Brief Communication: A modified Korteweg–de Vries equation for Rossby–Khantadze waves in a sheared zonal flow of the ionospheric E layer

Kahlon, Laila Zafar; Shah, Hassan Amir; Kaladze, Tamaz David; Ain, Qura Tul; Bukhari, Syed Assad

doi:https://doi.org/10.5194/npg-31-1-2024

Articles | Volume 31, issue 1

https://doi.org/10.5194/npg-31-1-2024

© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/npg-31-1-2024

© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 31, issue 1

Brief communication

|

09 Jan 2024

Brief communication |

| 09 Jan 2024

Brief Communication: A modified Korteweg–de Vries equation for Rossby–Khantadze waves in a sheared zonal flow of the ionospheric E layer

Laila Zafar Kahlon, Hassan Amir Shah, Tamaz David Kaladze, Qura Tul Ain, and Syed Assad Bukhari

Download

Final revised paper (published on 09 Jan 2024)
Preprint (discussion started on 01 Jun 2023)

Interactive discussion

Status: closed

RC1:
'Comment on npg-2023-12', Anonymous Referee #1, 14 Jun 2023

See attached file

Citation: https://doi.org/10.5194/npg-2023-12-RC1
- AC1:
  'Reply on RC1', Laila Zafar Kahlon, 06 Jul 2023
  
  Dear Sir,
  Thank you so mucch for your valuable ccomments. By taking into account your suggestions, we have been improved the manuscript (correction lists attached), which would be updated/provided by conccerned journal' person.
  Best Regards
  
  Citation: https://doi.org/10.5194/npg-2023-12-AC1
  - RC2: 'Reply on AC1', Anonymous Referee #2, 06 Jul 2023
    
    I read the manuscript entitled as “Modified KdV equation for 1 Rossby-Khantadze waves in a 2 sheared zonal flow of the ionospheric E-layer”. The paper under review is devoted to the derivation of the modified Korteweg–De Vries equation for the Rossby-Khantadze waves in a sheared zonal flow of the ionospheric E-layer. According to the authors, they have shown that the modified Korteweg–De Vries equation also describes the Rossby-Khantadze waves for the case of an inhomogeneous magnetic field. The authors described in sufficient detail the calculations for deriving the equation by the method of multiscale expansions. However, the results are questionable.
    First, the system of equations (1) is derived from the three-fluid ionospheric equations under certain assumptions, which are not mentioned or discussed in the article. Such a system includes an equation for the electronic, ionic, and neutral components of the ionosphere; in addition, such a system includes collisions of electrons, ions, and the neutral component with each other. The authors believe that the system of equations (1) was obtained by simplifying the three-fluid model for the conditions of the E-layer of the ionosphere, although they do not mention this, and readers have to guess before that, which is not very good for such a wide-profile journal as Nonlinear Processes in Geophysics. Second, the absence of an equation for the electron component indicates that the law of electron flow is given. Third, regarding the neutral component, it is included in the equation for ζ. The physical meaning of ζ is also not explained in the article. In addition, it is not specified which collisions the authors neglect in the system of equations (1) and refer to the article by Kaladze in 2014.
    The main question remains: to what extent does all the assumptions made when deriving the system of equations (1) work for the case of an inhomogeneous magnetic field, in particular, what is the flow of the electronic component, how is the collision of particles with each other described in the presence of magnetic inhomogeneity? All these questions should be answered clearly in the article. I think the paper in this form should be rejected.
    
