Changes between Version 20 and Version 21 of GravoTurbulence

Timestamp:

11/08/11 16:19:00 (14 years ago)

Author:

Jonathan

Comment:

—

GravoTurbulence

@@ -30 +30 @@
 
 
+In all of these, there was initial pressure equilibrium (so different temperatues), although I was using a gamma=1.001 which assumes an isothermal gas.  Consider what happens when a gas at a density of 1 and a temperature of 100 K mixes with a gas at a density of 100 and a temperature of 1 K.  
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+The new density is [[latex($\rho=100+1=101$)]]
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+The new energy is [[latex($E=10^5+10^5=2\times 10^5$)]]
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+The new pressure is [[latex($P=2\times 10^2$)]]
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+And the new temperature is [[latex($T=200/101 \approx 2$)]]
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+So the dense gas at 100 K is instantly heated to 2 K and the equation of state is violated
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+If instead the gas is at the same temperature everywhere, then initial differences in density will cause expansion
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+[[Image(MultiPoleCollapse.png, width=400)]]
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+[attachment:MultiPoleCollapse.gif movie]
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+An alternative is to use the IICooling and to start with a much larger domain at a lower density with a small perturbation that will cause it to self-consistently develop large density perturbations.
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+[[Image(MPCollBig.png, width=400)]]
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+[attachment:MPCollBig.gif movie]
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 == Velocity Perturbations ==
 
 Virial equilibrium requires [[latex($2T=V$)]] where [[latex($V=\frac{3GM^2}{5R}$)]]
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+Or in the case of 2D [[latex($V=\frac{GM}{2}(\log(R)-\frac{1}{4})$)]]
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+If the kinetic energy is put into solenoidal motions with a spectral index [[latex($\alpha = -1$)]] so that [[latex($\hat{v}(k)\propto k^{\alpha}$)]], then energy dissipates fairly quickly and the whole thing collapses
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+[[Image(MPCollVir.png, width=400)]]
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+[attachment:MPCollVir.gif movie]