Nonlinear Effects on the Precessional Instability in Magnetized Turbulence

Round 1

Reviewer 1 Report

Referee report on the manuscript: “Nonlinear effects on the precessional instability in magnetized turbulence”, by Salhi, A., Khilifi, A., Cambon, C. (atmosphere-655849).

The article deals with a study of the effects of an imposed, uniform, magnetic field on the precessing instability for incompressible, homogeneous magnetohydrodynamic (MHD) turbulence. The study is performed under a well-defined configuration in which there is a rigid body rotation and a plane shear with constant rate which accounts for another rotation about an axis normal to both the original rigid rotation axis and the plane of the constant shear. The authors use different amplitudes of the imposed uniform magnetic field by finding that, when the magnetic field is stronger, the flow is two-dimensional (as it would be without the precessing effects) only at large scales, whilst the energy at smaller scales have a 3D distribution. Moreover, at the saturation of the instability, filamentary structures are observed in the velocity field.

The article in itself is quite interesting and it may be a relevant contribution for atmospheric physics. Therefore, in principle, I would recommend its publication in the journal “Atmosphere”.

However, I have some concerns about some points, that I try to explain here below.

First of all, I would strongly recommend the authors to carry out a thorough review of the manuscript: many sentences are written in (I apologize with the authors for saying this but I could not find a better expression) a quite “convolute” form and sometimes quite hard to understand. This is especially true for the introduction. I report here below some examples, but similar situations are common throughout the paper:

“The role of the Coriolis force, however, is subtle in general in the Earth’s atmosphere, and not completely dominant, as it is in the atmosphere of giant planets, where the organisation in zonal flows is essential (e.g., see, Galperin[3]).”

Could the authors please explain better what this sentence means? “Essential” for what?

“In all studies, the dynamics is very different, if only various initial data are considered, or if a large-sale forcing is present.”

Do the authors mean there is a strong dependency of the results of such studies on the chosen initial conditions or on the presence of a large-scale forcing? BTW, sale->scale is only one example of the many typos present in the manuscript. I suggest the authors to carefully double check the paper to avoid such errors...

“To which extent is this universality confirmed or not by studies in which the forcing is not stochastic and concentrated on a very thin band of small wavenumbers.”

Is this a question? A statement? I do not understand the meaning of that sentence, sorry...

All these odd-sounding (at least to me!) sentences are in the first 18 lines (2 paragraphs!) of the introduction (even if, I must honestly say, the situation improves a little bit in subsequent sections). I am myself not an english mother-tongue, therefore I do not want to express any judgement on the quality of the grammar (although, as I already said, there are many typos in the manuscript the authors should take care of), but reading a paper should not become a puzzle game and I strongly suggest the authors, for the sake of ease of reading, that they use a more “fluent” language throughout the whole paper.

My other concern is about the numerical resolution used in the simulations. A resolution of 256^3 is not that much and, at least in one of the shown cases, a convergence study is mandatory, in my opinion, to establish definitely that the results obtained are not a numerical artifact. The dealiasing technique chosen (the two-thirds rule, which is usual practice for incompressible flows), furtherly reduces the available spectral range. Basically, the “inertial” part of the spectra of kinetic energy extend over 1 decade in the key-vector space and the situation is even worse for the spectra of magnetic energy (see, for instance, fig. 8). The situation seems to be even worse for run 4 (e.g., figs. 10-11). Summarizing, I believe it would be better if the authors show (in the paper, or even just to me!), the results of even a single case with higher resolution, to be sure the dynamics is indeed independent of the number of gridpoints.

Concerning the rest of the paper, the results are well presented and clear and I believe that, in general, the article presents a quite good research. The minor changes I listed, however, are, in my opinion, useful to improve the quality and readability of an already good quality paper. After that, I would recommend for sure the article for publication on “Atmosphere”.

 

Author Response

Our reply is included in the pdf file.

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper discusses statistical properties of MHD turbulence for the interesting case where fluctuations develop over a "Mahalov background" (main rotation + precession + uniform shear), in the presence of an external magnetic field parallel to the main rotation axis. 

The authors carefully work out a linear stability analysis of the MHD equations of motion, which in fact finds good agreement with their DNS results.

I found particularly interesting that a well-defined, relatively extended, scaling range for the energy spectra can be observed form their simulations (Figs. 8,9, and 10), given that the initial flow configuration has a low Reynolds number (Taylor-Reynolds = 30), and at the same time linear stability analysis seems to be a meaningful tool to describe the statistically stationary regimes of fluctuations around the Mahalov background. May be the authors could provide a few comments on this point.

In this connection, once the initial Reynolds number of simulations is really low, I don't agree with the authors' statement that the initial flow configuration can be described as an instance of Kolmogorov isotropic turbulence. The initial state is at most an isotropic random flow. Thus, I think authors should rewrite the related comments that were done in Sec. IV and in the concluding section.

Just to make my point of view completely clear, my opinion is that the paper is scientifically sounding and provides a very interesting contribution to the problem of MHD turbulent flows in anisotropic backgrounds. I recommend its publication after some minor modifications (like the conceptual ones, discussed above).

Further minor points:

In the introductory section of the paper, the sentence "To which extent is this universality confirmed or not by studies in which the forcing is not stochastic and concentrated on a very thin band of small wavenumbers." seems to be incomplete. There are no top and bottom panels in Fig. 7. So its caption should be rewritten.

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Author Response

Our reply is included in the pdf file.

Author Response File: Author Response.pdf