magneto-hydrodynamic turbulence: from the ism to discs axel brandenburg (nordita, copenhagen)...
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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)
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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
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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.
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Brandenburg: MHD turbulence 4
Galactic discs: supernova-driven turbulence
Microgauss fields: Korpi et al (1999, ApJ)221
02 2/ uB
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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…
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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
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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)
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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
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Brandenburg: MHD turbulence 9
Peaked at resistive scale!?Peaked at resistive scale!?(nonhelical case)
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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
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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
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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?
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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
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Brandenburg: MHD turbulence 14
Bottleneck effect: Bottleneck effect: 1D vs 3D spectra1D vs 3D spectra
Why did wind tunnels not show this?
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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)
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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
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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)
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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!
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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
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Brandenburg: MHD turbulence 20
Flow outside shocks unchangedFlow outside shocks unchanged
Localized shocks: exceed color scale Outside shocks: smooth
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Brandenburg: MHD turbulence 21
Dynamos and Mach numberDynamos and Mach number
No signs of shocks in B-fieldor J-field (shown here)
advection dominates
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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
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Brandenburg: MHD turbulence 23
MRI: Local disc simulationsMRI: Local disc simulationsDynamo makes its own turbulence (no longer forced!)
Hyperviscosity 1283
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Brandenburg: MHD turbulence 24
Simulations with stratificationSimulations with stratification
cyclic B-fieldalpha-Omega dynamo?negative alpha
326431
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Brandenburg: MHD turbulence 25
High resolution direct simulationHigh resolution direct simulation
5123 resolution
singular!
2563 (direct, new) 323 (hyper, old)
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26
Disc viscosity: mostly outside discDisc viscosity: mostly outside disc
Brandenburg et al. (1996)
const turb ss cHc HczHc ss )(turb z-dependence of
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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
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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
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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
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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)
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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
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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