Wind-Driven Waves on the Air-Water Interface
Round 1
Reviewer 1 Report
The paper must be rejected to the "fluids" journal, for the following reasons:
1) the paper is suited for applied mathematics journal, the content and presentation does not correspond to journal about physics :
- we have comments and proof instead of having section, subsection and paragraph.
- the main part of the paper's contents are mathematics, with a method to solve integral equations
- we can not find any numerical results, and plots which are required to prove the efficiency of the method
- no comparisons with other similar or closed problems
2) the introduction is very poor, no covincing and short, avoiding any reference to usual bibliography on flow instability
3) we can just find 5 references of a paper of 35 pages. The authors write sometimes some references to personal communications with colleagues, it is unusual, when we can find answer with certified papers.
4) There is no discussion about physics and I am not sure that physics is respected in the paper's developpement. For instance there is no discussion about the surface tension which play an important role in the model and physics of flows with interface
5) typically this problem should be treated with non dimensional numbers, as Reynolds number for instance (and others)
6) It is a problem of instability analysis of a fluid flow, where we can find thousand of references. It is a special case where the base flow can be time dependant
7) finally it is clear that the authors are "just" mathematicians, not physicians, to write a paper in such a journal they should work with a specialist in fluid mechanics.
8) I have other comments about the choice of the model, as considering a "double" Stokes layer with an auto similar profile, but I do not think that it is necessary to add something here.
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The paper shows a novel and complex mathematically analysis of a little-known and very complex physics related to waves generated by wind and pressure fields. In addition, the authors delve into the concept of white-capping, which is often little known and whose practical evaluation remains empirical and possibly inaccurate.
The presentation of the mathematical development of the scheme proposed by the authors is extremely complete and orderly, allowing to follow each step to justify each part of the physics involved in the problem. Congratulations for this.
For all these reasons, I consider that the article should be accepted for publication in FLUIDS with only the following minor changes and suggestions:
Line 53 typo: "dynamics"
Introduction:
I suggest that the authors include information (state-of-the art) of those numerical models that currently can (or try to) solve the surge generated by wind fields, so that the reader knows in what practical context the mathematical development that the authors present can be considered, and in this way, know the possible disadvantages that these numerical solutions may have with respect to the physics they try to solve, what fitting hypotheses they present and how these can be improved through what the authors propose.
Conclusions:
I suggest that the authors include a comment on these two effects:
- locally generated surge from extreme storms (e.g. hurricanes), whether the proposed equations would adequately address these physical effects by considering the possible "two-way" coupling that may occur at the interface of large (with large heights) wind-generated waves that may imprint a significant variation in the available area of energy exchange between wind and surge, i.e. whether the proposed scheme can foresee the creation of a high-energy wave field whose "roughness" is increasing and relevant.
- If the equations can co-exist with a previously generated wave (SWELL type) from the far- field and how this would interact with a locally generated wave (SEA), what considerations had to be taken into account in the mathematical scheme.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 3 Report
A pdf file is attached.
Comments for author File: Comments.pdf
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
