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Magneto-hydrodynamic Magneto-hydrodynamic turbulence: from the ISM to discsturbulence: from the ISM to discs
Axel BrandenburgAxel Brandenburg (Nordita, Copenhagen) (Nordita, Copenhagen)Collaborators:Collaborators:
Nils Erland HaugenNils Erland Haugen (Univ. Trondheim) (Univ. Trondheim)
Wolfgang DoblerWolfgang Dobler (Freiburg (Freiburg Calgary) Calgary)
Tarek YousefTarek Yousef (Univ. Trondheim) (Univ. Trondheim)
Antony MeeAntony Mee (Univ. Newcastle) (Univ. Newcastle)
Brandenburg: MHD turbulence 2
Sources of turbulenceSources of turbulence
• Gravitational and thermal energy– Turbulence mediated by instabilities
• convection
• MRI (magneto-rotational, Balbus-Hawley)
• Explicit driving by SN explosions– localized thermal (perhaps kinetic) sources
Brandenburg: MHD turbulence 3
Conversion between different energy formsConversion between different energy forms
Thermal energy
Magnetic energy
Kinetic energy
Potential energy
u
BJu
/2J
22 S
pu
Examples:thermal convectionmagnetic buoyancymagnetorotational inst.
Brandenburg: MHD turbulence 4
Galactic discs: supernova-driven turbulence
Microgauss fields: Korpi et al (1999, ApJ)221
02 2/ uB
Brandenburg: MHD turbulence 5
Huge range of length scalesHuge range of length scales
• Driving mechanism:– SN explosions– parsec scale
• Dissipation scale– 108 cm (interstellar scintillation)
• What is the scale of B-field
• Linear theory: smallest scale!Korpi et al. (1999), Sarson et al. (2003)Korpi et al. (1999), Sarson et al. (2003)
no dynamo here…
Brandenburg: MHD turbulence 6
Important questionsImportant questions• Is there a dynamo? (Or is resolution too poor?)• Is the turbulent B-field a small scale feature?• How important is compressibility?
– Does the turbulence become “acoustic” (ie potential)?
• PPM, hyperviscosity, shock viscosity, etc– Can they screw things up?
• Bottleneck effect (real or artifact?)
• Does the actual Prandtl number matter?– We are never able to do the real thing
Fundamental questions more idealized simulations
Brandenburg: MHD turbulence 7
11stst problem: small scale dynamo problem: small scale dynamo• According to linear theory, field would be
regenerated at the resistive scale
Schekochihin et al (2003)Schekochihin et al (2003)
(Kazantsev 1968)
Brandenburg: MHD turbulence 8
Forced turbulence: B-field Forced turbulence: B-field dynamo-generateddynamo-generated
magnetic peak: resistive scale?magnetic peak: resistive scale?
Maron & Cowley (2001)Maron & Cowley (2001)
Kin. spectrum
Magn.spectrum
Brandenburg: MHD turbulence 9
Peaked at resistive scale!?Peaked at resistive scale!?(nonhelical case)
Brandenburg: MHD turbulence 10
Pencil CodePencil Code
• Started in Sept. 2001 with Wolfgang Dobler
• High order (6th order in space, 3rd order in time)
• Cache & memory efficient
• MPI, can run PacxMPI (across countries!)
• Maintained/developed by many people (CVS!)
• Automatic validation (over night or any time)
• Max resolution currently 10243
Brandenburg: MHD turbulence 11
Kazantsev spectrum (kinematic)Kazantsev spectrum (kinematic)
Kazantsev spectrum Kazantsev spectrum confirmed (even for confirmed (even for =1) =1)
Spectrum remains highly Spectrum remains highly time-dependenttime-dependent
Opposite limit, no scale separation, forcing at kf=1-2
Brandenburg: MHD turbulence 12
256 processor run at 1024256 processor run at 102433
1st Result: not peaked at resistive scale -- Kolmogov scaling!
Haugen et al. (2003, A
pJ 597, L141)
-3/2slope?
Brandenburg: MHD turbulence 13
22ndnd problem: deviations from Kolmogorov? problem: deviations from Kolmogorov?
Porter, Pouquet, & Woodward (1998) using PPM, 10243 meshpoints
Kaneda et al. (2003) on the Earth simulator, 40963 meshpoints
(dashed: Pencil-Code with 10243 )
compensated spectrum
Brandenburg: MHD turbulence 14
Bottleneck effect: Bottleneck effect: 1D vs 3D spectra1D vs 3D spectra
Why did wind tunnels not show this?
