Changes which Maarit has already put into the PDF are marked with ***. Comments for internal discussion/action in []. General aspects like wrong footnote numbering or wrong symbols for mean EMF and force are not mentioned here. +++ Added to the pdf +++ Abstract, l. 10: "isotropic magnetic" -> "magneto-kinetic" +++ Abstract, line 11 "wavevectors having small components" -> "wavevectors whose components correspond to the largest scales" +++p. 1, right col., l. 14: by -> by a +++ l. 7 from below: insert "effect" behind SC +++p. 2, left col., l. 4: insert "effect" behind "(MSC)" *** +++ last l.: A=1 -> equal to 1 %MJK equal to one I think +++ l. 6 above Sec. 2: thee -> the *** +++ right col., l. 2: "PENCIL-CODE^1" -> "PENCIL-CODE^1, see e.g. \cite{PC2020}." *** +++ Eqs. (3),(4): "S\hat{x}A_y" -> "S A_y \hat{x}"; "S\hat{y}U_x" -> "S U_x \hat{y}" *** +++ Eq. (4): add comma at end +++ Eq. (5): write as "\cal D = \partial_t + S x \partial_y" +++ l. 5 below (5): "considered" -> "assumed" +++ below (6): add factor 1/2 behind "=", add "traceless" in front of "rate-of-strain", +++ add "\delta_{ij}" behind "\nabla\cdot\UU" +++ l. 4 above Sec. 2.2: neglected -> dropped +++ l. 2 above Sec. 2.2: "the SOCA" -> SOCA +++ p. 3, left col., Eq. (8), l. 1: bigger outer brackets %MJK If this sentence is to be removed, no need for this: below (8): zero should be bold %MR: But now the statement \mean{F_{K,M}}=0 is somehow scattered. Shouldn't we say it once and for all at the earliest % possible moment, that is when the mean is introduced? %MJK Is this discussion now resolved? Matthias, please check! +++ Sec. 2.3.3, l. 6/7: "50 time units" -> "$0.5 viscous times$" +++ p. 4, Sec. 2.6, l. 3: insert behind [new] ${\cal A}/k_1$: ", further the viscous time scale $T_\nu=(\nu k_1^2)^{-1}$." %MJK In the form ", and the viscous time scale $T_\nu=(\nu k_1^2)^{-1}$." +++ p. 5, Table 1, caption: [new] "S=-25 \nu k_1^2" -> "S=-25/T_\nu" +++ end of 1st para: add "In FMHD, the sound speed was set to $100/k_1 T_\nu$." +++ p. 6, left col., l. 5 from below: delete ", with equal contributions from the kinetic and magnetic forcings" +++ p. 7, Sec. 3.2.1, l.4: [new] "S=-25 \nu k_1^2" -> "S=-25/T_\nu" +++ p. 9, Sec. 3.2.3, l.4: [new] "S=-25 \nu k_1^2" -> "S=-25/T_\nu" +++ p. 15, left col., l. 9: "50 (in code units)" -> "$0.5 T_\nu$" +++ In section 2.3.1 and 2.3.2 the symbol for the turbulent electromotive force +++ \newcommand{\meanEMF}{\overline{\mbox{\boldmath ${\cal E}$}}{}}{} +++ has been replaced with an incorrect symbol is all places except Eq. (15). +++ The same is true for the mean ponderomotive force +++ \newcommand{\meanFFFF}{\overline{\mbox{\boldmath ${\cal F}$}}{}}{}, being +++ correct only in Equation 16. +++ Sec. 2.3.1, l. 2: "$\overline{\bm{\cal E}}$" -> "the mean electromotive force $\overline{\bm{\cal E}} = \overline{\bm{uu} \times \bm{bb}}$" +++ l. 4: "the case" -> so +++ right col., Eq.(12): add minus signs in front of both expressions, change "+" into "-" +++ 2nd para, l. 6: "because it" -> ", which" +++ above Eq. (13): several -> four +++ l. 7 below Eq. (16): "These four coefficients" -> "The coefficients $\boldsymbol{\alpha}$, $\boldsymbol{\beta}$, $\boldsymbol{\gamma}$ and $\boldsymbol{\delta}$" +++ "and $\bm{f}_{\rm K,M}=\bm{F}_{\rm K,M}-\overline{\bm F}_{\rm K,M}$." (shorter, no possible confusion with vector index) +++ %MJK The line just before 2.3.1 can now be deleted +++ %MJK Further, $\overline{\FF}_{\rm K}=\overline{\FF}_{\rm M}=\bm 0$, that is, the forcings are pure fluctuations. p. 4. 