the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Brief Communication: Modified KdV 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
Syed Assad Bukhari
Abstract. The nonlinear system of equations for Rossby-Khantadze waves in a weakly ionospheric plasma by incooperating sheared zonal flow is given. It is shown that in the presence of multiple-scale analysis, our obtained set of equations can be decomposed into one- dimensional equation which we call nonlinear modified KdV (MKdV) equation illustrating the propagation of solitary Rossby-Khantadze waves.
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Laila Zafar Kahlon et al.
Status: final response (author comments only)
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RC1: 'Comment on npg-2023-12', Anonymous Referee #1, 14 Jun 2023
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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
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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
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AC2: 'Reply on RC3', Laila Zafar Kahlon, 13 Jul 2023
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RC3: 'Reply on RC2', Anonymous Referee #2, 12 Jul 2023
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RC2: 'Reply on AC1', Anonymous Referee #2, 06 Jul 2023
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AC1: 'Reply on RC1', Laila Zafar Kahlon, 06 Jul 2023
Laila Zafar Kahlon et al.
Laila Zafar Kahlon et al.
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