Multi-Fractality, Universality and Singularity in Turbulence
Round 1
Reviewer 1 Report
Warmest Greetings and ALL the Best. The referee strongly recommends this excellent review paper for publication in Fractal and Fractional after necessary/minor changes; please see the attachment.
Comments for author File: 
Comments.pdf
Author Response
I thank the referee for his nice comments and useful remarks.
I have made all correction mentioned by the referees except for:
-remark 10:
Indeed I read the paper and could not see the connection with equation 16 or with the topic of the present paper. Moreover, the
equation (16) has not yet been studied theoretically, as it is very recent.
Reviewer 2 Report
Review Manuscript ID: fractalfract-1941330
Type of manuscript: Review
Title: Multi-fractality, universality and singularity in turbulence
Authors: Bérengère Dubrulle *
Submitted to the section: Complexity, Multifractals, Turbulence and Complexity in Geoscience and Space Science
Date: 16 September 2022
The author has nicely written a piece review article that is interesting, particularly for colleagues who are working in fluid mechanics and turbulence, and also applied mathematicians or physicists who would like to marry their expertise with applications in atmospheric and oceanic sciences. The article could be recommended for publication with a high priority. Here are some minor remarks.
* Missing a comma in the title, consider adding it.
* Some classical papers, such as Kolmogorov's paper from 1941 and other important papers, could be added to the reference list and be cited accordingly.
* 2/3 --> two-thirds
* Line 22: space needed
* What is K41? Is it related to the first remark?
* Equation (2) should be clarified, are you talking about triple integral over the (vector) variable y over here? If yes, how about x? From the notation, it seems that x and y are not vectors but variables in the space coordinate system. Do you ignore the vertical contribution z over here? These points should be clarified as they might confuse some readers.
* 50's --> 1950s
* Add and cite the paper(s) from Landau.
* What is h-rescaling? By the way, h should be written in math mode.
* After (4): for any \lambda and h \in \mathbb{R} or \mathbb{C} (??).
* Line 86: min and max should be written in the upright text mode, not in the math mode.
* its collaborator --> his collaborators
* Line 131: Constraints --> constraints
* e.g; --> e.g.,
* Line 156: [14, 16-19]
* i.e. --> i.e.,
* Improve the format for Table 1.
* Lines 184 and 187: remove space before colon and comma, respectively.
* Line 194: the operation for tilde was mentioned but not demonstrated.
* Line 194: resp. --> respectively
* Line 210: missing citation??
* When discussing the singularity, make a connection to "phase singularity", which has some applications in nonlinear waves. Include important references on this topic as well.
Author Response
I thank the referee for his/her nice comments and constructive remarks.
I have made all correction except for your last remark, because the phase singularity, indeed a very interesting topic, does not fit in the singularity picture convened by the multifractal theory.
Reviewer 3 Report
The article may be accepted in its present form. Comments for authors are given in the attachment
Comments for author File: Comments.pdf
Author Response
I thank the referee for his interesting comments. As he did not ask for any corrections, I did not take any actions. However, I will think about his comment regarding the Vostok application.
