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MHDinduction & dynamo
ENS LYO
N
Laboratoire de PhysiqueEcole Normale supérieure
Lyon (France)
Jean-François Pinton
pinton@ens-lyon.frhttp://perso.ens-lyon.fr/jean-francois.pinton
Collaboration with
Philippe Odier, Mickael Bourgoin, Romain Volk
VKG : Stanislas Kripchenko, Petr Frick
VKS : François Daviaud, Arnaud Chiffaudel, Stephan Fauve, François Petrelis, Louis Marié
Numerics : Yanick Ricard, Yannick Ponty Hélène Politano
ENS LYO
N
Motivations and approach:
• Non-linear physics, fluid turbulence
• Induction mechanisms high Rm, low Pm
•Dynamo- `non - analytical’ dynamos?- bifuraction in the presence of
noise- saturation and dynamical
regime
Dynamo fields are self-tailored, and we wish we could control the flow !
Question addressed :
3D flowLiquid metal : Ga, Na
B-measurement
In situ
Mean induction ?
Fluctuations ?
Induction in mhd flows
B-eq. only : field is too small to modify imposed u
B0 imposed by external coils / currents
Boundary conditions : flow + vessel + outside
Equations & parameters
Liquid Gallium / Sodium
Turbulent flows
Weak applied field
Strong, non-linear induction
Measurement of induction in VK flows
Gallium at ENS-LyonSodium at CEA-Cadarache
•M. Bourgoin, et al., Phys. Fluids, 14 (9), 3046, (2001).•L. Marie et al., Magnetohydrodynamics, 38, 163, (2002).•F. Pétrélis et al., Phys. Rev. Lett., 90(17), 174501, (2003).•M. Bourgoin et al., Magnetohydrodynamics, in press, (2004).
Von Karman flows
Power
Velocityfeed-back
H=2R
RB0 B0//
3D Hallprobe
Pressureprobe
Motor 1
Motor 2
Power
Velocityfeed-back
Thermocouple
VKS1 experimentat CEA-Cadarache
von Karman counter-2D(differential rotation)
R
H=2R
-0.2 -0.1 0 0.1 0.2-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
-0.2 -0.1 0 0.1 0.2-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Toroidal poloidal
Omega effect
R
H=2R
Twisting of mag field lines by shear
linear
saturation B1
induit
Vitesse azimutale
-0.2 -0.1 0 0.1 0.2-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
x (m)
Vitesse poloïdale
-0.2 -0.1 0 0.1 0.2-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
x (m)
z (m
)
mesuresLDV
H=2R
HzR
(L. Marié, CEA)
xy
z
Von Karman 1D(helicity)
« alpha » effect
0 10 20 30 40 50 60 700
1
2
3
4
5
6
7
8
9
H=2R
HzR
VKG
BIz
Rm
saturation
quadratic
quadratic
Na, Cadarache
Ga, Lyon
« alpha » effect
Parker’s stretch and twist mechanism
H=2R
HzR
R R R
Turbulent fluctuations
30 30.5 31 31.5 32 32.5 330
20
40
60
histogram10
110
210
310
410
5-20
0
20
40
60
0 10 20 30 40 50 60-20
0
20
40
60
time (s)
Bin
d,z (
G)
applied B0 mean induced bz
time (s)
Bz (G
)
Turbulent fluctuations
100
101
102
100
102
104
0 - 1
- 11/3
f (Hz)
b²~
ΩΩ/10
br
bθ
bz
3 particularregions
Mean induction:an iterative approach (assuming stationarity)
real boundary condition
An iterative study of time independent induction effects in mhdM. Bourgoin, P. Odier, J.-F. Pinton and Y. Ricard,
Physics of Fluids, in press (2004).
Iterative approach
avec
Induction in the presence of an applied field
+ C.L.
Solving for B, I,
CL Neumann :(CL insulating)
Ex.1: -effect in VK
Potentiel électrique
Ex.1: -effect in VK
linéaire
saturation
R
Ex.2: -effect in VK
Ex.2: -effect in VK
Ex.2: -effect in VK
Ex.3: boundary effect in VK
Turbulent fluctuations : a mixed LES - DNS scheme
periodic boundary condition
Simulation of induction at low magnetic Prandtl number Y. Ponty, H. Politano and J.-F. Pinton:,
Physal Review Letters, in press, (2004).
Turbulence : coupled LES-DNS
Include turbulence, but :viscous dissipative scale : = L/Re3/4
magnetic ohmic scale : B = L/Rm3/4
1/L 1/
PS
D
uB
DNS LES
1/B
Taylor-Green vortex flow- pseudo spectral code 1283
-Pm = 0.001, Rm=7, R=100
-Chollet-Lesieur cutoff(k,t) ≈ (a + b(k/Kc)8)sqrt(E(Kc,t)/Kc)
TG, local induction
TG, global mode
VKS exp.
TG simulLocal
TG, global mode
VKS exp.
TG simulB-energy
In progress
Earth dynamo
VKS dynamo
Turbulence & induction
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