R. Oran csem.engin.umich.edu SHINE 09 May 2005 Campaign Event: Introducing Turbulence Rona Oran Igor V. Sokolov Richard Frazin Ward Manchester Tamas I

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



are needed to see this picture. Summary of Results from SHINE 2008Summary of Results from SHINE 2008

• 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.



are needed to see this picture. 2008 Results Revisited2008 Results Revisited

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.



are needed to see this picture. Introducing Alfven Waves TurbulenceIntroducing Alfven Waves Turbulence

• 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.



are needed to see this picture. MHD - Wave Turbulence ModelMHD - Wave Turbulence Model

• 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.



are needed to see this picture. Modified MHD EquationsModified MHD Equations

Background momentum equation:

Background energy equation:

Where P is the wave stress spectral density.

wave stress gradient force

Work done bywave stress

wave energydissipation



are needed to see this picture. WT Equation - Low Frequency Alfven WavesWT Equation - Low Frequency Alfven Waves

• 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



are needed to see this picture. Computational ModelComputational Model

• 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.



are needed to see this picture. Model InputsModel Inputs

• 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



are needed to see this picture. Inner Boundary ConditionsInner Boundary Conditions

• 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.



are needed to see this picture.

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



are needed to see this picture. Results - CR2029Results - CR2029



are needed to see this picture. Results - CR2029Results - CR2029



are needed to see this picture. ConclusionsConclusions

• 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 .



are needed to see this picture. Future WorkFuture Work

• 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.

Documents

R. Oran csem.engin.umich.edu SHINE 09 May 2005 Campaign Event: Introducing Turbulence Rona Oran Igor V. Sokolov Richard Frazin Ward Manchester Tamas I