Direct and inverse cascades in the geodynamo

Nonlinear Processes in Geophysics

Volumn 15, Issue 6, 2008, Pages 873-880

  Reshetnyak, M ^a   Hejda, P ^b  

^a SCHMIDT INSTITUTE OF PHYSICS OF THE EARTH   (Russian Federation)

^b INSTITUTE OF MATHEMATICS   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

GEODYNAMICS; GEOMETRY; GEOSTROPHIC FLOW; KINEMATICS; KINETIC ENERGY; MAGNETIC FIELD; NUMERICAL MODEL; TURBULENCE;

EID: 56849087083     PISSN: 10235809     EISSN: 16077946     Source Type: Journal    
DOI: 10.5194/npg-15-873-2008     Document Type: Article

References (25)

1. Alexakis, A., Mininni, P. D., and Pouquet, A.: Turbulent cascades, transefer, and scale interactions in magentohydrodynamics, New J. Phys., 9, 1-20, 2007.
2. Batchelor, G. K.: The theory of homogeneous turbulence, Cambridge University Press, Cambridge, 1953.
3. Buffett, B.: A comparison of subgrid-scale models for large-eddy simulations of convection in the Earth's core, Geophys. J. Int., 153, 753-765, 2003.
4. Busse, F. H.: Thermal instabilities in rapidly rotating systems, J. Fluid Mech., 44, 441-460, 1970.
5. Cattaneo, F., Emonet, T., and Weis, N.: On the interaction between convection and magnetic fields, Astrophys. J., 588, 1183-1198, 2003.
6. Chandrasekhar, S.: Hydrodynamic and hydromagnetic stability, Dover Publications. Inc., NY, 1961.
7. Constantin, P.: Energy spectrum of quasigeostrophic turbulence, Phys. Rev. Lett., 89(18), 184 501-184 504, 2002.
8. Frisch, U., Pouquet, A., Léorat, J., and Mazure, A..: Possibility of an inverse cascade of a magnetic helicity in magnetohydrodynamic turbulence, J. Fluid Mech., 68, part 4, 769-778, 1975.
9. Frisch, U.: Turbulence: the legacy of A. N. Kolmogorov, Cambridge University Press, Cambridge, 1995.
10. Harden, H. and Hansen, U.: A finite-volume solution method for thermal convection and dynamo problems in spherical shells, Geophys. J. Int., 161, 522-532, 2005.
11. Hejda, P. and Reshetnyak, M.: Control volume method for the thermal convection problem in a rotating spherical shell: test on the benchmark solution, Stud. Geophys. Geod., 48, 741-746, 2004.
12. Hollerbach, R. and Rüdiger, R.: The Magnetic Universe, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2004.
13. Hossain, M.: Reduction of the dimensionality of turbulence due to a strong rotation, Phys. Fluids. 6(4), 1077-1080, 1994.
14. Jones, C. A.: Convection-driven geodynamo models, Phil. Trans. R. Soc. London, 358, 873-897, 2000.
15. Jones, C. A. and Roberts, P. H.: Convection driven dynamos in a rotating plane layer, J. Fluid Mech., 404, 311-343, 2000.
16. Kageyama, A. and Sato, T.: Velocity and magnetic field structures in a magnetohydrodynamic dynamo, Phys. Plasma, 4(5), 1569-1575, 1997.
17. Kono, M. and Roberts, P.: Recent geodynamo simulations and observations of the geomagnetic field, Rev. Geophys., 40(10), B1-B41, 2002.
18. Kraichnan, R. H. and Montgomery, D.: Two-dimensional turbulence, Rep. Prog. Phys., 43, 547-619, 1980.
19. Meneguzzi, M. and Pouquet, A.: Turbulent dynamos driven by convection, J. Fluid Mech., 205, 297-318, 1989.
20. Orszag, S. A.: Numerical simulation of incompressible flows within simple boundaries, I. Galerkin (spectral) representations, Stud. Appl. Math. L., 4, 293-327, 1971.
21. Matsushima, M., Nakajima, T., and Roberts, P.: The anisotropy of local turbulence in the Earth's core, Earth Planets Space, 51, 277-286, 1999.
22. Tabeling, P.: Two-dimensional turbulence: a physicist approach. Phys. Reports., 362, 1-62, 2002.
23. Verma, M.: Statistical theory of magnetohydrodynamic turbulence: recent results, Phys. Reports, 401, 229-380, 2004.
24. Waleffe, F.: The nature of triad interactions in homogeneous turbulence, Phys. Fluids., A4(2), 350-363, 1992.
25. Zeldovich, Y. B., Ruzmaikin, A. A., and Sokoloff, D.D.: Magnetic fields in astrophysics, Gordon and Breach, NY, 1983.