Shock-Induced Mesoparticles and Turbulence Occurrence

Round 1

Reviewer 1 Report

This contribution deals with the interesting issue of defining the appearance of meso-particles in a solid induced by a shock. Also, the authors claim that such meso-particles experience a transition towards a turbulent state of motion which, in my opinion is a strong assertion.

The article is appropriate for the journal, but the English must be really improved.

One important point that I would like to emphasize is that the contribution really is more similar to a chapter book than to a journal article. The contribution appears to compile results obtained by the authors during the preceding years which are presented together. This fact is reflected in the high number of self-citations (21 out of 45, 47%) and that illustrating figures are often reprinted from previous publications (only 3 figures from 13 do not give the explicit publication where they have been taken). In this sense, authors should clearly state what is the main novelty of the manuscript.

On the other hand, I understand that under intense enough impacts the kinetic energy of the impactor transforms into rotational-shear wave structures on the mesoscales on the solids, similar to the vortex detachment from a sharp corner in a fluid. However, the generation of rotational structures is just one of the characteristics of the turbulent motion. In fact, the authors mention “Although we cannot see turbulent motions directly in a solid, in experiments it is possible to register in real time such characteristics of motion at different scales that make it available to trace the transition to turbulence”. Therefore, in my opinion classifying those phenomena as turbulent is not appropriate because turbulent motion has many other characteristics (such as self-similarity) that are not clear that exist in the studied situation.

Moreover, the manuscript is not easy to read as equations are not correctly located within the text, some symbols are not properly defined, and some terms are not adequately explained. Therefore, the manuscript should be improved, because it is not intended to be read only by specialists in the field.

Regarding English writing, the manuscript must be thoroughly revised. Below there are some examples to be corrected:

a)       Line 54: “descried”

b)      Line 71: “deformiation”

c)       Line 128: “recording” should be “recorded”

d)      Equation in line 125: what do the brackets mean?

e)      Legend of Fig. 11. It seems that it is incomplete

f)        Line 349: “hasn’t” should be “has not”

g)       Equation in line 395: what does “Sp” mean?

h)      Line 479: “correlations” should be “correlation”

i)        Line 551-552. “However, it is possible to see the mesoparticle f conditions are provided under …” Something is not correct.

j)        Correct the Russian text in Fig. 12

k)       Line 599 “can being”

l)        Fig. 3: there is no label in the right vertical axis.

Also, the presentation of equations and the quality of the figures must be impr

Author Response

The experimental results used in the article have indeed been obtained over decades of research and published.However, the purpose of these studies was rather practical - to determine the strength of materials under impact loading,change in the internal structure of the material and its effect on its mechanical properties.

A new theoretical approach to the description of fast processes based on the dynamics of spatio-temporal correlations made it possible to look at the results of these experiments from a different point of view. It turned out that the fragmented parts of the correlations can be identified with mesoparticles inside the waveform and can even be visualized under spall conditions. The interaction of particles with each other generates not only their own moments of rotation, but also orbital moments relative to the shifted center of inertia of the particle, which is the result of a non-equilibrium distribution of spatial correlations.

This finding is new and has not been published before.

Of course, it would be possible not to include figures from the published articles, but we thought it would be better to see the results confirming our conclusions directly in the text than to look for them from other sources. For the same purpose, the published theoretical results without which it is impossible to substantiate the conclusions made in the paper are partially presented. Besides, the fact is that the theoretical approach used is not generally accepted, so we have to repeat some of its results for clarity of understanding. Perhaps that is why the article became like a chapter from a book. 

Since there is still no rigorous theory of turbulence based on first principles, there is no unambiguous rigorous definition of the concept of turbulence. We consider that turbulence is not a state of the system but an evolutionary process that accompanies any momentum transport far from local thermodynamic equilibrium. Therefore, it is recognized by all researchers that the phenomenon of turbulence is extremely diverse; it has many different characteristic features at different stage of the process that manifest themselves in different ways depending on specific conditions. Of course, the transition of shear motion into rotation is only one of these characteristics but as many consider one of the most important. Therefore, we believe that the occurrence of torques on the mesoscale due to an increase in the mass velocity gradient on the macroscale can be attributed to the manifestation of transition to turbulence.

 The text of the article has been completely revised both from the standpoint of clarity of presentation and from the standpoint of language. Some figures and references are removed; some explanations are added; all errors and typos corrected.

I am extremely grateful to the reviewer who took the time to point out annoying errors and typos to us, which we, of course, corrected in the revised version of the manuscript.

Reviewer 2 Report

The Authors attempt to demonstrate that a rigorous theoretical framework, aimed at portraying formation and interactions of turbulent structures at different scales, is a required tool to describe high-speed processes in any medium.

The main outcome of the presented study is that meso-particles, obtained as a result of the fragmentation of spatiotemporal correlations upon impact, move at different speeds in a medium with dispersion as wave packets. 

A consistent description of their motion calls for a redefinition of the concept of energy far from local thermodynamic equilibrium.

The article contains sufficiently original results to be published in MDPI.
It is also suitably formatted for publication.

I have spotted a misprint in line 712 ('to to' --> 'to').

I recommend the manuscript for publication in MDPI Particles, after the correction of the misprint.

Author Response

In order to improve our manuscript the text of the article has been completely revised both from the standpoint of clarity of presentation and from the standpoint of language.

Some figures and references are removed; some explanations are added; all errors and typos corrected.

Round 2

Reviewer 1 Report

After reading the revised manuscript I think that it can be published. However, I would recommend checking the format of figures and equations and the review of English grammar and spelling.