Dear Jono,

>I’m actually pretty surprised by these differences you see here, so I wonder 
>if we could do a bit more investigation. In particular, it seems to me 
>that we ran very similar numerical experiments – except, as you say, the 
>compressibility, perhaps a slightly different Rm, and a different Pm – so 
>it’s quite surprising that the results look quite different. 

Our Rms were around 2, 3.5 or 12, and the corresponding Pms 3.33, 5, and 20.
I think we tried to match them closely to your runs in 2016 ApJ paper, hence
I do not think there is much of a variation, at least not enough to explain
the differences. 

>You convincingly measure eta_yx<0 in the kinetic one, where we definitely 
>measured eta_yx>0 using the kinematic TFM with NL sims (points in figure 
>5 from the ApJ paper), so I’m a bit confused here. One possibility is that 
>yours have somewhat higher Re (or that Pm has an effect), since eta_yx 
>does seem to want to turn over at the higher Re in our plot.

Both NLTFM and QKTFM give the same results in the kinetically forced 
case, hence this is not a method dependent result. All Rms investigated 
yield the same result. The measured effect seems significant when the errors
are estimated as we do, but the effect is very weak, when one plugs the
results into the 0D model. I think we are measuring here something that
could be consistent with zero, but we get a slightly negative value 
possibly due to the imperfections of the model and measurements. 
It would be quite bold to claim this as a SC effect, which we try to 
also clearly state in the manuscript.

>In the interests of narrowing this down – both the MSC and the 
>kinematically forced runs – I would be keen to run a few simulations 
>at identical parameters with snoopy (as long as these aren’t too expensive). 
>While I can get most of the parameters from the paper, there were a 
>couple I wasn’t sure about (is the mean density is one?) – so would 
>you mind providing your simulation parameters (just to make sure 
>I don’t stuff it up)? E.g., in the code units: box size, urms, etc.? 
>Then I’ll try and run identical snoopy simulations, to see whether 
>it is an incompressibility thing (which would be surprising), or a 
>difference with parameters. I won’t be able to do any of the TFM 
>stuff, but we can at least easily look at the structures.
>
>Does that sound okay to you?

Sure, I have made a tar package of one of the simulations (SKM1ad), and you 
can then easily look at the input params and also output numbers.

One thing to notice here is that, in the case of magnetic forcing, we could
not properly interpret the runs made with our standard forcing function, which
produced mean fields "ballistically". Hence, we reverted into using the
decimated forcing function, which seems to retain the dynamo instability
seen in the kinematically forced case. You can find both of the wavevectors
used from the tar package: k.dat is the decimated one, k_old.dat is the
standard one.

Because of these problems, I am personally inclined to think that 
we should completely drop the magnetic forcing cases, and look 
for genuinely generated SSD, which is definitely something we are 
planning to primarily concentrate on now.

>I took a quick look, and it might be a little non-trivial, but shouldn’t 
>be too bad I think. We never did the full calculation, it just came 
>from examining the origin of different terms (as in the toy model 
>from the JPP paper). I’ll get back to you soon on this.

OK, thanks.

>Sure, we’d be happy to explain this, and apologies for any confusion! 
>The basic point was just that there are two completely different 
>mechanisms that people call “stochastic alpha” (or various 
>variants of this). The first is the standard shear mechanism 
>as in your equation 25 – this is strong sometimes and can grow 
>large scale fields, as you find. The second is the Kraichnan-Moffat 
>mechanism, which can nominally work even without shear. This one 
>requires not just larger off-diagonal components, but actually that 
>the correlation of the diagonal components (xx with yy), exceed 
>both the dissipation and the off-diagonal components. In your 
>measurements, the xx is bigger than the yy (figure 3), so they 
>clearly can’t be that well correlated, so this seems unlikely. 
>We have no disagreement that the mechanism of equation 25 could work though. 

Thanks for the further clarifications!

We are now working rather intensively with the fully compressible TFM,
and will keep you posted on the developments.

BR, Maarit et al.