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Ri<br />

0.001<br />

0.000<br />

�0.001<br />

�0.002<br />

�0.003<br />

Richardson number &<br />

Thermal diffusion time<br />

�0.004<br />

0.1 1.0 10.0 100.0<br />

r[AU]<br />

� therm<br />

12/13/2009 Hubert Klahr - Planet Formation - MPIA<br />

Heidelberg<br />

N 2 = 1<br />

100.0<br />

10.0<br />

1.0<br />

⇤<br />

Ri 2 =<br />

H<br />

R ⇥s⇥p<br />

N 2<br />

3<br />

2<br />

⇥ 2<br />

⇧therm = H 2 / D<br />

The saturated state presents a turbulent flow dominated b<br />

(Mamatsashvili & Chagelishvili 2007 ;Heinemann & Papaloizo<br />

fluctuation of 10% of the speed of sound and producing -valu<br />

10 3. Vortices are forming spontaneously out of the creation o<br />

⌅cv<br />

0.1<br />

0.1 1.0 10.0 100.0<br />

r[AU]<br />

vortices show no sign of decay, yet draw the energy out of the g<br />

providing entropy flux downward the gradient, like in standard<br />

Wednesday, September 5, 12<br />

MRI BI<br />

16<br />

2

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