MHD induction & dynamo

1. ENS LYON MHDinduction & dynamo Laboratoire de Physique Ecole Normale supérieure Lyon (France) Jean-François Pinton pinton@ens-lyon.fr http://perso.ens-lyon.fr/jean-francois.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 flowsGallium 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).

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

9. VKS1 experimentat CEA-Cadarache

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

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

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

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

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

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

16. Turbulent fluctuations br 0 - 1 bθ 4 10 bz - 11/3 2 10 ~ b² 0 10 Ω Ω/10 0 1 2 10 10 10 f (Hz) 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 saturation linéaire

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 schemeperiodic 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 u B 1/h 1/L 1/hB LES DNS

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