Similarity and dynamic similarity models for large-eddy simulations of a rotating convection-driven dynamo

Geophysical Journal International

Volumn 172, Issue 1, 2008, Pages 103-114

  Chen, Qiaoning ^a   Jones, Chris A ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Dynamo: theories and simulations; Numerical solutions

Indexed keywords

COMPUTER SIMULATION; GEODYNAMICS; GEODYNAMO; KINETIC ENERGY; LARGE EDDY SIMULATION; PARAMETERIZATION; THEORETICAL STUDY;

EID: 37449008826     PISSN: 0956540X     EISSN: 1365246X     Source Type: Journal    
DOI: 10.1111/j.1365-246X.2007.03621.x     Document Type: Article

References (38)

1. Bardina, J., Ferziger, J.H. & Reynolds, W.C., 1980. Improved subgrid scale models for large-eddy simulations, Am. Inst. Aeronaut. Astronaut. Paper, 80-1357.
2. Boyd, J.P., 2001. Chebyshev and Fourier Spectral Methods, 2nd edn revised, Dover Publications, Mineola, New York.
3. Braginsky, S.I. & Meytlis, V.P., 1990. Local turbulence in the Earth's core, Geophys. Astrophys. Fluid Dyn., 55, 71-87.
4. Buffett, B.A., 2003. A comparison of subgrid-scale models for large-eddy simulations of convection in the Earth's core, Geophys. J. Int., 153, 753-765.
5. Busse, F.H., Grote, E. & Tilgner, A., 1998. On convection driven dynamos in rotating spherical shells, Stud. Geophys. Geod., 42, 1-6.
6. Chen, Q. & Glatzmaier, G.A., 2005. Large eddy simulations of two-dimensional turbulent convection in a density-stratified fluid, Geophys. Astrophys. Fluid Dyn., 99, 355-375.
7. Chen, Q., Chen, S., Eyink, G.L. & Holm, D.D., 2005. Resonant interactions in rotating homogeneous three-dimensional turbulence, J. Fluid Mech., 542, 139-164.
8. Childress, S. & Soward, A.M., 1972. Convection driven hydromagnetic dynamo, Phys. Rev. Lett., 29, 837-839.
9. Christensen, U.R., Olson, P. & Glatzmaier, G.A., 1999. Numerical modelling of the geodynamo: A systematic parameter study. Geophys. J. Int., 138, 393-409.
10. Donald, J.T. & Roberts, P.H., 2004. The effect of anisotropic heat transport in the Earth's core on the geodynamo, Geophys. Astrophys. Fluid Dyn., 98, 367-384.
11. Fautrelle, Y. & Childress, S., 1982. Convective dynamos with intermediate and strong fields, Geophys. Astrophys. Fluid Dyn., 22, 235-279.
12. Frisch, U., Pouquet, A., Leorat, J. & Mazure, A., 1975. Possibility of an inverse cascade of magnetic helicity in magnetohydrodynamic turbulence, J. Fluid Mech., 68, 769-778.
13. Germano, M., 1986. A proposal for a redefinition of the turbulent stresses in the filtered Navier-Stokes equations, Phys. Fluids, 29, 2323-2324.
14. Germano, M., Piomelli, U., Moin, P. & Cabot, W.H., 1991. A dynamic subgrid-scale eddy viscosity model, Phys. Fluids A, 3, 1760-1765.
15. Glatzmaier, G.A. & Roberts, P.H., 1995. A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle, Phys. Earth planet. Inter., 91, 63-75.
16. Jones, C.A. & Roberts, P.H., 2000. Convection-driven dynamos in a rotating plane layer, J. Fluid Mech., 404, 311-343.
17. Jones, C.A. & Roberts, P.H., 2005. Turbulence models and plane layer dynamos, in Fluid Dynamics and Dynamos in Astrophysics and Geophysics, pp. 295-330, eds Soward, A.M., Jones, C.A., Hughes, D.W. & Weiss, N.O., CRC Press, Baton Rouge.
