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Magnetohydrodynamic turbulence


Maron, Jason L. (2001) Magnetohydrodynamic turbulence. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/x455-kq95.


We simulate incompressible, MHD turbulence using a pseudo-spectral code. Our major conclusions are as follows.

1) MHD turbulence is most conveniently described in terms of counter propagating shear Alfvén and slow waves. Shear Alfvén waves control the cascade dynamics. Slow waves play a passive role and adopt the spectrum set by the shear Alfvén waves. Cascades composed entirely of shear Alfvén waves do not generate a significant measure of slow waves.

2) MHD turbulence is anisotropic with energy cascading more rapidly along k than along k, where k and k refer to wavevector components perpendicular and parallel to the local magnetic field. Anisotropy increases with increasing k such that excited modes are confined inside a cone bounded by k ∝ kγ where γ less than 1. The opening angle of the cone, θ(k) ∝ k-(1-γ), defines the scale dependent anisotropy.

3) MHD turbulence is generically strong in the sense that the waves which comprise it suffer order unity distortions on timescales comparable to their periods. Nevertheless, turbulent fluctuations are small deep inside the inertial range. Their energy density is less than that of the background field by a factor θ2 (k)≪1.

4) MHD cascades are best understood geometrically. Wave packets suffer distortions as they move along magnetic field lines perturbed by counter propagating waves. Field lines perturbed by unidirectional waves map planes perpendicular to the local field into each other. Shear Alfvén waves are responsible for the mapping's shear and slow waves for its dilatation. The amplitude of the former exceeds that of the latter by 1/θ(k) which accounts for dominance of the shear Alfvén waves in controlling the cascade dynamics.

5) Passive scalars mixed by MHD turbulence adopt the same power spectrum as the velocity and magnetic field perturbations.

6) Decaying MHD turbulence is unstable to an increase of the imbalance between the flux of waves propagating in opposite directions along the magnetic field. Forced MHD turbulence displays order unity fluctuations with respect to the balanced state if excited at low k by δ(t) correlated forcing. It appears to be statistically stable to the unlimited growth of imbalance.

7) Gradients of the dynamic variables are focused into sheets aligned with the magnetic field whose thickness is comparable to the dissipation scale. Sheets formed by oppositely directed waves are uncorrelated. We suspect that these are vortex sheets which the mean magnetic field prevents from rolling up.

8) Items (1)-(5) lend support to the model of strong MHD turbulence put forth by Goldreich and Sridhar (1995, 1997). Results from our simulations are also consistent with the GS prediction γ = 2/3. The sole not able discrepancy is that the 1D power law spectra, E(k) ∝ k-∝, determined from our simulations exhibit ∝ ≈ 3/2, whereas the GS model predicts ∝ = 5/3.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Physics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Goldreich, Peter Martin
Group:Astronomy Department
Thesis Committee:
  • Unknown, Unknown
Defense Date:19 September 2000
Record Number:CaltechTHESIS:05052014-152343905
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8219
Deposited By: Benjamin Perez
Deposited On:06 May 2014 14:42
Last Modified:19 Apr 2021 22:33

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