    Citation: https://doi.org/10.5194/npg-2023-12-RC2
    
    RC3: 'Reply on RC2', Anonymous Referee #2, 12 Jul 2023
    
    It seems to me that the authors did not understand the essence of my remarks, so I repeat them again.
    First, if the authors consider that their article is in the field of the ionosphere, they should add to the Mathematical Preliminaries section a more or less detailed description of how to derive the system (1) and what assumptions should be made in this case. The authors refer to [14], but nine years have passed since then, and the theory of partially ionized plasma as applied to the ionosphere has been substantially developed. Moreover, in [14], naturally, there are references to earlier articles by the same team, in which these equations were substantiated to one degree or another. The paper [14], to which the authors refer, was carried out at a time when results in the field of Rossby waves were easily transferred from similar results in thermonuclear plasma, in particular, concerning drift waves. Now, in connection with the problems of space weather, the situation in the ionosphere has changed a lot, so this article cannot be considered a paper in the ionosphere.
    Second, if the authors consider that their article is in the field of non-linear problems of geophysics, a completely different derivation of the modified Korteweg–De Vries equation for the Rossby-Khantadze waves is required. First of all, it is necessary to show that within the framework of quadratic nonlinearity there are no nonlinear effects within the framework of a weakly nonlinear theory. This is usually done either by a qualitative analysis of dispersion equations for waves and an analysis of the impossibility of phase-matching conditions, or by introducing all scales into the asymptotic expansion in a weakly nonlinear theory and obtaining linear equations for quadratic nonlinearity. Without this, the paper cannot be accepted for Nonlinear Processes in Geophysics at all. I think that the article requires a very significant revision.
    
    Citation: https://doi.org/10.5194/npg-2023-12-RC3
    
    AC2: 'Reply on RC3', Laila Zafar Kahlon, 13 Jul 2023
    
    The comment was uploaded in the form of a supplement: https://npg.copernicus.org/preprints/npg-2023-12/npg-2023-12-AC2-supplement.pdf
    
    Citation: https://doi.org/10.5194/npg-2023-12-AC2

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

AR by Laila Zafar Kahlon on behalf of the Authors (31 Jul 2023) Author's response Manuscript

EF by Sarah Buchmann (03 Aug 2023) Author's tracked changes

ED: Reconsider after major revisions (further review by editor and referees) (20 Aug 2023) by Victor Shrira

AR by Laila Zafar Kahlon on behalf of the Authors (18 Sep 2023) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (20 Sep 2023) by Victor Shrira

RR by Anonymous Referee #1 (05 Oct 2023)

RR by Anonymous Referee #3 (19 Oct 2023)

Suggestions for revision or reasons for rejection

Suggestions for Revision:

Language and Presentation:
the revised manuscript has shown improvements in language and clarity.

Mathematical Exploration:
The manuscript's discussion around the derived MKdV equation and its association with quadratic nonlinearity needs further elaboration. Specifically:
1. Provide a detailed exploration of the vanishing quadratic nonlinearity.
2. Discuss the potential interplay of both quadratic and cubic nonlinearities in a perturbed system.
3. Offer a clear, step-by-step justification for these mathematical nuances.

Emphasis on mKdV Equation:
While the manuscript acknowledges the mKdV equation, it could benefit from:
1. Emphasizing its nature as an exactly solvable equation with diverse solution methods.
2. Providing a clear rationale for the authors' specific interest in the soliton-like solution over other potential solutions.

Significance of Discussed Waves:
Delve deeper into the significance of the discussed waves by:
1. Highlighting their zonal type and relevance during specific atmospheric events in more detail.
2. Providing a comprehensive exploration into the scales of these solitary waves and their overarching significance.

Reasons for Rejection (if not revised):

Incomplete Mathematical Justification:
The manuscript lacks a comprehensive exploration and justification of the mathematical nuances, especially around the mKdV equation.

Lack of Depth in Wave Significance:
The manuscript does not provide an in-depth discussion on the scales and overarching significance of the discussed waves, which is crucial for a holistic understanding of the topic.

Ambiguities in Presentation:
Despite improvements, there remain sections in the manuscript where the clarity of presentation could be enhanced.

Also, see the attached Referee Report (pdf).

Referee Report: PDF

Hide

RR by Anonymous Referee #2 (21 Oct 2023)

ED: Publish subject to minor revisions (review by editor) (30 Oct 2023) by Victor Shrira

AR by Laila Zafar Kahlon on behalf of the Authors (17 Nov 2023) Author's response Author's tracked changes Manuscript

ED: Publish as is (19 Nov 2023) by Victor Shrira

AR by Laila Zafar Kahlon on behalf of the Authors (23 Nov 2023) Author's response Manuscript

Short summary

It is shown that sheared Rossby–Khantadze waves can propagate due to inhomogeneities, taking into account the Earth's angular velocity and the magnetic field. Along with the Hall conductivity, these waves can couple in the ionospheric E region.The novelty of the present work is the consideration of magnetic field inhomogeneity, which was not considered before and reduced our considered system of equations to a 1D modified KdV equation.