Intermittency in fluid and magnetohydrodynamics (MHD) turbulence analyzed  through  the prism of moment scaling predictions of multifractal models

Pouquet, Annick; Marino, Raffaele; Politano, Hélène; Ponty, Yannick; Rosenberg, Duane

doi:https://doi.org/10.5194/npg-32-243-2025

Articles | Volume 32, issue 3

https://doi.org/10.5194/npg-32-243-2025

© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/npg-32-243-2025

© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 32, issue 3

Research article

|

23 Jul 2025

Research article |

| 23 Jul 2025

Intermittency in fluid and magnetohydrodynamics (MHD) turbulence analyzed through the prism of moment scaling predictions of multifractal models

Annick Pouquet, Raffaele Marino, Hélène Politano, Yannick Ponty, and Duane Rosenberg

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Final revised paper (published on 23 Jul 2025)
Preprint (discussion started on 19 Dec 2024)

Interactive discussion

Status: closed

RC1: 'Comment on egusphere-2024-3900', Anonymous Referee #1, 14 Feb 2025

This article is an interesting study on the detection of intermittency in different fluids, which is a vast subject. After an excellent introduction with a review, the article presents a new study on the relationship between kurtosis and skewness. The authors discuss a possible parabolic relationship between these two quantities. This relation is based on direct numerical simulations at moderate resolution. Although the study is considered preliminary, it is already interesting and I think it can be published in NPG. I have a few comments which I list below.
Comments:
The abstract begins with the assertion that in the presence of waves, certain characteristics remain in turbulence, such as intermittency. I think that when the amplitude of these waves is weak, we generally do not find intermittency. Am I wrong? Please add a comment.
After equation (2), I think the total pressure equation is not written correctly. The magnetic field/pressure should appear. Is it incompressible?
I am having trouble reading Figure 2, especially the abscissa. And the file name at the top seems useless. Please improve it.
Figure 3 is even harder to follow. I suggest adding references (a, b, c, d...) and using these names to comment on the results. In addition, it is sometimes difficult to read the information, as in the bottom left-hand figure. This is important because the discussion is mostly focused on it.
Line 128: where can we find the definition of Q5?
A comparison is made (page 8) with papers on MHD. I would suggest also comparing with Horbury & Balogh (1997) where a log-Poisson distribution is proposed. Is it possible to make a comparison?
In conclusion, I find the paper interesting and after these small improvements, I think it can be published. I would also like to congratulate the first author, as I see that the article is written in the context of the Lewis Fry Richardson 2024 medal. So congratulations for your wonderful contribution to turbulence!

Citation: https://doi.org/10.5194/egusphere-2024-3900-RC1
RC2: 'Comment on egusphere-2024-3900', Anonymous Referee #2, 14 Feb 2025

The report is attached

Citation: https://doi.org/10.5194/egusphere-2024-3900-RC2
AC1: 'response to referees (PCs) 1 and 2', Annick Pouquet, 06 Mar 2025

The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-3900/egusphere-2024-3900-AC1-supplement.pdf

Citation: https://doi.org/10.5194/egusphere-2024-3900-AC1
EC1:
'Comment on egusphere-2024-3900', Shaun Lovejoy, 05 Apr 2025
General comments:
This paper discusses numerous results of numerical experiments covering a range of turbulent flows, investigating the relationship between the Kurtosis and skewness (and other normalized moment ratios). Both referees greatly appreciated your manuscript and strongly recommended its publication with only minor corrections. I am delighted to share their opinion adding some suggestions (see below).
Yet, I do not feel fully satisfied by some of your replies to the referees; various scientific issues - some of which were brought up by the referees - have not been fully resolved (see especially the comments by referee 2 comment # 10, Conclusions). These comments allude to the consideration of more general multifractal models notably models having unbounded orders of singularities (such as the cited universal multifractal model). These have significant differences with respect to the bounded singularity models discussed in this paper and their consideration may significantly improve the physical interpretation of the parabolic law. However at this point, this discussion may be best pursued elsewhere.
Detailed comments:
In some places there appears “multi-fractal” with hyphen, please remove it.

In figure 3, but especially 4, the fonts that are badly distorted, presumably by stretching. Please improve the quality. In figure 2, the fonts are barely legible, please your larger ones.

In section 5.3, please include the definition of SOC that you are using, there are several, including one that focus on the SOC property of divergence of high order statistical moments. Yet it seems that such divergences are not considered in the paper.

Please define PRM2 in the text, not a footnote.

The caption to figure 3 has “run xxx” I presume this is incorrect?

It was not mentioned that the monofractal lower limit for a_Q is 3 – i.e. a cubic, not a parabolic law - and this would be helpful in judging figure 4 which violates this.
Citation: https://doi.org/10.5194/egusphere-2024-3900-EC1

Peer review completion

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

AR by Annick Pouquet on behalf of the Authors (06 Mar 2025) Author's response Author's tracked changes Manuscript

ED: Publish subject to minor revisions (review by editor) (05 Apr 2025) by Shaun Lovejoy

General comments:
This paper discusses numerous results of numerical experiments covering a range of turbulent flows, investigating the relationship between the Kurtosis and skewness (and other normalized moment ratios). This revised version is an improvement that can be published with minor modifications (see below).
Yet, I could not help but feel unsatisfied; various scientific issues - some of which were brought up by the referees - have not been fully resolved (see especially the comments by referee 2 comment # 10). These comments allude to the consideration of more general multifractal models notably models having unbounded orders of singularities (such as the cited universal multifractal model). These have significant differences with respect to the bounded singularity models discussed in this paper and their consideration may significantly change the physical interpretation of the parabolic law. However at this point, this discussion is best pursued elsewhere.
Detailed comments:
1. In some places there appears “multi-fractal” with hyphen, please remove it.
2. In figure 3, but especially 4, the fonts that are badly distorted, presumably by stretching. Please improve the quality. In figure 2, the fonts are barely legible, please use larger ones.
3. In section 5.3, please include the definition of SOC that you are using. Most definitions include the basic SOC property of divergence of high order statistical moments even though such divergences were not considered in the paper.
4. Please define PRM2 in the text, not a footnote.
5. The caption to figure 3 has “run xxx” I presume this is incorrect?
6. It was not mentioned that the monofractal lower limit for Q is 3 – i.e. a cubic, not parabolic law - and this would be helpful in judging figure 4 which violates this.

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AR by Annick Pouquet on behalf of the Authors (15 Apr 2025) Author's response Author's tracked changes Manuscript

ED: Publish as is (16 Apr 2025) by Shaun Lovejoy

AR by Annick Pouquet on behalf of the Authors (17 Apr 2025) Author's response Manuscript

Short summary

Turbulence is found in many natural systems. We study its statistics in terms of scaling laws of up to fourth-order normalized moments for the velocity or magnetic fields through their relative behavior. We show analytically using existing intermittency models that the physical dimension of structures becomes irrelevant. The strongest intermittent structure has a parabolic scaling as found previously and confirmed by long simulations. More analysis will be performed using simplified models.