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Remapping from Turbulence sims to 3D Cloud collapse sims

So I have two data sets from isotropic turbulence (isothermal and iicool) that consist of the density, velocity, (and energy for the IICool run) on a 512³ mesh that I am remapping to a the middle half of a level 3 region of a simulation with a 1024³ effective resolution…

Both should have been driven to the same mach number though the isothermal simulation has a higher temperature and XMU (20 K and 1.4 and a gamma of 1.0) where the IICool simulation has an equilibrium temp of 16.98 and an XMU of 1.27 and a gamma of 1.6666

See blog:johannjc03062012b

The Isothermal run can be rescaled in density, length, or time - to a different density and/or temperature and/or size as long as the mach number is constant. This leaves us with two free parameters. We want a virialized cloud, and we want the peak density to be within the Jeans length at the 512 resolution…?

The current peak density is 40622 which is to be expected for mach 21.5 turbulence with a background density of 100? 100*21.5²=46225

However at a temperature of 10 this gives a jeans length of only 0.192981859204160 pc. If we want to resolve everything by a jeans length of 32 cells… then this requires each cell be .012 pc or the cloud at 512² resolution - be only 6 pc across.. We could lower the density, or raise the temperature …

J_L = X \frac{R}{256} = \sqrt{\frac{\gamma k_B \pi}{G}} \frac{T^{1/2}}{n^{1/2} \chi}

\alpha = \frac{2KE}{U} =\frac{5 \gamma k_B}{3 G} \frac{T}{n R^2 \chi^2} M^2 = \frac{5}{3\pi}\frac{J_L^2}{R^2} M^2

So if we have a virialized cloud, the Jeans length at the mean density will be 1.37 R/M and density enhancements of M² will have Jeans lengths of order 1.37 R/M^2 which means we will need a resolution of X \frac{R}{256} = 1.37 \frac{R}{M^2} \rightarrow M^2 <= 1.37 \times 256/X which allows for Mach 4 turbulence…

M \propto n \chi R^3

Options:

Generate lower mach number turbulence and make region larger and less dense?
Begin simulation with higher resolution… But it would be nice to get a chombo file complete with a solution for the potential to start with…

It would be nice to start with turbulence that wouldn't be strongly gravitating - at least locally … but would still be virialized… With IICool this should be possible - since virial equilibrium could be predominantly thermal support with lower mach number flows - that would trigger thermal instabilities and collapse would ensue…

astrobear

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Remapping from Turbulence sims to 3D Cloud collapse sims

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