Abstract
Aspects of convection theory, expounded elsewhere in this book for plane layers, are here generalized to spherical geometry. Particular attention is focussed on the important example of convection in the Earth’s mantle, to the theory of which an introduction is given. Finally attention is transferred to the Earth’s core. Aspects of magnetoconvection in a rotating sphere are described, these being extensions to spherical geometry of the plane layer models discussed by the author in his chapter on dynamo theory elsewhere in this book.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Acheson, D.J., ‘On the Hydromagnetic Stability of a Rotating Fluid Annulus,’ J. Fluid Mech., 52, 529–541 (1972).
Acheson, D.J., ‘‘Stable’ Density Stratification as a Catalyst to Instability,’ J. Fluid Mech., 96, 723–733 (1980).
Busse, F.H., ‘Thermal Instabilities in Rapidly Rotating Systems,’ J. Fluid Mech. 44, 441–460 (1970).
Busse, F.H., ‘A Model of the Geodynamo,’ Geophys. J. R. Astr. Soc., 42, 437–459 (1975).
Chapman, D.S. and Pollack, H.N., ‘Global heat flow: degree 18 spherical harmonic representation’ (abstract). EOS Trans. AGU., 61,383 (1980).
Fearn, D.R. ‘Thermal and Magnetic Instabilities in a Rapidly Rotating Fluid Sphere,’ Geophys. Astrophys. Fluid Dynam., 14, 103–126 (1979).
Fearn, D.R. and Proctor, M.R.E., ‘Hydromagnetic Waves in a Differentially Rotating Sphere,’ J. Fluid Mech., 128, 1–20 (1983).
Fearn, D.R. and Proctor, M.R.E., ‘Self-Consistent Dynamo Models Driven by Hydromagnetic Instabilities,’ Phys. Earth Planet.Int., 36, 78–84 (1984).
Glatzmaier, G.A. and Gilman, P.A., ‘Compressible Convection in a Rotating Spherical Shell. I. Anelastic Equations,’Astrophys. J. Suppl. 45, 335–349 (1981).
Lamb, H. ‘On the Oscillations of a Viscous Spheroid,’ Proc. Lond. Math. Soc., 13, 51–66 (1881).
McKenzie, D.P., Roberts, J.M., and Weiss N.O. ‘Convection in the Earth’s Mantle: Towards a Numerical Simulation,’ J. Fluid Mech., 62, 465–538 (1974).
Peckover, R.S. and Hutchinson, I.H. ‘Convective Rolls driven by Internal Heat Sources,’ Phys. Fluids, 17, 1369–1372 (1974).
Peltier, W.R. ‘Mantle Convection and Viscoelasticity,’ Ann. Rev. Fluid Mech., 17, 561–608 (1985).
Roberts, P.H. ‘Convection in a Self-Gravitating Fluid Sphere,’ Mathematika, 12, 128–137 (1965).
Roberts, P.H. ‘On the Thermal Instability of a Rotating Fluid Sphere Containing Heat Sources,’ Phil. Trans. R. Soc. Lond. A, 263, 93–117 (1968).
Schubert, G., Yeun, D.A. and Turcotte, D.L. ‘Role of Phase Transitions in a Dynamic Mantle’, Geophys. J.R. Astron. Soc., 42,705–735 (1975).
Soward, A.M. ‘On the Finite Amplitude Thermal Instability of a Rapidly Rotating Fluid Sphere’, Geophys. Astrophys. Fluid Dyn., 9, 19–74 (1977).
Tozer, D.C. ‘The Present Thermal State of the Terrestrial Planets’, Phys. Earth Planet. Int., 6, 182–197 (1972).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 D. Reidel Publishing Company, Dordrecht, Holland
About this chapter
Cite this chapter
Roberts, P.H. (1987). Convection in Spherical Systems. In: Nicolis, C., Nicolis, G. (eds) Irreversible Phenomena and Dynamical Systems Analysis in Geosciences. NATO ASI Series, vol 192. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4778-8_4
Download citation
DOI: https://doi.org/10.1007/978-94-009-4778-8_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8620-2
Online ISBN: 978-94-009-4778-8
eBook Packages: Springer Book Archive