the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 19 Dec 2024
Intermittency in fluid and MHD turbulence analyzed through the prism of moment scaling predictions of multifractal models
Abstract. In the presence of waves due e.g. to gravity, rotation or a quasi-uniform magnetic field, energy transfer time-scales, spectra and physical structures within turbulent flows differ from the fully developed fluid case, but some features remain such as intermittency or quasi-parabolic behaviors of normalized moments of relevant fields. After reviewing some of the roles intermittency can play in various geophysical flows, we present results of direct numerical simulations at moderate resolution and run for long times. We show that the power-law scaling relations between kurtosis K and skewness S found in multiple and diverse environments can be recovered using existing multifractal intermittency frameworks. In the specific context of the She-Lévêque model (1994) generalized to MHD and developed as a two-parameter system in Politano and Pouquet (1995), we find that a parabolic K (S) law can be recovered for maximal intermittency involving the most extreme dissipative structures.
-
Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
-
Preprint
(1177 KB)
-
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(1177 KB) - Metadata XML
- BibTeX
- EndNote
- Final revised paper
Journal article(s) based on this preprint
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
-
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
-
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 aQ 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
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
-
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
-
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 aQ 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
Journal article(s) based on this preprint
Viewed
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 209 | 108 | 22 | 339 | 14 | 30 |
- HTML: 209
- PDF: 108
- XML: 22
- Total: 339
- BibTeX: 14
- EndNote: 30
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
Annick Pouquet
Raffaele Marino
Helene Politano
Yannick Ponty
Duane Rosenberg
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(1177 KB) - Metadata XML