Hostname: page-component-76fb5796d-22dnz Total loading time: 0 Render date: 2024-04-26T18:51:28.725Z Has data issue: false hasContentIssue false
  • English
  • Français

Mean-field theory of differential rotation in density stratified turbulent convection

Part of: 50 years of Mean Field Electrodynamics

Published online by Cambridge University Press:  23 April 2018

I. Rogachevskii  and
N. Kleeorin
I. Rogachevskii*
Affiliation:
Department of Mechanical Engineering, Ben-Gurion University of the Negev, P. O. Box 653, 84105 Beer-Sheva, Israel Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
N. Kleeorin
Affiliation:
Department of Mechanical Engineering, Ben-Gurion University of the Negev, P. O. Box 653, 84105 Beer-Sheva, Israel Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
*
†Email address for correspondence: gary@bgu.ac.il
Get access Rights & Permissions [Opens in a new window]

Abstract

A mean-field theory of differential rotation in a density stratified turbulent convection has been developed. This theory is based on the combined effects of the turbulent heat flux and anisotropy of turbulent convection on the Reynolds stress. A coupled system of dynamical budget equations consisting in the equations for the Reynolds stress, the entropy fluctuations and the turbulent heat flux has been solved. To close the system of these equations, the spectral $\unicode[STIX]{x1D70F}$ approach, which is valid for large Reynolds and Péclet numbers, has been applied. The adopted model of the background turbulent convection takes into account an increase of the turbulence anisotropy and a decrease of the turbulent correlation time with the rotation rate. This theory yields the radial profile of the differential rotation which is in agreement with that for the solar differential rotation.

