Test-field method: selected and related references

Notes summarizing some essential results (with references)

Early and original papers by Schrinner et al.

Schrinner, M., Rädler, K.-H., Schmitt, D., Rheinhardt, M., & Christensen, U.: 2005, ``Mean-field view on rotating magnetoconvection and a geodynamo model,'' Astron. Nachr.326, 245-249 (ADS)

Schrinner, M., Rädler, K.-H., Schmitt, D., Rheinhardt, M., & Christensen, U.: 2007, ``Mean-field concept and direct numerical simulations of rotating magnetoconvection and the geodynamo,'' Geophys. Astrophys. Fluid Dynamics101, 81-116 (ADS)

Brandenburg, A.: 2005, ``Turbulence and its parametrization in accretion discs,'' Astron. Nachr. 326, 787-797 (astro-ph/0510015, ADS, PDF)

Nonlinear and quasi-kinematic test-field method

Brandenburg, A., Rädler, K.-H., Rheinhardt, M., & Subramanian, K.: 2008, ``Magnetic quenching of alpha and diffusivity tensors in helical turbulence,'' Astrophys. J. Lett. 687, L49-L52 (arXiv:0805.1287, ADS, PDF)

Tilgner, A., & Brandenburg, A.: 2008, ``A growing dynamo from a saturated Roberts flow dynamo,'' Monthly Notices Roy. Astron. Soc. 391, 1477-1481 (arXiv:0808.2141, ADS, PDF)

Hubbard, A., Del Sordo, F., Käpylä, P. J., & Brandenburg, A.: 2009, ``The $\alpha$ effect with imposed and dynamo-generated magnetic fields,'' Monthly Notices Roy. Astron. Soc. 398, 1891-1899 (arXiv:0904.2773, ADS, PDF)

Rheinhardt, M., & Brandenburg, A.: 2010, ``Test-field method for mean-field coefficients with MHD background,'' Astron. Astrophys. 520, A28 (arXiv:1004.0689, ADS, DOI, PDF); see also note on α-quenching ∝1/B4.

Chatterjee, P., Mitra, D., Rheinhardt, M., & Brandenburg, A.: 2011, ``Alpha effect due to buoyancy instability of a magnetic layer,'' Astron. Astrophys. 534, A46 (arXiv:1011.1218, ADS, DOI, PDF)

Brandenburg, A., Chatterjee, P., Del Sordo, F., Hubbard, A., Käpylä, P. J., & Rheinhardt, M.: 2010, ``Turbulent transport in hydromagnetic flows,'' Phys. Scr. T142, 014028 (arXiv:1004.5380, ADS, DOI, PDF)

Rogachevskii, I., Kleeorin, N., Brandenburg, A., & Eichler, D.: 2012, ``Cosmic ray current-driven turbulence and mean-field dynamo effect,'' Astrophys. J. 753, 6 (arXiv:1204.4246, ADS, DOI, PDF)

Memory effects in space and time

Brandenburg, A., Rädler, K.-H., & Schrinner, M.: 2008, ``Scale dependence of alpha effect and turbulent diffusivity,'' Astron. Astrophys. 482, 739-746 (arXiv:0801.1320, ADS, PDF)

Hubbard, A., & Brandenburg, A.: 2009, ``Memory effects in turbulent transport,'' Astrophys. J. 706, 712-726 (arXiv:0811.2561, ADS, PDF)

Rheinhardt, M., & Brandenburg, A.: 2012, ``Modeling spatio-temporal nonlocality in mean-field dynamos,'' Astron. Nachr. 333, 71-77 (arXiv:1110.2891, ADS, DOI, HTML, PDF)

Rheinhardt, M., Devlen, E., Rädler, K.-H., & Brandenburg, A.: 2014, ``Mean-field dynamo action from delayed transport,'' Mon. Not. Roy. Astron. Soc. 441, 116-126 (arXiv:1401.5026, DOI, PDF)

For non-locality in time (i.e. memory effects), but without test fields, see also:

Brandenburg, A., Käpylä, P., & Mohammed, A.: 2004, ``Non-Fickian diffusion and tau-approximation from numerical turbulence,'' Phys. Fluids 16, 1020-1027 (astro-ph/0306521, ADS, PDF)

Helical and nonhelical turbulence, with and without shear

Brandenburg, A., Rädler, K.-H., Rheinhardt, M., & Käpylä, P. J.: 2008, ``Magnetic diffusivity tensor and dynamo effects in rotating and shearing turbulence,'' Astrophys. J. 676, 740-751 (arXiv:0710.4059, ADS, PDF)

Mitra, D., Käpylä, P. J., Tavakol, R., & Brandenburg, A.: 2009, ``Alpha effect and diffusivity in helical turbulence with shear,'' Astron. Astrophys. 495, 1-8 (arXiv:0806.1608, ADS, PDF)

Sur, S., Brandenburg, A., & Subramanian, K.: 2008, ``Kinematic alpha effect in isotropic turbulence simulations,'' Monthly Notices Roy. Astron. Soc. 385, L15-L19 (arXiv:0711.3789, ADS, PDF)