2.4 first para, 3rd line +++ In most of our simulations, we apply this forcing for both f_K and f_M in Eqs. (7) and (8). +++ -> +++ In most of our simulations, we apply this recipe for both kinetic and magnetic forcings in Equations (1), (2), (7), and (8). +++ p. 4, left col., l. 3: zero should be bold +++ Sec. 2.3.3, l. 6/7: "time units" -> "code time units" +++ Sec. 2.4, l. 2/3: "non-helical plane waves." -> "plane waves, here restricted to be non-helical." +++ l. 4: "that fit" -> "such that they fit" +++ l. 12: set full stop behind closing " +++ right col. l. 1: zero should be bold, insert "= \bm{F}_{\rm M}" in front of "=" +++ Sec. 3, l. 2: "and/or third refers" -> "and third refer" +++ last l.: add "(henceforth magneto-kinetic)" behind "forcing" ["with equal amplitude" unclear without units] +++ what about "with amplitudes equal up to a factor of $\rho^{-1/2}$ in the magnetic force." %MJK This is now fixed in two different places +++ p. 4, last para before results, 1st and 2nd line: +++ please change +++ "...rms value of a field V as Vrms=〈V2〉1/2 while +++ Bi,rms = áBi ñz +++ 2 1 2 are the rms values of the mean field +++ components. " +++ to +++ "...rms value of the magnetic field as +++ $B_{\rm rms} = \langle {\bm B}^2\rangle^{1/2}$ while +++ $\meanB_{i,{\rm rms}}=\big\langle \meanB_i^2 \big\rangle_z^{1/2}$ are the +++ rms values of the mean field components." +++ p. 4, last para before results, after "... averaging over a coordinate $\xi$." +++ please add +++ "For the velocity field, we define a time-averaged rms value +++ $u_{\rm rms} = \langle {\bm u}^2\rangle^{1/2}_t$." %MR: Here we would actually need "\langle \langle {\bm u}^2 \rangle \rangle^{1/2}_t" otherwise it would only be an average over t. "\langle {\bm u}^2 \rangle^{1/2}_{V,t}" perhaps also possible. +++ p. 5, Table 1: restore number alignment in cols. 3,6,7 +++ in Notes: “a,” -> “a”, “decimated forcing.” -> “decimated forcing”. +++ [unit of S?] %MJK Fixed throughout, in three places altogether. +++ left col., Sec. 3.1, l. 3: "with an" -> "and an" +++ right col., l. 6: "the nearly the same, ... ," -> "nearly the same with ..." +++ 2nd para, l. 9/10: "k/k_1" -> "k_z/k_1" (2 times) p. 6, Fig. 1, caption: "a higher-Rm FK run (black), an SK run (orange)" -> "higher-$\Rm$ FK (black) and SK (orange) runs" %MJK This was already dealt with in Q3 +++ "a decimated SKM run" -> "a lower-$\Rm$ decimated SKM run" +++ left col., l. 2: "k=1" -> "k_z=k_1" +++ [l. 5 from below: meaning of "with equal contributions from the kinetic and magnetic forcings"?] %MJK This is now fixed in two different places. +++ right col., 2nd para, l. 1: "k_z=1" -> "k_z=k_1" +++ 3rd para, l. 2: delete "(henceforth magneto-kinetically)" +++ 4th para: "k_{\rm min} = 2" -> "k_{\rm min}=2 k_1" +++ l. 5:"(black lines)" -> "(blue lines)" *** +++ l. 7: "blue lines" -> "black lines" *** +++ l. 9 from below: also -> further +++ p. 7, Sec. 3.2.1, unit of S change to S/T_{\nu} +++ 2nd para, l. 3: so that -> such that +++ l. 5: "3/4" -> "75 %" +++ l. 8: "SC origin" -> "SC-effect origin" +++ last para, l. 4: \eta should be bold [l. 6: "α values are similar or a bit larger, and clearly exceed the η_yx component" How to compare?] %MJK See my comment above. Now important to say from the perspective that eta_yx is very small. +++ The problematic two sentences were modified. Remember to change in the text file. +++ p. 9, right col, l. 3: "the wavenumber" -> "$k_z/k_{1z}$" +++ right col., [bottom: "while α_yy is slightly larger than them, but clearly smaller than α_xx" problematic!] +++ %MJK Yes, it does not hold in the kinetically forced run, where we now refer to, I think. +++ %MJK I think it would suffice to say [remove the mention of alpha_yy, as it does nothing spectacular]. +++ The diagonal α components exhibit larger values +++ than the off-diagonal ones, α_xx being especially strong. The off-diagonal +++ components are very similar to each other. +++ [Fig. 3: improve ij/ ] +++ %MJK Figured out how to improve, the same issue was in 4 and 5, now corrected. +++ p. 9, Table 2: restore number alignment in col. 6 +++ [mention aspect ratio in caption?] +++ %MJK OK, although it is said in the text, but for clarity, maybe. +++ left col., l. 2/3: "$\eta_{xx}$ linearly increases while $\eta_{yy}$ linearly decreases in the SOCA normalization." -> +++ "in the