Joint Distribution of the Wave Crest and Its Associated Period for Nonlinear Random Waves of Finite Bandwidth

Round 1

Reviewer 1 Report

The paper presents an analytic derivation of the joint distribution of wave lengths and crest heights, based on a non linear wave theory.   Some experimental data from previous researches have also been taken into account and compared favourably with the theory.  Even if not immediately useful to the engineering practise, the work provides however a deep and interesting insight on the mechanics of a fundamental problem of marine science and engineering.

I suggest that the Author take some care to clarify the terms and the definitions he uses:  the word “crest “ is often used to mean “crest height”;  what the Author calls “wave elevation” (line 54 and elsewhere)  is more often called  ”sea surface elevation “;  “wave height” and “crest height” are not the same thing,  but then why is fig 9 presented as “wave crest vs period” in line 430-431, and the as “wave peak vs period” in the caption (line 447)?

I also have some perplexity about the statements on line 545 and on 402 and following:  “wave crest and period have been perceived to be mutually independent random processes …”.  I do not have all the references handy but certainly, for instance,  ref 4 (Tayfun 1993) does not seem to suggest anything like that:  it actually deals with the Joint Distribution of  Wave Heights and   Periods .  Also   Srokosz and Challenor, “Joint distributions of wave height and period: A critical comparison” Ocean Engineering, Volume 14, Issue 4, 1987  ( which by the way is an important paper, and could be included among your references ) provide important information on the correlation between wave heights and period. May be I have misunderstood the meaning of the sentence, but so would the average reader:  the Author should therefore clarify or amend the statement.

Some other remarks and suggestions are also reported in the attached text.

Despite these rather minor drawbacks, the work  is well conceived and properly carried out, and I certainly support publication, with no need for further revision once these recommendations have been taken into account.

Comments for author File: Comments.pdf

Author Response

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Reviewer 2 Report

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Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

The statistical properties of nonlinear random waves of finite bandwidth are analysed theoretically.  The analysis gives some useful insights into these statistics, with implications for modelling large waves and their impacts and challenging some previous ideas and assumptions.  Overall I think this is worthy of publication, but there are some matters that need considering.  These are presented in the order they appear in the paper – some are minor corrections, some more substantial points.

 

There are too many short paragraphs, some containing only one sentence.  These need combining to form longer paragraphs.  The Abstract should be a single paragraph.

11 derive; 12 proceed [use present tense in Abstract]

14 bandwidth of the wave

20 The peak period decreases due to

31 Despite its great

34 This lack of attention

39 through their application

~95 briefly explain the structure of the rest of the paper at the end of section 1

186 I think the entry in the bottom left of the matrix should be rho_3, not rho_2?

218 Do the terms Q, Q1, Q2 and Q3 have a meaning you can explain?

I see all the Q are O(epsilon) except for the 1 at the start of Q1, and indeed could all (apart from the 1) be expressed as a multiple of epsilon/2(1-rho^2).

You comment that xi is <=0.03 in practice.  At xi=0.03 I think m = -5.815 and epsilon = 0.138, perhaps a plot of m and epsilon vs xi, and some comment on this for practical applications would be useful.

256 At epsilon = 0

313 nonlinearity is increasing

385 eqn (71) seems to have LHs and RHS identical – please clarify/explain

449 influences

506 use “is increased” instead of “profound” (in general “profound” isn’t used correctly)

516 If the underlying

549 and becomes large

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

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Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf