A comparison of subgrid-scale models for large-eddy simulations of convection in the Earth's core

Geophysical Journal International

Volumn 153, Issue 3, 2003, Pages 753-765

  Buffett, Bruce A ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Convection; Dynamo theory; Earth's core; Geomagnetism

Indexed keywords

CONVECTION; EARTH ROTATION; GEODYNAMICS; GEOMAGNETISM; LARGE EDDY SIMULATION;

EID: 0038508829     PISSN: 0956540X     EISSN: None     Source Type: Journal    
DOI: 10.1046/j.1365-246X.2003.01930.x     Document Type: Article

References (41)

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. Braginsky, S.I. & Meytlis, V.P., 1990. Local turbulence in the Earth's core. Geophys. astrophys. Fluid. Dyn., 55, 71-87.
3. Braginsky, S.I. & Roberts, P.H., 1995. Equations governing convection in Earth's core and the geodynamo, Geophys. astrophys. Fluid. Dyn., 79, 1-97.
4. Buffett, B.A. & Bloxham, J., 2002. Energetics of numerical geodynamo models, Geophys. J. Int., 149, 211-221.
5. Busse, F.H., 2000. Homogeneous dynamos in planetary cores and in the laboratory, Ann. Rev. Fluid Mech., 32, 383-408.
6. Cantin, N., Vincent, A.P. & Yuen, D.A., 2000. Large-eddy simulations of thermal convection at high Rayleigh number. Geophys. J. Int., 140, 163-174.
7. s, Phys. Fluids, 9, 1368-1378.
8. Canuto, C., Hussaini, M.Y., Quarteroni, A. & Zang, T.A., 1988. Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin.
9. Christensen, U., Olson, P. & Glatzmaier, G.A., 1998. A dynamo model interpretation of geomagnetic field structures, Geophys. Res. Lett., 25, 1565-1568.
10. Christensen, U., Olson, P. & Glatzmaier, G.A., 1999. Numerical modelling of the geodynamo: a systematic parameter study, Geophys. J. Int., 138, 393-409.
11. Clarke, R.A., Ferziger, J.H. & Reynolds, W.C., 1979. Evaluation of subgrid-scale models using an accurately simulated turbulent flow, J. Fluid Mech., 91, 1-16.
12. Dobson, D.P., 2000. Fe-57 and Co tracer diffusion in liquid Fe-FeS at 2 and 5 GPa, Phys. Earth planet. Inter., 120, 137-144.
13. Germano, M., 1986. A proposal for a redefinition of the turbulent stresses in the filtered Navier-Stokes equations, Phys. Fluid, 29, 2323-2324.
14. Glatzmaier, G.A., 2002. Geodynamo simulations: how realistic are they?. Ann. Rev. Earth Planet. Sci., 30, 237-257.
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. Glatzmaier, G.A. & Roberts, P.H., 1996. An anelastic evolutionary geodynamo simulation driven by compositional and thermal convection, Physica D, 97, 81-94.
17. Grote, E., Busse, F.H. & Tilgner, A., 2000. Effects of hyperdiffusion on dynamo simulations, Geophys. Res. Lett., 27, 2001-2004.
18. Krause, F. & Radler, H.-K., 1979. On the theory of the geomagnetic dynamo based on mean field electrodynamics, Phys. Earth planet. Inter., 20, 158-171.
19. Kuang, W. & Bloxham, J., 1997. An Earth-like numerical dynamo model, Nature, 389, 371-374.
20. Kuang, W. & Bloxham, J., 1999. Numerical modelling of magnetohydrodynamic convection in a rapidly rotating spherical shell: weak and strong field dynamo action, J. Comp. Phys., 153, 51-81.
21. Leonard, A., 1974. Energy cascade in large-eddy simulations of turbulent flow, Adv. Geophys., 18, 237-248.
22. Lesieur, M. & Métais, O., 1996. New trends in large-eddy simulations of turbulence, Ann. Rev. Fluid. Mech., 28, 45-82.
23. Lilly, D.K., 1967. The representation of small-scale turbulence in numerical simulation experiments. in Proc. IBM Scientific Computing Symp. Environ. Sci., IBM Data Processing Division, White Plains, NY, pp. 195-211.
24. Liu, S., Meneveau, C. & Katz, J., 1994. On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet, J. Fluid. Mech., 275, 83-119.
25. Matsushima, M., 2001. Expression of turbulent heat flux in the Earth's core in terms of a second moment closure model, Phys. Earth planet. Inter., 128, 137-148.
26. Matsushima, M., Nakajima, T. & Roberts, P.H., 1999. The anisotropy of local turbulence in the Earth's core, Earth Planets Space, 51, 277-286.
27. Meneveau, C. & Katz, J., 2000. Scale-invariance and turbulence models for large-eddy simulation, Ann. Rev. Fluid. Mech., 32, 1-32.
28. Moffatt, H.K., 1970. Turbulent dynamo action at low magnetic Reynolds number, J. Fluid. Mech., 41, 435-452.
29. Moin, P. & Kim, J., 1982. Numerical investigations of turbulent channel flow, J. Fluid. Mech., 118, 341-377.
30. Olson, P., Christensen, U. & Glatzmaier, G.A., 1999. Numerical modeling of the geodynamo: Mechanisms of field generation and equilibration, J. geophys. Res., 104, 10 383-10 404.
31. Orszag, S.A., 1971. Numerical simulation of incompressible flows within simple boundaries: 1. Galerkin (spectral) representations, Stud. Appl. Math., 50, 293-327.
32. Roberts, P.H. & Glatzmaier, G.A., 2000. Geodynamo theory and simulations, Rev. Mod. Phys., 72, 1081-1123.
33. Rogallo, R.S. & Moin, P., 1984. Numerical simulation of turbulent flows, Ann. Rev. Fluid. Mech., 16, 99-137.
34. 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.
35. Smagorinsky, J., 1963. General circulation experiments with the primitive equations, I. The basic experiment, Mon. Weather Rev., 91, 99-164.
36. St Pierre, M.G., 1996. On the local nature of turbulence in Earth's outer core, Geophys. astrophys. Fluid. Dyn., 83, 293-306.
37. Vocadlo, L., Alfe, D., Price, G.D. & Gillan, M.J., 2000. First principle calculations of the diffusivity and viscosity of liquid Fe-FeS at experimentally accessible conditions, Phys. Earth planet. Inter., 120, 145-152.
38. Vreman, B., Geurts, B. & Kuerten, H., 1997. Large-eddy simulations of turbulent mixing layer, J. Fluid. Mech., 339, 357-390.
39. Winckelmans, G.S., Wray, A.S., Vasilyev, O.V. & Jeanmart, H., 2001. Explicit-filtering large-eddy simulation using the tensor-diffusivity model supplemented by a dynamic Smagorinsky term, Phys. Fluid., 13, 1385-1403.
40. Zhang, K., 1994. On coupling between the Poincaré equation and the heat equation, J. Fluid. Mech., 268, 211-229.
41. Zhang, K. & Jones, C., 1997. The effect of hyperviscosity on geodynamo models, Geophys. Res. Lett., 24, 2869-2872.