Influence of Bed Variations on Linear Wave Propagation beyond the Mild Slope Condition

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

I reviewed the manuscript “Influence of bed variations on linear wave propagation beyond the mild slope condition” by Gonzalo Simarro. Author uses the WKB approximation and solves higher-order slope-related terms to analyze the influence of varying depth, including the gradient and laplacian of water depth. There are some comments and queries that need to be addressed for a better understanding. After these minor revisions the article can be accepted.

1. The introduction should be rewritten to reflect the novelty of the manuscript. The author introduces several formulas about waves in introduction. What are their shortcomings? Then, the author should explain why the WKB approximation is employed in this manuscript.

2 The full name of WKB should have been written when it first appeared in the manuscript.

3. Is i equal to -1 under the square root in line 96?

4. Author is advised to use the same font size in figures.

5. It is suggested that the author improve the content of the symbol table to facilitate readers' understanding.

6. The format of the reference document should be uniform, for example, should the title of the document be capitalized with each word or with the first letter of the sentence?

7. The authors are advised to increase the comparison with previous methods.

8. English should be modified by professional English speakers.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

English should be modified by professional English speakers.

Author Response

Please find a pdf attached

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

In this paper, the author employs the WKB approximation to derive a new dispersion relationship that accounts for bed slope effects. This relationship is applied to scenarios such as nearshore wind-generated waves and tsunami propagation, with the aim of improving the accuracy of wave modeling in these contexts. However, in my opinion, it is not suitable for publication as a scientific paper for the following reasons.

 

One of the primary issues with the paper is the inconsistency in how equations are expressed, particularly when compared to standard practices established in previous studies. In wave propagation modeling, there are well-established conventions for presenting equations that ensure clarity and facilitate comparison across different studies. However, this paper deviates from these norms, making it difficult for readers familiar with the standard approaches to follow the derivations. This inconsistency could lead to confusion, especially when trying to relate the new model to existing ones.

Another critical concern is the lack of comparison to previous studies and experimental data. For a new model to be credible and widely accepted, it must be validated not only against traditional models but also against other modified models. Unfortunately, the paper does not provide sufficient comparisons between the new dispersion relationship and those used in previous studies (e.g., Ge et al., 2020). Moreover, there is a noticeable absence of validation using experimental data, which is essential to demonstrate the practical applicability and accuracy of the model. Without these comparisons, it is difficult to assess whether the new approach offers a meaningful improvement over existing methods or if it merely presents a theoretical alternative without proven benefits.

Lastly, the paper lacks a comprehensive literature review, particularly regarding nonlinear mild-slope equation models, extended Boussinesq models, and the treatment of bed slope in previous models for both shallow and deep water. These areas are well-established in the field of wave modeling, and any new model must be clearly positioned within this existing body of work. The paper does not adequately discuss these foundational models or how the proposed approach differs from or improves upon them. This omission raises concerns about the core part of the paper, specifically the derivation of the equation in Section 3, which does not seem entirely sound. It is essential to explain the fundamental points in the derivation via the WKB approximation, clarify the procedures used in previous models, and indicate the differences or similarities between the present and past studies. For example, the author should address: (1) what the independent variables in A and θ are; (2) why the phase function and the wavenumber vector do not have the same order; and (3) why A0 is considered to be of order 1. Additionally, key explanations are missing, such as: (1) why the term at the first order is not included in Equation 17; and (2) the rationale for neglecting the effect of the denominator in specifying the order in Equation 18.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

 

This paper considers the effects of a variable depth on shallow water waves. The mathematics is solid and the work is good. However, major revision is required especially in comparison with and discussion of previous recent work, and in improving physical explanations. I can recommend it if revised accordingly. 

 

 

1. Rewrite lines 44-50 for clarity. Correct mistakes in spelling (step vs steep)
2. Improve the introduction to include more details of the problem you are studying
3. How is your work different from that of [13]? Clearly explain the uniqueness of your work
4. At present, literature review is weak. Expand it by adding more references and discussing significant results from them. For example, there are numerous papers on physics of waves on water of variable depth, and on those over nonuniform depth and bathymetry. 
5. You must make efforts to comprehensively discuss the similarities and differences between your work and those recently published in this area, so that your work will get highlighted.
6. Please clarify and justify the irrotational motion assumption. By doing so, you are naturally neglecting viscous dissipation. Would this be acceptable?
7. L105 is incomplete, it is  not clear how (7b) is automatically satisfied.
8. Though the author claims that the comparison of both approaches are beyond scope in L252-253, they must at least provide tangential statements for completeness and for readers interested in proceeding further.
9. Figure 4 in its current presentation is hard to follow and understand. Please revise for clarity.
10. Please improve the discussion of physical explanations in this manuscript for better understanding. 

Comments on the Quality of English Language

Minor changes required.

Author Response

Please find a pdf attached

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

I hereby express my sincere gratitude to the author for the efforts in addressing my inquiries regarding the initial version of the manuscript. Overall, I find this paper to be a valuable contribution to the field.

Reviewer 3 Report

Comments and Suggestions for Authors

Nil

Comments on the Quality of English Language

Minor editing of English language required.