Models of Turbulent Angular Momentum Transport Beyond the Parameterization

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Models of Turbulent Angular Momentum Transport
Beyond the ? Parameterization
Martin Pessah Institute for Advanced Study
C.K. Chan - ITC, Harvard D. Psaltis - University.
of Arizona
Workshop on Saturation and Transport Properties
of MRI-Driven Turbulence - IAS- June 16, 2008
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107Mo
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Angular momentum transport in turbulent media
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• Issues
• Dynamics? is not constant
• Causality Information propagates across sonic
  points (Stress reacts instantly to changes in
  the flow)
• Stability criterion Standard model works always
  (Stresses only for MRI-unstable disks)
• Viscosity MRI does not behave like Newtonian
  viscosity

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large scales
small scales
MRI drives MHD turbulence at a well defined scale
which depends only on the magnetic field and the
shear
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small scales
large scales
(Talk by C.K. Chan later today)
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We can derive an equation for angular momentum
conservation
which involves 2nd order correlations
We can derive equations for 2nd order
correlations
but they involve 3rd order correlations
We can derive equations for 3nd order
correlations
Need for a CLOSURE model beyond alpha!!
(Closure models with no mean fields papers by
Kato et al 90s Ogilvie 2003)
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Kato Yoshizawa, 1995
Pressure-strain tensor, tends to isotropize the
turbulence
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Ogilvie 2003
C1, C5 energy dissip.
C2 return to isotropy in decaying turbulence
C3, C4 energy transfer
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W tensor dynamically important!
-Maxwell
Reynolds
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The parameter ? controls the ratio between
Reynolds Maxwell stresses
The model produces initial exponential growth and
leads to stresses with ratios in agreement with
the saturated regime
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The parameter ? controls the level at which the
magnetic energy saturates
A physically motivated model for angular momentum
transport Keplerian disks that incorporates the
MRI
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Pessah, Chan, Psaltis, 2006b
Simulations by Hawley et al. 1995
Pessah, Chan, Psaltis, 2006b
A model for MRI-driven angular momentum
transport in agreement with numerical simulations
Simulations by Hawley et al. 1995
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Pessah, Chan, Psaltis, 2007 Sano et al. 2004
Deeper understanding of scalings? Non-zero
Bz (few Beq) Magnetic pressure must be
important in setting H Spectral
hardening (Blaes et al. 2006)
(Talk by S. Fromang later today)
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Pessah Chan, 2008
(Various limits studied by Sano et al., Lesaffre
Balbus, Lesur Longaretti, )
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Pm1
Pm
Pm1
Pm
Lowest ratio magnetic-to-kinetic Ideal MHD
Linear MRI effective at low/high Pm as long as Re
large Need higher Re to drive MHD turbulence at
low Pm (Lesur Longaretti, 2007 Fromang et al.,
2007)
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(Goodman Xu, 1994)
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Pessah Chan, 2008
Pm1
Pm
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PRELIMINARY (with J. Goodman, in prep.)
Parasitic Instabilities seem to be weaker at high
Pm Hint for difficulties to drive MRI at low
Pm? Can the destruction of primary MRI modes by
parasitic instabilities explain (Re, Pm)
dependencies?