18. Kageyama, A., Sato, T., Watanabe, K., Horiuchi, R., Hayashi, T., Todo, Y., Watanabe, T.H. & Takamaru, H., 1995. Computer simulation of a magnetohydrodynamic dynamo, Phys. Plasma., 2, 1421-1431.
19. Kida, S., Araki, K. & Kitauchi, H., 1997. Periodic reversals of magnetic field generated by thermal convection in a rotating spherical shell, J. Phys. Soc. Jpn., 66, 2194-2201.
20. Kuang, W. & Bloxham, J., 1997. An Earth-like numerical dynamo model, Nature, 389, 371-374.
21. Leonard, A., 1974. Energy cascade in large-eddy simulations of turbulent flow, Adv. Geophys., 18, 237-248.
22. Lilly, D.K., 1992. Proposed modification of the Germano subgrid-scale closure method, Phys. Fluids A, 14, 633-635.
23. Matsui, H. & Buffett, B.A., 2005. Sub-grid scale model for convection-driven dynamo in a rotating plane layer, Phys. Earth planet. Inter., 153, 108-123.
24. Matsushima, M., 2005. A scale-similarity model for the subgrid scale flux with application to MHD turbulance in the Earth's core, Phys. Earth Planet Inter., 153, 74-82.
25. Meneguzzi, M. & Pouquet, A., 1989. Turbulent dynamos driven by convection, J. Fluid Mech., 35, 319-340.
26. Meneveau, C. & Katz, J., 2000. Scale-invariance and turbulence models for large-eddy simulation, Annu. Rev. Fluid Mech., 32, 1-32.
27. Olson, P. & Christensen, U.R., 2006. Dipole moment scaling for convection-driven planetary dynamos, Earth planet. Sci. Lett., 250, 561-571.
28. Phillips, C.G. & Ivers, D.J., 2001. Special interactions of rapidly-rotating anisotropic turbulent viscous and thermal diffusion in the Earth's core, Phys. Earth planet. Inter., 128, 93-107.
29. Phillips, C.G. & Ivers, D.J., 2003. Strong field anisotropic diffusion models for the Earth's core, Phys. Earth planet. Inter., 140, 13-28.
30. Pierre, M.St., 1994. The strong field branch of the Childress-Soward dynamo, in Stellar and Planetary Dynamos, pp. 295-302, eds Proctor, M.R.E. & Gilbert, A.D., Cambridge University Press, Cambridge, UK.
31. Piomelli, U., 1993. High Reynolds number calculations using the dynamic subgrid-scale model, Phys. Fluids A, 5, 1484-1490.
32. Pouquet, A., Frisch, U. & Leorat, J., 1976. Strong MHD helical turbulence and nonlinear dynamo effect, J. Fluid Mech., 77, 321-354.
33. Rotvig, J. & Jones, C.A., 2002. Rotating convection-driven dynamos at low Ekman number, Phys. Rev. E, 66, 056308.
34. Sakuraba, A. & Kono, M., 1999. Effects of the inner core on the numerical simulation of the magnetohydrodynamic dynamo, Phys. Earth planet. Inter., 11, 105-121.
35. Shimizu, H. & Loper, D.E., 1997. Time and length scales of buoyancy-driven flow structures in a rotating hydromagnetic fluid. Phys. Earth planet. Inter., 104, 307-329.
36. Soward, A.M., 1974. A convection driven dynamo. I: The weak field case. Philos. Trans. R. Soc. Lond. A, 275, 661-651.
37. Sreenivasan, B. & Jones, C.A., 2006. The role of inertia in the evolution of spherical dynamos. Geophys. J. Int., 164, 467-476.
38. Wong, V.C. & Lilly, D.K., 1994. A comparison of two dynamic subgrid closure methods for turbulent thermal convection, Phys. Fluids, 6, 1016-1023.