r. oran csem.engin.umich.edu shine 09 may 2005 campaign event: introducing turbulence rona oran igor...
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R. Oran csem.engin.umich.edu SHINE 09
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May 2005 Campaign Event: Introducing May 2005 Campaign Event: Introducing TurbulenceTurbulence
Rona OranIgor V. SokolovRichard Frazin
Ward ManchesterTamas I. Gombosi
CSEM, University of Michigan
Ofer CohenHSCA
R. Oran csem.engin.umich.edu SHINE 09
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• Out of equilibrium flux rope model superposed on a steady state MHD corona.• The dynamical solution presented had good agreement with the shock arrival time to earth.
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However…• Steady state solution highly criticized for use of variable polytropic index.
• The polytropic model, although it achieved good agreement with ambient solar wind observed at 1AU, is not self - consistent and distort the physics, especially at shocks.
• Work done on thermodynamic MHD models, most prominently by the SAIC group (see Lionello, Linker and Mikic, 2009) inspire further attempts at a self - consistent model which will improve the physical basis for our solution.
R. Oran csem.engin.umich.edu SHINE 09
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• Turbulent MHD waves have been suggested in the past as a possible mechanism both to heat the corona and to accelerate the solar wind.
• Hinode observations suggest energy input is sufficient to drive the solar wind acceleration and heating (e.g. Pontiue et. al. 2007) .
• Heating : Alfven wave dissipation at cyclotron frequency( likely intensified by the energy cascade process).
• Wind acceleration : work done by wave pressure gradient force.
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• We employ a wave kinetic approach for describing the transport of MHD waves in a background MHD plasma.
• The wave transport equation for narrow band wave trains is given by:
• here I is the wave energy spatial and spectral density and is a specific wave mode.
• Advantage: describes the spectral evolution.
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Background momentum equation:
Background energy equation:
Where P is the wave stress spectral density.
wave stress gradient force
Work done bywave stress
wave energydissipation
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• In this limit the wave stress spectral density becomes:
• Thus the pressure is scalar and the total wave pressure is:
• The WT equation takes the form:
• 2-way coupling of the WT equation to the MHD equations : Wave pressure acts on the background flow, while background solution determines wave propagation and spectral evolution.
Advection inspace
Advection infrequency
Dissipation
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• The WT equation is fully coupled to the BATSRUS code in the SWMF.
• The spatial grid is a 3D block adaptive Cartesian grid.
• In each spatial cell we construct a uniform frequency grid whose range / resolution is defined by the user.
• Both parallel and anti-parallel propagating waves are considered (currently share the same grid).
• Solution of WT equation is performed by Strang splitting of the spatial and frequency operators.
• The solution in 2nd order accurate in space, time and frequency.
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• Magnetogram driven potential field extrapolation.
• Spectrum: Can be defined by the user. This allows the testing of various theories by comparing results to observations. • In the current work, we assume a Kolmogorov spectrum as the initial condition, i.e.
I k-5/3
(in accordance with observations of mean-free-path of protons in the heliosphere). The initial distribution in space can be rather arbitrary, since it quickly advects according to the MHD state.• Level of imbalance:
Itot = I+ + I-
I+ = Itot I-= (1 - )Itot 0< <1
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• Radial magnetic field - high resolution MDI magnetogram data provided by Y. Liu, Stanford.
• Specify Alfven waves Poynting vector at 1Rs:
• Solar wind expansion factors
• WSA model terminal velocity at 1AU
• Impose conservation of energy along flux tubes (Suzuki, 2006)
• In-going waves which reach the inner boundary are absorbed.
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Magnetogram - driven steady-state solution of the solar corona (up to 24 Rs). Free parameters of the model and the uncertainties are:• Mass density at solar surface.• Magnetogram scaling factor.Spectrum:• fmin= 1x10-4Hz• fmax = 100 Hz(in accordance with Pontieu et. al. 2007)
Roe solver scheme, adaptive mesh refinement.
Initial grid resolution: 0.001 Rs near the Sun
Currently the advection in frequency space is not presented.
Simulation OutlineSimulation Outline
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• First calculations in the SWMF of a steady state solar corona/
solar wind which is entirely driven by Alfven wave pressure and
the boundary conditions fully driven by the WSA model.
• Fast solar wind speeds are too high - conversion rate of wave
energy into heating is too low. This might be solved when we
take the wave dissipation into account.
• Compared to the previous polytropic model, we can now describe
the corona self - consistently without distorting the physics,
especially shock wave compression ratio which depend on .
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• Repeat our dynamical simulation of the CME with the emphasis
on more realistic shock wave:
• Full implementation of spectral evolution
• Extend the model to the Inner Heliosphere (IH) model to
enable comparison of results to observations at 1AU.