979) thesis, written later, is treated before discussing the earlier ninth-order Fenton (1972) solitary wave paper. Presumably this is because the latter is just a solution that takes no recourse to boundary conditions, as the Goring thesis does, right?
Response 2: Yes, right. The work by Fenton focused on the solution in mathematics, however, the work by Goring focused on how to determine the boundary condition, or saying the relationship between the paddle motion and wave profile. Goring's method can be applied for the solitary wave with any order, first order or ninth order. In section 2, we emphasize more how to determine the relationship between the paddle motion and wave profile. So, we discuss the work of Goring first.
Point 3: The first and ninth-order solitary numerical wave solutions are compared to each other and to experimentally observed water elevations. The ninth-order solutions are said to be favored for showing weaker trailing waves. However, this is not what the experimental results show. In fact, the experimentally observed waves display larger amplitudes of trailing waves. a tendency better shown by the first-order solution. A more objective comparison (in terms of propagation speed and shape) should therefore be performed, e.g. by showing root-mean-square differences of both numerical predictions with experimentally observed elevation records.
Response 3: If we have a very close look at the curves, we can see that the experimental data also show that the profile based on ninth-order solution is slightly better in the time range of 3.75 to 5 second, please see the figs below. The small difference is not so easy to be perceived, but the profile based on ninth-order solution is really better. What a pity! Our workstation hard disks damage. We have spent a lot time and money to recovery the data, but failed. We do not have the original data to show the root-mean-square between the numerical prediction and experimental data.
Point 4: The interaction of the solitary wave with the step-topography is interesting though studied only numerically and not very quantitatively. How much of the incident solitary wave is reflected/transmitted? What would be the maximum height of a solitary wave on a depth h/2 and can one explain from this the apparent instability of the transmitted part of the solitary wave?
Response 4: Yes, what you concern is very interesting. We cannot analyze the issues now, due to the lack of original data, because of the damage of our workstation hard disks.
Reviewer 2 Report
Major revision is suggested. Detailed comments are attached in the attachment.
Comments for author File: Comments.pdf
Author Response
We feel so sorry to response so late, due to the damage of the hard disks and COVID-19. We have spent a lot time and money to recovery the data, but failed.
Response to Reviewer 2 Comments
Point 1: The first issue is the innovation of the article. As far as the reviewer knows, there are some existing wave-making methods in OpenFOAM, for example, waves2Foam and olaFoamThese existing methods can also generate solitary waves. What are the progresses when the new module of dynamic boundary condition proposed here are compared to these existing methods? Are the solitary waves generated by the former more accurate than those generated by the latter two methods?
Response 1: Yes, the approach of prescribing flow velocity and wave evaluation on the domain boundary can be used to generate solitary waves, e.g. the wave2Foam. Howver, according our experience, the present approach will be more effective to reduce wave amplitude decay. Our present work will be expanded to have a detailed comparison in this regard. We revised this issues in the paper.
Point 2: The second issue occurs in Section 7 “Propagation characteristics in a step-type flume”. The wave transmission, reflection and transformation over uneven bottom are common for the water waves. One of the most typical examples is the Bragg reflection phenomenon (Investigation on the effects of Bragg reflection on harbor oscillations), which exists many similarities to the solitary wave transformation on a step topography and should be mentioned in this section. In addition, the capacity of OpenFOAM in reproducing the wave transformation over uneven bottom should be fully validated prior to being used to simulate the solitary wave propagating over a step bottom.
Response 2: Yes, what you concern is very interesting. We cannot analyze the issues now, due to the lack of original data, because of the damage of our workstation hard disks.
Point 3: The third issue occurs in the Introduction part. Many expressions lack preciseness. For example, “After travelling a long distance, a tsunami wave will evolve into a solitary wave” In fact, when tsunamis travel into coastal areas, they may also evolve into N-waves(Numerical investigation of transient harbor oscillations induced by N-waves) or successive solitary waves (On hydrodynamic characteristics of transient harbor resonance excited by double solitary waves). These conditions need also to be mentioned in the introduction Furthermore, how to understand “A tsunami wave may be caused by a current-induced scour’?
Response 3: We revised these issues in the paper.
Point 4: The variables in all the figures (e.g., eta, x, etc) should be italicized. The issue occurs in manyfigures.
Response 4: We revised these issues in the paper.
Round 2
Reviewer 1 Report
I am sorry to hear that the measurements have been lost due to a computer crash, so that you are unable to respond to some of my questions. However, I find the present version of sufficient interest to justify its publication.
Author Response
we revised the paper.
Author Response File: Author Response.pdf
Reviewer 2 Report
Specific comments are attached in the attachment.
Comments for author File: Comments.pdf
Author Response
we revised the paper.
Author Response File: Author Response.pdf
Round 3
Reviewer 2 Report
Some problems in the second round are still not well addressed. See the below.
(1) In the first paragraph of Introduction section, "... successive solitary waves (Gao 2017,2021)" should be ".... successive solitary waves (Gao 2017,2021a)".
(2) At the line above Fig. 12, "... as reported by Gao et al (2021)" should be "... as reported by Gao et al (2021b)".
(3) For the References section, the name of the first authors for the first three references is NOT "Gao, J.H.". It should be "Gao, J.L.".
(4) The year of the second reference "(2021)" should be "(2021a)".
(5) The year of the third reference "(2021)" should be "(2021b)".
Author Response
we revised all the issues.
Author Response File: Author Response.pdf
Round 4
Reviewer 2 Report
The present version can be accepted.
