Hubert KLAHR

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Radial surfacedensity gradient: + Radial temperature gradient: = Radial pressure gradient: & Radial entropy gradient: As a consequence: 1.: Radially buoyancy: 2.: vertical shear /thermal wind: 12/13/2009 <strong>Hubert</strong> Klahr - Planet Formation - MPIA Heidelberg 40
Richardson number & N 2 = thermal diffusion time 1 ⇤ H Ri 2 = N 2 R ⇥ s⇥ p 2 3 2 ⇥ 2 ⇧ therm = H 2 / D ⌅c v The saturated state presents a turbulent flow dominated b Ri 0.001 0.000 0.001 0.002 0.003 MRI BI 0.004 0.1 1.0 10.0 100.0 r[AU] therm 100.0 (Mamatsashvili & Chagelishvili 2007 ;Heinemann & Papaloizo 10.0 fluctuation of 10% of the speed of sound and producing 1.0 12/13/2009 <strong>Hubert</strong> Klahr - Planet Formation - MPIA Heidelberg 0.1 0.1 1.0 10.0 100.0 r[AU] 41 -valu 10 3. Vortices are forming spontaneously out of the creation o vortices show no sign of decay, yet draw the energy out of the g providing entropy flux downward the gradient, like in standard
Page 1 and 2: Les Houches, Feb. 7 th , 2013 Disk
Page 3 and 4: Outline: The role of Turbulence in
Page 5 and 6: Planet Formation time Surface stick
Page 7 and 8: Laminar disk: No growth beyond 10cm
Page 9 and 10: What if there is no global turbulen
Page 11 and 12: 10 cm sized boulders: V e r t i c a
Page 13 and 14: Turbulence in Disks: Candidates •
Page 15 and 16: Pluto Code: HLLD Upwind CT, piecewi
Page 17 and 18: Development of MHD Turbulence From
Page 19 and 20: 2,000,000 boulders of 1m size 12/13
Page 21 and 22: MHD plus self-gravity for the dust,
Page 23 and 24: 14 years back... ...before I was do
Page 25 and 26: 3D - Radiation Hydro of Convection
Page 27 and 28: Vorticity Vorticity: Pencil Code: L
Page 29 and 30: 2D - vertically integrated disk (Kl
Page 35 and 36: Density: zimuthal 12/13/2009 Hubert
Page 37 and 38: 12/13/2009 Hubert Klahr - Planet Fo
Page 39: Klahr & Raettig in prep. Using data
Page 43 and 44: Pluto Code: 1024^2; WENO3-RK3; HLLE
Page 45 and 46: 2D Local (radial - vertical), Inclu
Page 47 and 48: 2D axissymetric Pluto Simulation: O
Page 49 and 50: 12/13/2009 Hubert Klahr - Planet Fo
Page 51 and 52: Full 3D Pluto Simulation: Spontanou
Page 53 and 54: Vertical Buoyancy Frequency: Includ
Page 55 and 56: Interface MRI - Dead Zone Disk Weat
Page 57 and 58: St = 0.05 particles (few millimeter

Hubert KLAHR

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