ENS MHD induction & dynamo LYON Laboratoire de Physique

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ENS MHD induction & dynamo LYON Laboratoire de Physique Ecole Normale supérieure Lyon (France) Jean-François Pinton pinton@ens-lyon.fr http://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 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 !

Question addressed : B-measurement In situ 3D flow Liquid metal : Ga, Na 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-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), 174501, (2003). M. Bourgoin et al., Magnetohydrodynamics, in press, (2004).

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

VKS1 experiment at CEA-Cadarache

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

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

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)

« 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

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

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

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

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).

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

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

Ex.1: w-effect in VK Potentiel électrique

Ex.1: w-effect in VK linéaire saturation

Ex.2: a-effect in VK R

Ex.2: a-effect in VK

Ex.2: a-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 : h = L/Re3/4 magnetic ohmic scale : hB = L/Rm3/4 PSD B u 1/L 1/hB 1/h DNS LES

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)

TG, local induction

TG, global mode VKS exp. TG simul Local

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

In progress VKS dynamo Turbulence & induction Earth dynamo