Hi Axel, Apologies about the delay. Please find attached the kinetic energy spectra for the same three simulations, as before. I have averaged the kinetic energy spectra over the same time-range as the magnetic energy spectra, corresponding with the kinematic phase of the dynamo. Cheers, Neco On 9 Nov 2022 at 1:13 AM +1100, Axel Brandenburg , wrote: Hi Neco, Could you also please send me your velocity spectra (time averaged and obviously not compensated) that belong to the magnetic spectra? Axel On Thu, Nov 03, 2022 at 02:05:36PM +0000, Neco Kriel wrote: Quick correction: at the same resolution and plasma parameters, FLASH simulations have a lower effective Reynolds number than PENCIL. Cheers, Neco On 4 Nov 2022, 1:03 AM +1100, Neco Kriel , wrote: Hi Axel, I think this is a very interesting comparison; thanks for sharing it. As you mentioned in your note, and by comparing the energy spectra like this, it seems clear that FLASH simulations probe the dissipative scales more so than PENCIL does, and conversely PENCIL probes the inertial scales more than FLASH. I am not completely sure why this is, but I suspect it might be because FLASH uses an approximate Riemann solver, whereas PENCIL employs higher order solvers (both in space and time). Therefore, at the same resolution and plasma parameters, FLASH simulations have a higher effective Reynolds number, and hence are more dissipative. (This is why we perform resolution studies: to understand and remove the effects of numerical resolution on our results). On another note, I think that your method of collapsing the magnetic energy spectra on-top of one another is an interesting way to compute a resistive scale. I am curious, however, which simulation you are collapsing your magnetic spectra with respect to? Is it with respect to your Pm=1 simulation? If so, then your Pm=1 simulation has a particular Re and Rm (Re=Rm=1680). So, if you ran another Pm=1 simulation, say, with Re=Rm=3000, then one should expect that the absolute dissipation scale values you measure when you collapse all of your other simulations onto that new Pm=1 (Re=Rm=3000) simulation will be different to your previous Pm=1 (Re=Rm=1680) simulation. See for example the figure I have attached. Here I create four mock models of a magnetic-type energy spectrum to demonstrate my point. In the top left panel I plot each model as is (and I report each model’s true dissipation scale in the legend). Then in the top right panel I plot all of the models normalised by their true dissipation scale. From our simulations, we do not know these absolute dissipation scales as a priory, however. So, from my understanding, you instead collapse your magnetic energy spectra on-top of a reference spectrum (as discussed above, perhaps your Pm=1 simulation). In the bottom left and bottom right panels I collapse the models onto the red and black models, respectively. We see that the absolute dissipation scale that we measure by doing so results in a different absolute value. Now, I don’t believe there is a problem by doing this, it just means that one should standardise the energy spectrum that we collapse with respect to, otherwise we will all be quoting different dissipation scales. Please correct me if I have miss-represented what you have done, or if I am missing something. Cheers, Neco On 3 Nov 2022, 8:20 PM +1100, Christoph Federrath , wrote: Hi Axel, all, This is a very nice and encouraging comparison that shows we are essentially obtaining the same results, from two quite different codes, with very different numerical schemes (Riemann solver, etc…). Maybe you can now stop saying in your many papers that our FLASH code has questionable dissipation properties...with approximate Riemann solver, etc… :-) …but seriously, these kinds of comparisons are important to gain trust in all our works, within the community and beyond! Cheers, Christoph On 3 Nov 2022, at 3:24 pm, Axel Brandenburg > wrote: Hi Neco, Many thanks for your data. I attach a notes file with some comparisons. In the meantime, we also realized that your value of Pr_M,crit=1.3 applies to the nonlinearly saturated state. We have now checked that value for our nonlinearly saturated runs and also find a value of about 1. We'll have this in the appendix of our revised paper. So, in conclusion, there is actually no discrepancy with your runs. The remaining differences described in the notes are minor, but perhaps still interesting in their own right. What do you think? Cheers, Axel On Wed, Nov 02, 2022 at 03:25:11AM +0000, Neco Kriel wrote: Hi Axel, I have attached three json-files, each storing the following parameters for each of our Re3600Pm1, Re1700Pm2, and Re600Pm5 simulation runs: * Re, Rm, Pm: plasma Reynolds numbers * Gamma: average growth-rate of the magnetic energy over the kinematic phase * list_mag_power_comp_ave: and the time-averaged, compensated magnetic energy spectrum: P_mag(k, t) / \int dk P_mag(k,t) I have also attached a figure to show the data in pictorial form. Kind regards, Neco Kriel On 27 Oct 2022, 2:07 PM +1100, Neco Kriel >, wrote: In equation 2 of your study, I see that you will need the growth rate (gamma) to define k_eta^{KA}. So I will send you a file with the time-averaged, compensated magnetic energy spectra in the kinematic phase, along with gamma in this kinematic phase for those three simulations. Just for transparency, the time range of the kinematic phase will be defined as in Kriel et al. 2022: 10^{-7} < E_ratio < 10^{-2}. Cheers, Neco On 27 Oct 2022, 1:54 PM +1100, Axel Brandenburg >, wrote: Thanks, Neco, for your quick reply. Time averaged data would be sufficient, but for the kinematic phase, you'd need to average spectra that are compensated against the growth. Cheers, Axel On Thu, Oct 27, 2022 at 02:29:00AM +0000, Neco Kriel wrote: Dear Axel, I am happy to share the data for these simulations with you. I will double check the data for these simulations and format something to send you. Is it just the time-averaged magnetic and kinetic energy spectra data that you would like? Kind regards, Neco Kriel On 27 Oct 2022, 1:22 PM +1100, Axel Brandenburg >, wrote: Dear Neco, James, Amit, and Christoph, In connection with your recent paper on "Fundamental scales in the kinematic phase of the turbulent dynamo" in MNRAS, we would be very interested in comparing with your spectra, especially those for Runs Re3600Pm1, Re1700Pm2, Re600Pm5. A simple text file for the kinetic and magnetic energy spectra would be fine, or any other format of your choice. We would also be interested in the earlier kinematic phase. Many thanks, Axel —Associate Professor Christoph FederrathResearch School of Astronomy & AstrophysicsAustralian National University, Canberra, ACT, AustraliaTel: +61-2-6125-0217Web: https://aus01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.mso.anu.edu.au%2F~chfeder&data=05%7C01%7Cneco.kriel%40anu.edu.au%7Ccd59e801460a414cd27308dac1936768%7Ce37d725cab5c46249ae5f0533e486437%7C0%7C0%7C638035136118834838%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=fJKI9zAwsX3m9liQD0k2jqeAA3MOAHVyrq0K9hTRPJo%3D&reserved=0