Brief communication: Modulation instability of internal waves in a smoothly stratified shallow fluid with a constant buoyancy frequency

Chow, Kwok Wing; Chan, Hiu Ning; Grimshaw, Roger H. J.

doi:https://doi.org/10.5194/nhess-19-583-2019

Articles | Volume 19, issue 3

https://doi.org/10.5194/nhess-19-583-2019

© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/nhess-19-583-2019

© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 19, issue 3

Brief communication

|

19 Mar 2019

Brief communication |

| 19 Mar 2019

Brief communication: Modulation instability of internal waves in a smoothly stratified shallow fluid with a constant buoyancy frequency

Kwok Wing Chow, Hiu Ning Chan, and Roger H. J. Grimshaw

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Final revised paper (published on 19 Mar 2019)
Preprint (discussion started on 14 Aug 2018)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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- Supplement

RC1: 'Referee Report', Efim Pelinovsky, 16 Aug 2018
- AC1: 'Response to comments by the Referee', Kwok Wing Chow, 16 Aug 2018
RC2: 'Review of Brief communication: The occurrence of rogue waves in the interior of the oceans: A modelling and computational study, by Chow et al.', Anonymous Referee #2, 31 Oct 2018
- AC2: 'Response to comments by the Referee', Kwok Wing Chow, 12 Nov 2018

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

ED: Reconsider after major revisions (further review by editor and referees) (03 Dec 2018) by Ira Didenkulova

AR by Anna Wenzel on behalf of the Authors (15 Jan 2019) Author's response Manuscript

ED: Referee Nomination & Report Request started (15 Jan 2019) by Ira Didenkulova

RR by Anonymous Referee #2 (23 Jan 2019)

Suggestions for revision or reasons for rejection

I am not satisfied with the rebuttal and the revised version of this manuscript. I have to say that I am even more confused than I was after reading the first submission. The manuscript still lacks basic details to make it accessible to a broad audience, which apparently is the aim of the authors. The shortness of the work is justified by the 4-page limit of the brief communication. However, this limit refers to the journal full format, while authors limit themselves to 4 pages in the pre-print format. I am pretty sure that the total length of the present manuscript would cover maximum 3 pages in the journal full format. In addition, just looking at published brief communications in NHESS, length can be stretched to 5-6 pages. Therefore, there is still quite a lot of room for the authors to clarify their work. Note that I am in general in favour for short publications, but this must not be done by compromising clarity. In my opinion, the manuscript in its present form contains interesting science but it is not well presented and hence it is not suitable/ready for publication.

Specific comments:

1. In answering my previous comment (3), the authors state that they are studying “internal rogue waves as opposed to surface waves”. Yet, the introduction is strongly focussed on surface rogue waves. This is quite confusing and led to my suggestions for missing references. The authors should focus more on the main topic of their work and highlight the new and striking results they have achieved. In addition, if one of the goal is to reach a broad audience, it would be beneficial to briefly explain potential relevance of this work in other filed of physics or engineering.

2. In my comment (5) I requested more information on the simulations and initial conditions. Both rebuttal and amendments in the manuscript, however, are quite general and, in my view, not accessible by a broad, general audience. E.g. What are the initial condition? The authors states that they chose a modulation instability mode with the optimised growth rate. What does this mean? What condition should I use if I want to replicate these results? The sentence at lines 5-7 at page 4 tries to explain the initial conditions, but it is too technical that general audience would not be able to understand. Another question was related to the values of the key parameters. Unfortunately, the authors only listed the parameters without providing the requested values, again leaving the reviewer and possible readers unaware of the initial set up of the model.

3. Throughout the manuscript the authors states that the goal is to establish a class of rogue wave occurrence through the effect of density stratification. I am not convinced this goal is achieved. In my comment (5) I asked what was the effect of density. However, the manuscript only describes one of condition of density profile with a constant buoyancy frequency No. How do results change if the value of No changes? To achieve the goal, I would expect a sensitivity analysis based on the density. Note also that the authors state in the conclusions that constant buoyancy might not play a critica role. I am not sure this conclusion is justified by the presented work. Also, what if N is not constant? This is a relevant question if the goal is to establish the effect of density stratification.

4. I really don’t understand the discussion on kh. For a unidirectional sea state, modulational instability ceases for kh < 1.36, although it can survive if oblique modulations are applied (this has been verified down to kh = 1 I guess). The authors state that internal rogue waves appear for kh < 0.766n\pi. The value of modes n ranges from 1 to 5 (in Table 1). Therefore kh is between 2.4 (for n=1) and 12 (for n=5). These values are considerably larger than the 1.36 threshold and definitively are not of shallow water depth conditions and only marginally consider intermediate water depths. This is very confusing; how can the authors claim that internal rogue waves may arise in shallow and intermediate water regimes, for which kh should be lower than say 2? Maybe I am misunderstanding the manuscript, but if this is the case, the authors should make a significant effort to explain their work more comprehensively. If the reviewer cannot understand, it is likely that the broad audience would not understand either.

5. Results presented in section 3 are not particularly new to me, at least in a way they are presented. Authors describe the occurrence of rogue waves as we know it on the water surface. What are the striking results that relate to internal wave and deserve a brief communication? I am struggle to understand this from Fig. 1 and 2.

6. The authors use an ad-hoc initial condition to achieve maximum instability. Why do the authors claim at line 12 (page 4) that rogue waves emerge spontaneously? It seems to me they are just forcing them to occur and this is far from being spontaneous.

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RR by Yury Stepanyants (05 Feb 2019)

ED: Publish subject to minor revisions (review by editor) (21 Feb 2019) by Ira Didenkulova

AR by Kwok Wing Chow on behalf of the Authors (28 Feb 2019) Author's response Manuscript

ED: Publish as is (05 Mar 2019) by Ira Didenkulova

Short summary

Oceanic rogue waves are unexpectedly large displacements from a tranquil background and pose dangers to shipping and offshore structures. A formulation of such abrupt, transient motions in the interior of the oceans is proposed. For constant buoyancy frequency, such internal rogue waves can occur in shallow fluids of various internal mode numbers, which is in strong contrast with surface rogue waves. Internal waves are crucial in oceanography as they affect transport of heat, mass and energy.