SOCA normalization, $\eta_{xx}$ increases linearly while $\eta_{yy}$ decreases linearly" +++ 2nd para, penulimate l.: shear -> $|S|$ [Sec. 3.2.3., 1st para: unit of S?] %MJK See above. +++ right col. l. 1: add "$k_z$" behind "wavenumber" l. 3: "the wavenumber" -> "k_z L_z" %MJK I introduced now k_{1z} for the vertical wavenumber, used in Table 3, and in the text, to avoid confusions. %MJK Please see paper.tex. +++ l. 6: "kinetic and magnetic forcing" -> "magneto-kinetic forcing" +++ [2nd para: "The negative values measured for η_xy tend to get smaller in taller boxes." +++ understood? +++ %MJK what is meant is less negative, hence "smaller" -> "weaker" would be better "while the case \cal A = 1 (SKM1ad) shows higher values of the transport coefficients not agreeing with this trend." only true for \eta_yx!] %MJK Here we talk about the fluctuations in alpha and eta, and this definitely holds for those. +++ l. 8 from below: "the effect" -> "an effect" +++ last l.: delete "should have" +++p. 10, [Fig. 4: \eta_11 -> \eta_xx etc., Sh_k -> \rm Sh_K] +++ Fig. 5: [italic yx] +++ %MJK OK, done. +++ caption: "kinetic and magnetic" -> "magneto-kinetic" +++ +++ left col., l. 2: memory -> non-local +++ Table 3: don't use full column width, restore alignment in 1st col. +++ p. 11, left col. above (26): "effect is" -> "effect through $\eta_{yx}$," +++ right col., Eq.(27): "\cal D \bm{A}" -> "\partial_t \bm{A}" +++ 2nd para, l. 7: magnetic -> magneto-kinetic +++ l. 3 from below: cause -> causes +++ 3rd para, l. 6 from below: add "in Table 3" behind "with an asterisk" +++p. 12: Fig 6, caption end: k^2 -> k_z^2 +++ left col., l. 3: "SC" -> "SC effect" +++ l. 7: "$D_{\eta S}$" -> "$D_{\eta_{\rm rms} S}$" *** +++ l. 7 from below: "SC" -> "SC-effect" +++ right col. last l.: kinetic and magnetic -> magneto-kinetic +++p. 13, left col., l. 4: "damp" -> "damp down" +++ right col., Eq.(27): "\partial_t \bm{A}" [new] -> "\partial_t \overline{\bm{A}}" +++ (28): make outer brackets bigger +++ 2nd l. below Eq. (28): add behind "zero means," "and standard deviations equal to the respective rms values," +++ l. 6: dynamo numbers -> $D_{\alpha S}$ +++ last para, l. 1: magnetic -> magneto-kinetic +++ l. 7 from below: no comma +++ right col l. 7: "such that it decreases" -> "such that its modulus decreases" p. 14: right col., [l. 3: m=2 self explaining?] %MJK I would think so. Make a suggestion how to improve! %MR: A suggestion is not so easy. That's why I asked. If we agree that it is self-explaining we leave it as it is. %MJK We leave it then? %MR: Perhaps we ask Axel. p. 15: Table 4: don't inflate to full width [Run SKM1a007 not explained] %MJK See Matthias_left.txt for details +++ [Fig. 10: Where is orange in lower panel?] +++ %MJK Underneath all the others. Zoom in, you will see it here and there. This we have also discussed N times before. +++ %MR: To see it, one has to zoom by 400%. So I doubt that many readers would do it. +++ % Better to add in the caption: +++ "Note that the {\sf jb} results are almost completely on top of the {\sf bu} ones." +++ %MJK OK, I guess you a right, and we might as well do it. +++ App. 4, l. 4: "and assume" -> ", assume" +++ Eq. (C1): sizes of left and right bracket pairs () and < > don't match +++ more space between \tau and I (2 times) +++ put (C1) on first line +++ p. 16, left col., (C3): too long, bracket sizes don't match +++ l. 1: y_0 -> y +++ l. 3: "\rho_0 \mu_0" -> "\rho"; [...] -> (...) +++ l. 4: first 0 should be bold +++ (C5)-(C6): align first + and - on each line +++ number each line +++ because of that: %MJK I posted what is written below as it is, without trying to understand any of it. +++ below (C7): "the second contribution in (C5)" -> "(C6)" +++ "by parts in (C6)" -> "by parts in (C7)" +++ right col.: "(C6) and (C7)" -> "(C7) -- (C9)" +++ "the first term in (C5)" -> "(C5)" +++ right col., in 2.: insert "-effect" behind MSC +++ no indentation before (