Stratified turbulence

Käpylä, P. J., Korpi, M. J., & Brandenburg, A.: 2009, ``Alpha effect and turbulent diffusion from convection,'' Astron. Astrophys. 500, 633-646 (arXiv:0812.1792, ADS, PDF)

Brandenburg, A., Rädler, K.-H., & Kemel, K.: 2012, ``Mean-field transport in stratified and/or rotating turbulence,'' Astron. Astrophys. 539, A35 (arXiv:1108.2264, ADS, ADS, DOI, PDF)

Brandenburg, A., Gressel, O., Käpylä, P. J., Kleeorin, N., Mantere, M. J., Rogachevskii, I.: 212, ``New scaling for the alpha effect in slowly rotating turbulence,'' Astrophys. J., in press (arXiv:1208.5004, HTML, PDF)

Galloway-Proctor, Taylor-Green, as well as Roberts-II, III, and IV flows

Rädler, K.-H., & Brandenburg, A.: 2009, ``Mean-field effects in the Galloway-Proctor flow,'' Monthly Notices Roy. Astron. Soc. 393, 113-125 (arXiv:0809.0851, ADS, PDF)

Devlen, E., Brandenburg, A., & Mitra, D.: 2012, ``A mean field dynamo from negative eddy diffusivity,'' Mon. Not. Roy. Astron. Soc., submitted (arXiv:1212.2626, PDF)

Rheinhardt, M., Devlen, E., Rädler, K.-H., & Brandenburg, A.: 2014, ``Mean-field dynamo action from delayed transport,'' Mon. Not. Roy. Astron. Soc. 441, 116-126 (arXiv:1401.5026, DOI, PDF)

Potential flows

Rädler, K.-H., Brandenburg, A., Del Sordo, F., & Rheinhardt, M.: 2011, ``Mean-field diffusivities in passive scalar and magnetic transport in irrotational flows,'' Phys. Rev. E 84, 4 (arXiv:1104.1613, ADS, DOI, PDF)

Passive scalar advection

Brandenburg, A., Svedin, A., & Vasil, G. M.: 2009, ``Turbulent diffusion with rotation or magnetic fields,'' Monthly Notices Roy. Astron. Soc. 395, 1599-1606 (arXiv:0901.2112, ADS, PDF)

Madarassy, E. J. M., & Brandenburg, A.: 2010, ``Calibrating passive scalar transport in shear-flow turbulence,'' Phys. Rev. E 82, 016304 (arXiv:0906.3314, ADS, PDF)

Kitchatinov, L. L., & Brandenburg, A.: 2012, ``Transport of angular momentum and chemical species by anisotropic mixing in stellar radiative interiors,'' Astron. Nachr. 333, 230-236 (arXiv:1201.2484, ADS, DOI, PDF)

Related review material:

Brandenburg, A., & Subramanian, K.: 2005, ``Astrophysical magnetic fields and nonlinear dynamo theory,'' Phys. Rep. 417, 1-209 (astro-ph/0405052, ADS, PDF)

Brandenburg, A.: 2005, ``The case for a distributed solar dynamo shaped by near-surface shear,'' Astrophys. J. 625, 539-547 (astro-ph/0502275, ADS, PDF)


References and links:

Sur, S., Brandenburg, A., & Subramanian, K.: 2008, ``Kinematic alpha effect in isotropic turbulence simulations,'' Monthly Notices Roy. Astron. Soc. 385, L15-L19 (arXiv:0711.3789, ADS, PDF)

Brandenburg, A.: 2005, ``The case for a distributed solar dynamo shaped by near-surface shear,'' Astrophys. J. 625, 539-547 (astro-ph/0502275, ADS, PDF)

Vishniac, E. T., & Brandenburg, A.: 1997, ``An incoherent alpha-Omega dynamo in accretion disks,'' Astrophys. J. 475, 263-274 (astro-ph/9510038, ADS, PDF)

See also:

Mean-field dynamo in a homogeneous turbulence with shear and kinetic helicity fluctuations by N. Kleeorin, I. Rogachevskii, http://arxiv.org/abs/0711.4726

Generation of magnetic field by combined action of turbulence and shear, by T. A. Yousef, T. Heinemann, A. A. Schekochihin, N. Kleeorin, I. Rogachevskii, A. B. Iskakov, S. C. Cowley, J. C. McWilliams, http://arxiv.org/abs/0710.3359

On the effects of turbulence on a screw dynamo, by K.-H. Rädler and R. Stepanov, http://adsabs.harvard.edu/abs/2006GApFD.100..379R

Do mean-field dynamos in nonrotating turbulent shear-flows exist? by G. Rüdiger and L.L. Kitchatinov, http://adsabs.harvard.edu/abs/2006AN....327..298R

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$Date: 2017/09/04 21:40:40 $, $Author: brandenb $, $Revision: 1.12 $