Brandenburg: MHD turbulence 15
Relation to ‘laboratory’ 1D spectraRelation to ‘laboratory’ 1D spectra2222
3 )(4)( kuku kdkE kD yxkyxkE zzD d d ),,(2)(
2
1 u
kkkkkkkzk
z d )(4d ),(42
0
2
uu
kk
E
zk
D d 3
0zk
222zkkk
Dobler et al. (2003, P
RE
026304)
Brandenburg: MHD turbulence 16
Third-order hyperviscosityThird-order hyperviscosity
Different resolution: bottleneck & inertial range
SS12)(
nn
Traceless rate of strain tensor
uuF 431631
visc 1n
3rd order dynamical hyperviscosity 3 22
32 S
Hyperviscous heat
Brandenburg: MHD turbulence 17
Comparison: hyper vs normalComparison: hyper vs normal
onset of bottleneck at same position
height of bottleneck increased
2nd Result: inertial range unaffected by artificial diffusion
Hau
gen
& B
rand
enbu
rg (
PR
E, a
stro
-ph/
0402
301)
Brandenburg: MHD turbulence 18
33rdrd Problem: compressibility? Problem: compressibility?
Direct simulation, =5 Direct and shock-capturing simulations, =1
Shocks sweep up all the field: dynamo harder?
-- or artifact of shock diffusion?
Bimodal behavior!
Brandenburg: MHD turbulence 19
Potential flow subdominantPotential flow subdominant
Potential component more important,but remains subdominant
Shock-capturing viscosity:affects only small scales
ψ u
Brandenburg: MHD turbulence 20
Flow outside shocks unchangedFlow outside shocks unchanged
Localized shocks: exceed color scale Outside shocks: smooth
Brandenburg: MHD turbulence 21
Dynamos and Mach numberDynamos and Mach number
No signs of shocks in B-fieldor J-field (shown here)
advection dominates
Brandenburg: MHD turbulence 22
33rdrd Result: dynamo unaffected Result: dynamo unaffectedby compressibility and shocksby compressibility and shocks
• Depends on Rm of vortical flow component
• Bimodal: Rm=35 (w/o shocks), 70 (w/ shocks)
Important overall conclusion:simulations hardly in asymptotic regime
• a need to reconsider earlier lo-res simulations: here discs
Brandenburg: MHD turbulence 23
MRI: Local disc simulationsMRI: Local disc simulationsDynamo makes its own turbulence (no longer forced!)
Hyperviscosity 1283
Brandenburg: MHD turbulence 24
Simulations with stratificationSimulations with stratification
cyclic B-fieldalpha-Omega dynamo?negative alpha
326431
Brandenburg: MHD turbulence 25
High resolution direct simulationHigh resolution direct simulation
5123 resolution
singular!
2563 (direct, new) 323 (hyper, old)
26
Disc viscosity: mostly outside discDisc viscosity: mostly outside disc
Brandenburg et al. (1996)
const turb ss cHc HczHc ss )(turb z-dependence of
27
Heating near disc boundaryHeating near disc boundary
Turner (2004)
radp
radp
gasp
2
2...J
u
t
Tcv
022 / Bu
weak z-dependence of energy density
0/ BJ where
Brandenburg: MHD turbulence 28
Magnetic “contamination” on larger scalesMagnetic “contamination” on larger scales
• Outflow with dynamo field (not imposed)
• Disc wind: Poynting flux
10,000 galaxies for 1 Gyr, 1044 erg/s each
G182
tV
cMN
F
FB sw
kin
poyntrms
Similar figure also for outflows from protostellar disc
Brandenburg: MHD turbulence 29
Unsteady outflowUnsteady outflow
transport from disc into the wind
BN/KL region in Orion:Greenhill et al (1998)vo
n R
ekow
ski e
t al.
(200
3, A
&A
398
, 825
)
Disc: mean field model
Further experiments: interaction with magnetosphereFurther experiments: interaction with magnetosphereAlternating fieldline uploading and downloadingAlternating fieldline uploading and downloading
Star connected with the disc Star disconnected from disc
Simil ar beh avior fo und b y G
oo dso n & W
ingl ee (19 99)vo
n R
ekow
skii
& B
rand
enbu
rg 2
004
(A&
A)
Brandenburg: MHD turbulence 31
Surprises from current researchSurprises from current research• B-field follows Kolmogorov scaling• Takes lots of resolution: bottleneck, diff-range• Dynamo basically ignores shocks
• Cosmic ray and thermal diffusion along B-lines• Self-consistent disc winds (proper radiation)• Partially ionized YSO discs• Dynamos at low : do they still work??
Future directionsFuture directions
Brandenburg: MHD turbulence 32
Examples of such surprises: Examples of such surprises: small magnetic Prandtl numberssmall magnetic Prandtl numbers
definitiondefinitionRRmm==uurmsrms/(/(kkff))
Is there SS dynamo actionIs there SS dynamo actionbelow below PPmm=0.125?=0.125?
Haugen, Brandenburg, Dobler PRE (in press)
Comparion w/ hyper