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