STABILITY AND TRANSPORT IN TAYLOR-COUETTE FLOW: APPLICATION TO PROTOPLANETARY DISKS B. DUBRULLE CNRS, Groupe instabilité et Turbulence SPEC/DRECAM/DSM, CEA Saclay F. HERSANT Obs. Meudon J-M HURE Obs. Meudon O. DAUCHOT CEA Saclay F. DAVIAUD CEA Saclay P-Y LONGARETTI Obs. Grenoble D. RICHARD Obs. Meudon J-P. ZAHN Obs Meudon
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STABILITY AND TRANSPORT IN TAYLOR- COUETTE FLOW: APPLICATION TO PROTOPLANETARY DISKS B. DUBRULLE CNRS, Groupe instabilité et Turbulence SPEC/DRECAM/DSM,
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STABILITY AND TRANSPORT IN TAYLOR-COUETTE FLOW: APPLICATION TO
Van den Berg et al, 2003Increase of transport withRough BC
Turbulent viscosity
10 -5
0.0001
0.001
0.01
1000 10 4 10 5 10 6
RC
4 G i
/ Re 2
Re
smooth boundaries
rough boundaries
Dubrulle et al, 2005
€
ν t = g(Re)h(RΩ ) Sr*2
Parametrization: Viscosity
In disk:
€
νT = α (Re,RΩ ) ΩH 2
RANS: Viscosité
€
S = −3
2Ω
r* = H
Disk structure: observations
105
107
109
1011
1013
1 10 100 1000
profils -GM Aur
n (cm^-3)
r(au)
MD=0.03 M
SOL
n = r -2.75
0,1
1
10
100
1 10 100 1000
profils -GM Aur
vrot
(km s
-1)
r(au)
M*=0.5 M
sol
v = r -0.5 +_0.1
M*=0.8 M
sol
1
10
100
1000
1 10 100 1000
profils -GM Aur
T (K)
r(au)
T = r -0.6 +-0.05
Interferpmetric obs.Inversion via 20 parameter minimization Keplerian model assumed
Radial structure of disks
(Dutrey et al)
Classic thin disk
Model with exces IR
Reynolds number in protoplanetary disks
r =100AU;Re=3×102
r =10 AU;Re=6×104
r =1 AU; Re=1.3×107
r =0.1AU;Re=2×109
Re=9×1014 v*
10kms−1
⎛ ⎝ ⎜
⎞ ⎠ ⎟
r*
1011cm⎛ ⎝ ⎜
⎞ ⎠ ⎟
104KT
n4×1019cm−3
⎛
⎝ ⎜
⎞
⎠ ⎟
Stability lines
1
100
10 4
10 6
10 8
10 10
10 12
10 14
10 16
0.001 0.01 0.1 1 10 100 1000
Reynolds
r (A. U.)
HD critical Reynolds number
MHD critical Reynolds number
Effective local Reynolds number
Protoplanetary disks are turbulent!
INSTABILITIES- THEORY-Summary
Non-linear Strato Magneto Linar
−1<2ΩS
<02ΩS
>−4m2 I0
I1
Ω2
N2
2ΩS
>−4m2 I0
I1
Ω2
Ω A2
105∞ 1000 3000
Critical Reynolds number in protoplanetary disk
Inviscid stability criterion
COMPARISON EXP/ASTRO
0
5
10
15
20
25
30
35
40
8840 8860 8880 8900 8920 8940 8960
Luminosity/L
0
JD-2.44E6
fluctuations flickering
Mean dissipation Statistics
BPTau
10 -13
10 -11
10 -9
10 -7
10 -5
0.001
0.1
10
10 12 10 13 10 14 10 15
Energy dissipation
Reynolds number
TTauri
FU Ori
laminar
turbulent min
turbulent max
ELARGISSEMENT DE RAIES
0.01
0.1
1
0.01 0.1 1 10 100 1000
Δ
( v km s
-1 )
( . . )r A U
Azimuthal velocity dispersion
0.01
0.1
1
10 4 10 5 10 6
Δ
( -1)v laboratory km s
*Re
Au laboratoire
Dans un disque protoplanetaire
Limite turb/lam
TURBULENCE ET FORMATION PLANETAIRE
Turbulence+cisaillement+rotation=tourbillons
Concentration locale de densitéFreine la migration interne des poussières
IMPORTANCE DE LA CYCLONICITE
BRACCO ET AL, 1999
Seuls les anti cyclones survivent dans un écoulement képlerien
ARGUMENTS GENERAUX
ul Ω
Ro=u
2lΩ≈l−2/3
Ro>1: la turbulence n’est pas influencée par la rotationRo<1: la turbulence est modifiée par la turbulence
Naivement: la turbulence bi-dimensionalise=> ralentit la cascade d’energie vers les petites échelles => favorise l’apparition de structures à longue durée de vie