Referee Comments:

Referee #1 (Comments to Both Author and Editor):

The present work is devoted to the investigation of influence of turbulent mixing on the decay rate of temperature perturbations. It is an interesting fundamental problem relevant for many applications.

The research is based on numerical simulations, so they play a crucial role and have to be well described. But there is still no full problem setup: the domain size is not provided, value T1 of perturbation amplitude is missing. Also please specify the units for \nu after eq. (16).
It is not clear for what quantity the energy spectra EK is calculated?
Please specify for what series of runs Fig. 2 is plotted?

Thus authors should make some amendments to the text to be ready for publication.

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Referee #2 (Comments to Both Author and Editor):

I must preface my review here by saying that this work is well outside of my field of expertise, which is in experimental environmental and industrial aerodynamics. I would therefore rate my own confidence in this review as "low", and cannot offer any assessment of either the novelty or the importance of this work. I will try, however, to offer some feedback.

First- incidentally the reason why I accepted the review- neither the title nor the abstract makes it clear that the subject of the paper is astrophysics. Because of the generality of the description (and the ambiguity of some of the discipline-specific terminology used), I had thought the paper would be about a novel technique for characterizing the performance of heat exchangers. It may be helpful to include in the (open access) abstract or title that the work is specific to the extreme environment inside stars.

The only other feedback I can offer is that I found the description of the numerical methodology to be somewhat lacking in detail. This may be a discipline-specific convention, but I would have expected to see an explicit description of all the boundary and initial conditions, a discussion of the sensitivity of the solutions to these, as well as of of the statistical convergence of the results. I also would have expected Fig 1 to appear later in the paper- this (it seems) is what has been used to validate the simulation, and would fit better into the logical chain of reasoning with the description of the methodology. It might also help the non-specialist to highlight that this was (I believe) a direct numerical simulation and didn't use any spatial or spectral models (which are almost universal in engineering) for small-scale structures.

Finally, a couple of trivial typos: the authors have omitted the units from viscosity on P4 under eq. 16, and although perhaps redundant, formally fig. 2 should include axes and scales on the spatial dimensions.

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Referee #4 (Comments to Both Author and Editor):

This is a solid paper reporting recent calculational results in radiative diffusion in turbulent flows. It should be published once the following minor changes are made to make it more accessible to the non-specialist:

I. Newtonian cooling should be defined when it is first used. This is an elementary concept, but it is easy to forget the definition, and some readers will be many decades past their introductory physics courses.
II. \ell, as defined here, is the absorption length, not the optical depth. The optical depth is
\int dx/\ell(x). In IV.D. k\ell is dimensionless.
Eddington approximation should be defined where it is first used.
III.A. "automatically" isn't quite the right word; it implies a process. "Implicitly" would be better, but deleting the word entirely would probably be best; "precluded" is enough.
III.B. A brief explanation or derivation of Eq. 11 would be useful.
What does "double logarithmic" mean?
III.C. What does "\delta-correlated" mean? That its temporal autocorrelation function is \delta(t)? If so, say so.
Following Eq. 14: Don't the authors mean |\tilde{f}|^2=1? f contains dimensional factors in {\cal N} that are not unity but depend on the strength of the forcing.