Keywords

astrophysical plasmasplasma nonlinear phenomena
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 2 , April 2018 , 735840201
Copyright
© Cambridge University Press 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Brandenburg, A., Gressel, O., Käpylä, P. J., Kleeorin, N., Mantere, M. J. & Rogachevskii, I. 2012 New scaling for the alpha effect in slowly rotating turbulence. Astrophys. J. 762 (2), 127.Google Scholar
Brandenburg, A., Käpylä, P. J. & Mohammed, A. 2004 Non-fickian diffusion and tau approximation from numerical turbulence. Phys. Fluids 16 (4), 1020–1027.Google Scholar
Brandenburg, A. & Subramanian, K. 2005 Astrophysical magnetic fields and nonlinear dynamo theory. Phys. Rep. 417 (1), 1–209.Google Scholar
Bukai, M., Eidelman, A., Elperin, T., Kleeorin, N., Rogachevskii, I. & Sapir-Katiraie, I. 2009 Effect of large-scale coherent structures on turbulent convection. Phys. Rev. E 79 (6), 066302.Google Scholar
Durney, B. R. 1985 On theories of rotating convection zones. Astrophys. J. 297, 787–798.Google Scholar
Durney, B. R. 1993 On the solar differential rotation-meridional motions associated with a slowly varying angular velocity. Astrophys. J. 407, 367–379.Google Scholar
Duvall, T. L., Harvey, J. W. & Pomerantz, M. A. 1986 Latitude and depth variation of solar rotation. Nature 321 (6069), 500–501.Google Scholar
Dziembowski, W. A., Goode, P. R. & Libbrecht, K. G. 1989 The radial gradient in the sun’s rotation. Astrophys. J. 337, L53–L57.Google Scholar
Elperin, T., Golubev, I., Kleeorin, N. & Rogachevskii, I. 2005 Excitation of large-scale inertial waves in a rotating inhomogeneous turbulence. Phys. Rev. E 71 (3), 036302.Google Scholar
Elperin, T., Kleeorin, N., Rogachevskii, I. & Zilitinkevich, S. 2002 Formation of large-scale semiorganized structures in turbulent convection. Phys. Rev. E 66 (6), 066305.Google Scholar
Elperin, T., Kleeorin, N., Rogachevskii, I. & Zilitinkevich, S. S. 2006 Tangling turbulence and semi-organized structures in convective boundary layers. Boundary-Layer Meteorol. 119 (3), 449–472.Google Scholar
Howard, R. & Harvey, J. 1970 Spectroscopic determinations of solar rotation. Solar Phys. 12 (1), 23–51.Google Scholar
Käpylä, P. J., Brandenburg, A., Kleeorin, N., Mantere, M. J. & Rogachevskii, I. 2012 Negative effective magnetic pressure in turbulent convection. Mon. Not. R. Astron. Soc. 422 (3), 2465–2473.Google Scholar
Kichatinov, L. L. & Rüdiger, G. 1993 Lambda-effect and differential rotation in stellar convection zones. Astron. Astrophys. 276, 96.Google Scholar
Kippenhahn, R. 1963 Differential rotation in stars with convective envelopes. Astrophys. J. 137, 664.Google Scholar
Kitchatinov, L. L. & Rüdiger, G. 2005 Differential rotation and meridional flow in the solar convection zone and beneath. Astron. Nachr. 326 (6), 379–385.Google Scholar
Kleeorin, N. & Rogachevskii, I. 2003 Effect of rotation on a developed turbulent stratified convection: the hydrodynamic helicity, the $\unicode[STIX]{x1D6FC}$ effect, and the effective drift velocity. Phys. Rev. E 67 (2), 026321.Google Scholar
Kleeorin, N. & Rogachevskii, I. 2006 Effect of heat flux on differential rotation in turbulent convection. Phys. Rev. E 73 (4), 046303.Google Scholar
Kleeorin, N., Rogachevskii, I. & Ruzmaikin, A. 1990 Magnetic force reversal and instability in a plasma with advanced magnetohydrodynamic turbulence. Sov. Phys. JETP 70, 878–883.Google Scholar
Kosovichev, A., Schou, J., Scherrer, P. H., Bogart, R. S., Bush, R. I., Hoeksema, J. T., Aloise, J., Bacon, L., Burnette, A., De Forest, C. et al. 1997 Structure and rotation of the solar interior: initial results from the mdi medium-l program. Solar Phys. 170, 43–61.Google Scholar
Krause, F. & Rädler, K.-H. 1980 Mean-Field Magnetohydrodynamics and Dynamo Theory. Pergamon.Google Scholar
McComb, W. D. 1990 The Physics of Fluid Turbulence. Clarendon.Google Scholar
Moffatt, H. K. 1978 Field Generation in Electrically Conducting Fluids. Cambridge University Press.Google Scholar
Monin, A. S. & Yaglom, A. M. 2013 Statistical Fluid Mechanics. Courier Corporation.Google Scholar
Orszag, S. A. 1970 Analytical theories of turbulence. J. Fluid Mech. 41 (2), 363–386.Google Scholar
Parker, E. N. 1979 Cosmical Magnetic Fields: their Origin and their Activity. Oxford University Press.Google Scholar
Pouquet, A., Frisch, U. & Léorat, J. 1976 Strong MHD helical turbulence and the nonlinear dynamo effect. J. Fluid Mech. 77 (2), 321–354.Google Scholar
Roberts, P. H. & Soward, A. M. 1975 A unified approach to mean field electrodynamics. Astron. Nachr. 296 (2), 49–64.Google Scholar
Rogachevskii, I. & Kleeorin, N. 2004 Nonlinear theory of a ‘shear–current’ effect and mean-field magnetic dynamos. Phys. Rev. E 70 (4), 046310.Google Scholar
Rogachevskii, I. & Kleeorin, N. 2007 Magnetic fluctuations and formation of large-scale inhomogeneous magnetic structures in a turbulent convection. Phys. Rev. E 76 (5), 056307.Google Scholar
Rogachevskii, I., Kleeorin, N., Brandenburg, A. & Eichler, D. 2012 Cosmic-ray current-driven turbulence and mean-field dynamo effect. Astrophys. J. 753 (1), 6.Google Scholar
Rogachevskii, I., Kleeorin, N., Käpylä, P. J. & Brandenburg, A. 2011 Pumping velocity in homogeneous helical turbulence with shear. Phys. Rev. E 84 (5), 056314.Google ScholarPubMed
Rüdiger, G. 1980 Reynolds stresses and differential rotation. i. On recent calculations of zonal fluxes in slowly rotating stars. Geophys. Astrophys. Fluid Dyn. 16 (1), 239–261.Google Scholar
Rüdiger, G. 1989 Differential Rotation and Stellar Convection: Sun and Solar-Type Stars, vol. 5. Taylor & Francis.Google Scholar
Rüdiger, G., Kitchatinov, L. L. & Hollerbach, R. 2013 Magnetic Processes in Astrophysics: Theory, Simulations, Experiments. Wiley-VCH.Google Scholar
Schou, J., Antia, H. M., Basu, S., Bogart, R. S., Bush, R. I., Chitre, S. M., Christensen-Dalsgaard, J., Di Mauro, M. P., Dziembowski, W. A., Eff-Darwich, A. et al. 1998 Helioseismic studies of differential rotation in the solar envelope by the solar oscillations investigation using the michelson Doppler imager. Astrophys. J. 505 (1), 390.Google Scholar
Snodgrass, H. B., Howard, R. & Webster, L. 1984 Recalibration of Mount Wilson Doppler measurements. Solar Phys. 90 (1), 199–202.CrossRefGoogle Scholar
Spruit, H. C. 1974 A model of the solar convection zone. Solar Phys. 34 (2), 277–290.Google Scholar
Thompson, M. J. 1990 A new inversion of solar rotational splitting data. Solar Phys. 125 (1), 1–12.Google Scholar
Zeldovich, Ya. B., Ruzmaikin, A. A. & Sokolov, D. D. 1983 Magnetic Fields in Astrophysics. Gordon and Breach Science Publishers.Google Scholar