1. ENS MHD induction & dynamo LYON Laboratoire de Physique
Ecole Normale supérieure
Lyon (France)
Jean-François Pinton

2. 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

3. ENS LYON 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 !

4. Question addressed : B-measurement In situ 3D flow
Liquid metal : Ga, Na
Mean induction ?
Fluctuations ?

5. 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

6. Equations & parameters
Liquid Gallium / Sodium
Turbulent flows
Weak applied field
Strong, non-linear induction

7. Measurement of induction in VK flows Gallium at ENS-Lyon Sodium 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), , (2003).
M. Bourgoin et al., Magnetohydrodynamics, in press, (2004).

8. Von Karman flows B0 B0// Motor 2 Motor 1 H=2R 3D Hall probe Pressure
Power
Velocity
feed-back
H=2R R
B0
B0//
3D Hall
probe
Pressure
Motor 1
Motor 2
Thermocouple

9. VKS1 experiment at CEA-Cadarache

10. von Karman counter-2D (differential rotation)W R
H=2R
poloidal
Toroidal

11. Omega effect W Twisting of mag field lines by shear B1q induit
H=2R
Twisting of mag field lines by shear
B1q
induit
saturation
linear

12. Von Karman 1D (helicity)W
H=2R
W=0 Hz R
Vitesse azimutale
Vitesse poloïdale x y z
z (m)
mesures
LDV
(L. Marié, CEA)
x (m)
x (m)

13. « alpha » effect W=0 Hz VKG W BIz Rm Na, Cadarache Ga, Lyon saturation
H=2R
W=0 Hz R
VKG
Na, Cadarache
Ga, Lyon
saturation
quadratic
BIz
quadratic Rm

14. « alpha » effect W=0 Hz W Parker’s stretch and twist mechanism R H=2R

15. Turbulent fluctuations
histogram
time (s)
Bind,z (G)
applied B0
mean induced bz
Bz (G)

16. Turbulent fluctuations10 1 2 4
- 1
- 11/3
f (Hz) b² ~ Ω
Ω/10 br bθ bz
3 particular
regions

17. Mean induction: an iterative approach (assuming stationarity) real boundary condition
An iterative study of time independent induction effects in mhd
M. Bourgoin, P. Odier, J.-F. Pinton and Y. Ricard,
Physics of Fluids, in press (2004).

18. Iterative approach Induction in the presence of an applied field avec
+ C.L.

19. Solving for B, I, F
CL Neumann :
(CL insulating)

20. Ex.1: w-effect in VK
Potentiel électrique

21. Ex.1: w-effect in VK
linéaire
saturation

22. Ex.2: a-effect in VK R

23. Ex.2: a-effect in VK

24. Ex.2: a-effect in VK

25. Ex.3: boundary effect in VK

26. 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).

27. Turbulence : coupled LES-DNS
Include turbulence, but :
viscous dissipative scale : h = L/Re3/4
magnetic ohmic scale : hB = L/Rm3/4
PSD B u
1/L
1/hB
1/h
DNS
LES

28. Taylor-Green vortex flow
pseudo spectral code 1283
Pm = 0.001, Rm=7, Rl=100
Chollet-Lesieur cutoff
h(k,t) ≈ (a + b(k/Kc)8)sqrt(E(Kc,t)/Kc)

29. TG, local induction

30. TG, global mode
VKS exp.
TG simul
Local

31. TG, global mode
VKS exp.
TG simul
B-energy

32. In progress
VKS dynamo
Turbulence & induction
Earth dynamo