Changes between Version 19 and Version 20 of GravoTurbulence

Timestamp:

10/31/11 13:39:57 (13 years ago)

Author:

Jonathan

Comment:

—

GravoTurbulence

@@ -13 +13 @@
 Goal is to put a cloud with random perturbations following a given power spectra [[latex($P_\xi(k)=Ak^\beta$)]] for [[latex($k_{\min} <= k <= k_{\max}$)]] where [[latex($\xi=\log(\rho)$)]].  The perturbations will be windowed on a region with a finite radius embedded in a much lower density region.  Since [[latex($\int{P_\xi(k)dk}  = \int{\hat{\xi}(k)k^2dk}$)]] we must have [[latex($\hat{\xi}(k) \propto k^\alpha$)]] where [[latex($\alpha = \beta-2$)]]
 
+Initially I tried a somewhat flat spectra [[latex($\alpha=0$)]] in 2D from k_min=4 to kmax=48 or from 6 pc to .5 pc.  This actually corresponds to a [[latex($\beta=1$)]] and led to higher power at shorter wavelengths.  As a result, the local density enhancements had typical size scales of .5 pc (8 cells) corresponding to [[latex($k=k_{\max}$)]] . 
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+The clump density was 400 and the temperature was 10K giving an overall Jeans length of 1.1 pc and free fall time of 1.7 Myr.
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+Most of these had densities of at least 800 (twice the mean) with several having densities of 1600 and a few with densities of 3200. The ones with a density of 800 would be stable to collapse and those with a density of 1600 have Jeans lengths of .26 pc and could potentially collapse - although the timescales would be similar to the timescales for the global collapse. This is in fact what we see... Two particles form before the entire thing collapses and then forms a binary system with periodic ejections of material.  Not sure if this is a protection issue, or material being slingshotted from the secondary.  Eventually the particles become unbound and begin to seemingly accelerate upwards.  This may be related to the way periodic BC's handle self gravity (which won't be a problem in 3D), or may be related to the particle kick #157.
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+Below is the initial density perturbation and here is the [attachment:collapse.gif movie]
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+[[Image(collapse.png, width=400)]]
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+So i modified the mean density to be 10, set [[latex($\alpha=-2$)]] so [[latex($\beta-1$)]] and strengthened the perturbation. Below is the initial density perturbation and here is the [attachment:hires.gif movie]
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+[[Image(hires.png, width=400)]]
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 == Velocity Perturbations ==
 
+Virial equilibrium requires [[latex($2T=V$)]] where [[latex($V=\frac{3GM^2}{5R}$)]]