RE: insertions, stats
Kerstein, Alan
Concerning nu, the problem is that cause and effect are reversed in LEM. LEM assumes a range of eddies without accounting for the physics that determines the small eddies. Physically, small eddies are prevented when their time scale is longer than the time needed for viscosity to wipe out a feature that is the size of the eddy. The criterion that I suggested is one of several basically equivalent ways of enforcing this.
However, you are concerned with scalar diffusivity D rather than viscosity nu. The ratio nu/D is the Schmidt number Sc if the scalar is species concentration or the Prandtl number Pr if the scalar is heat. For ordinary gases, they are both close to unity, e.g., Pr \approx 0.7. They are high in liquids, but Pr is low in liquid metals. (Physics puzzle: guess why.) The Part 6 paper discusses the empirical method that I used to express the model parameter Pe = D_T/D (Peclet number) in terms of the product Re * Sc for the purpose of inferring scalar field structure as a function of Sc.
Concerning the weird statistics you're getting, three things come to mind. First, when you plot instantaneous states (the built-in gnuplot files), do they look reasonable (wiggles relative to the mean trend)? Second, when you subtract out the imposed mean trend, do these states look spatially homogeneous? Third, is the stats grid fine enough to capture the range of scales you see in the gnuplot output? (I arbitrarily set a coarse value for the stats grid. If you plot some snapshots - not aggregated data - from the stats grid, you can judge whether the number of stats-grid cells needs to be changed. That parameter could be hard-wired in the code version you are using.) If the answers to these questions are yes, then the data is reasonable and autocorrelations and spectra of the mean-subtracted data (did you subtract the imposed gradient?) should be well behaved. If they are not, then I think you should test your data reduction algorithms on simple known cases such as a sine wave or sum of sine waves before doing more with the code output.
Setting the diffusivity to zero will make the mesh adaption the effective molecular-diffusion mechanism. This can only make things worse because it will add high-wavenumber noise that is smoothed out by the diffusion. I don't know whether you need more eddies to get better statistics, but presently it sounds like your problem is something more basic.
I'm sorry to hear that your new laptop still has problems. I hope you can get it stabilized without too much difficulty. Tuesday is a good day for you to visit, so we can plan on that - please let me know if there is any change.
I copied this to the google group because I think that some of this is of general interest.
Alan
________________________________________
From: Murer David [dmu...@student.ethz.ch]
Sent: Saturday, November 29, 2008 10:51 PM
To: Kerstein, Alan
Subject: RE: insertions, stats
Alan,
I have some questions regarding making plots for the scalar structure function
and the power spectrum
a) I unterstand how you came to the paraters you ghave me, what I don't understand is why
the viscosity \nu is the turbulent diffusivity between the Kolmogorov length Lk, and 2Lk.
Why is this relation needed anyway? Why can't I just fix \nu at some value which is convinient
b) I don't seem to be able to get a decent looking spectrum out of the autocorrelation function or any
scalar structure function which is a line let alone scale as it is predicted (For the values you gave me)
Perhaps the relevant scales where not resolved enough in the stats grid?
I followed your notes from last meeting and the paper "part 6..." where you explain about Bachelor and Obukhov-Corrsin scales to
try other paramters, but nothing really worked, it all looks just like random noise.
I usually have around 10000 eddies, do I need a lot more?
I thought that if I take out the diffusion, this would correspond to a Schmidt number of +\infinity, or a zero molecular diffusivity
and only influences from the rearrangements will be observed and the Kolmogorov scaling corresponding to the intertial-concective range
(E(k)\prop k^(-5/3) I mean) should be more obvious.
This brings me to another point of this e-mail, I couldn't send you any results of this simulation since my hard drive is acting funny again
and went spontanously into read only mode, and then I had to repair the file system manually.
I don't dare to continue working with this until I could do a backup on an external hard drive (I can do so tomorrow evening)
I would be grateful if you have me any hints for what I have to look out for when I'm able to run simulations again.
I'm working with your code btw.
What was strange in most of my results is that the autocorrelation was a straight line, most of the time going down
(sorry I don't have pictures at the moment).
If you have any obvious tips I would be glad, if not I will continue with this as soon as possible. I will probably have to
go to information systems on Monday (they have replacement laptops here at i-house), so would Tuesday be a good day to come to Livermore?
Have a nice Sunday
David