Turbulent dynamo and MHD turbulence: concepts and models.

A. Schekochihin

University of Oxford, UK

First course in the form of a Review during Workshop1, Wednesday 18 March 14h-15h30.

Bibliography:

LECTURE 1

General discussion of low Pm:

1. A. A. Schekochihin, A. B. Iskakov, S. C. Cowley, J. C. McWilliams, M. R. E. Proctor, and T. A. Yousef,
``Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers,''
New J. Phys. 9, 300 (2007) [e-print arXiv:0704.2002]

General discussion of large Pm and the Zeldovich argument for growth in linear fields:

2. A. A. Schekochihin and S. C. Cowley,
``Turbulence and magnetic fields in astrophysical plasmas,'' (pdf, 1.6 Mb --- version with better figures)
in: Magnetohydrodynamics: Historical Evolution and Trends, S. Molokov, R. Moreau, and H. K. Moffatt, Eds.
(Berlin: Springer, 2007), 85 [e-print astro-ph/0507686]

LECTURE 2

Spectra:

3. A. A. Schekochihin, S. A. Boldyrev, and R. M. Kulsrud,
``Spectra and growth rates of fluctuating magnetic fields in the kinematic dynamo theory with large magnetic Prandtl numbers,''
Astrophys. J. 567, 828 (2002) [e-print astro-ph/0103333]

General formalism for correlation-time expansion:

4. A. A. Schekochihin and R. M. Kulsrud,
``Finite-correlation-time effects in the kinematic dynamo problem,''
Phys. Plasmas 8, 4937 (2001) [e-print astro-ph/0002175]

Distribution of FTLEs for the Kazantsev flow ("metric approach"):

5. S. A. Boldyrev and A. A. Schekochihin,
``Geometric properties of passive random advection,''
Phys. Rev. E 62, 545 (2000) [e-print chao-dyn/9907034]

LECTURE 3

Curvature, etc:

6. A. Schekochihin, S. Cowley, J. Maron, and L. Malyshkin,
``Structure of small-scale magnetic fields in the kinematic dynamo theory,''

Finite-system effects for the dynamo:

7. A. A. Schekochihin, S. C. Cowley, J. L. Maron, and J. C. McWilliams,
``Self-similar turbulent dynamo,''

Finite-system effects for the scalar ("strange mode"):

8. A. A. Schekochihin, P. H. Haynes, and S. C. Cowley,
``Diffusion of passive scalar in a finite-scale random flow,''

LECTURE 4

Nonlinear models:

9. A. A. Schekochihin, S. C. Cowley, G. W. Hammett, J. L. Maron, and J. C. McWilliams,
``A model of nonlinear evolution and saturation of the turbulent MHD dynamo,''

10. A. A. Schekochihin, S. C. Cowley, S. F. Taylor, G. W. Hammett, J. L. Maron, and J. C. McWilliams,
``Saturated state of the nonlinear small-scale dynamo,''

A compendium of numerical results:

11. A. A. Schekochihin, S. C. Cowley, S. F. Taylor, J. L. Maron, and J. C. McWilliams,
``Simulations of the small-scale turbulent dynamo,''

Shear dynamo:

12. T. A. Yousef, T. Heinemann, F. Rincon, A. A. Schekochihin, N. Kleeorin, I. Rogachevskii, S. C. Cowley, and J. C. McWilliams,
``Numerical experiments on dynamo action in sheared and rotating turbulence,''

13. A. A. Schekochihin, T. Heinemann, N. Kleeorin, G. Lesur, A. Mallet, J. C. McWilliams, I. Rogachevskii, and T. A. Yousef,
``Magnetic-field generation by randomly forced shearing waves,''
Phys. Rev. Lett., submitted (2008) [e-print arXiv:0810.2225]


Wednesday 25 March, from 16h to 18h
Friday 27 March, from 10h to noon
Wednesday 1 April, from 16h to 18h
IHP, Room 314
11, rue Pierre et Marie Curie
75005 Paris