Introduction
Magnetohydrodynamic waves are propagating disturbances found in electrically conducting fluids permeated by magnetic fields where magnetic tension provides a restoring force on fluid parcels moving across field lines. The role played by magnetohydrodynamic waves, transporting disturbances in the flow and magnetic field and connecting disparate regions of the fluid, is crucial to our understanding of hydromagnetic systems. Magnetohydrodynamic waves in the Earth's liquid iron outer core have been proposed as the origin of changes of the Earth's magnetic field taking place on timescales of decades to centuries, and are thus of interest to both geomagnetists and paleomagnetists.
In the Earth's outer core, in addition to the magnetic forces acting on the electrically conducting fluid, we must also consider Coriolis forces resulting from planetary rotation, buoyancy forces due to gravity acting on density gradients and the constraints placed on flow by spherical shell geometry....
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Bibliography
Acheson, D.J., 1972. On hydromagnetic stability of a rotating fluid annulus. Journal of Fluid Mechanics, 52: 529–541.
Acheson, D.J., and Hide, R., 1973. Hydromagnetics of rotating fluids. Reports on Progress in Physics, 36: 159–221.
Alfvén, H., 1942. Existence of electromagnetic‐hydrodynamic waves. Nature, 150: 405–406.
Braginsky, S.I., 1964. Magnetohydrodynamics of the Earth's core. Geomagnetism and Aeronomy, 4: 898–916 (English translation, 698–712).
Braginsky, S.I., 1967. Magnetic waves in the Earth's core. Geomagnetism and Aeronomy, 7: 1050–1060 (English translation, 851–859).
Braginsky, S.I., 1972. Analytical description of the geomagnetic field of past epochs and determination of the spectrum of magnetic waves in the core of the Earth. Geomagnetism and Aeronomy, 12: 1092–1105 (English translation, 947–957).
Braginsky, S.I., 1974. Analytical description of the geomagnetic field of past epochs and determination of the spectrum of magnetic waves in the core of the Earth. II. Geomagnetism and Aeronomy, 14: 522–529 (English translation, 441–447).
Braginsky, S.I., 1989. Magnetohydrodynamic waves within the Earth. In James, D. E. (eds.), Encyclopedia of Solid Earth Geophysics. Kluwer Academic Publishers.
Braginsky, S.I., 1999. Dynamics of the stably stratified ocean at the top of the core. Physics of the Earth and Planetary Interiors, 111: 21–34.
Bullard, E.C., Freedman, C., Gellman, H., and Nixon, J., 1950. The westward drift of the Earth's magnetic field. Philosophical Transactions of the Royal Society of London, 243: 67–92.
Busse, F.H., 1976. Generation of planetary magnetism by convection. Physics of the Earth and Planetary Interiors, 12: 350–358.
Chandrasekhar, S., 1961. Hydrodynamic and Hydromagnetic Stability. Oxford: Oxford University Press.
Davidson, P.A., 2001. An Introduction to Magnetohydrodynamics. Cambridge: Cambridge University Press.
El Sawi, M., and Eltayeb, I.A., 1981. Wave action and critical surfaces for hydromagnetic‐inertial‐gravity waves. Quarterly Journal of Mechanics and Applied Mathematics, 34: 187–202.
Eltayeb, I.A., 1972. Hydromagnetic convection in a rapidly rotating fluid layer. Proceedings of the Royal Society of London Series A, 326: 229–254.
Eltayeb, I.A., 1981. Propagation and stability of wave motions in rotating magnetic systems. Physics of the Earth and Planetary Interiors, 24: 259–271.
Eltayeb, I.A., and Kumar S., 1977. Hydromagnetic convective instability of a rotating self‐gravitating fluid sphere containing a uniform distribution of heat sources. Proceedings of the Royal Society of London Series A, 353: 145–162.
Ewen, S.A., and Soward, A.M., 1994. Phase mixed rotating magnetoconvection and Taylor's condition. I. Amplitude equations. Geophysical and Astrophysical Fluid Dynamics, 77: 209–230.
Fearn, D.R., 1979. Thermal and magnetic instabilities in a rapidly rotating sphere. Geophysical and Astrophysical Fluid Dynamics, 14: 102–126.
Fearn, D.R., and Proctor M.R.E., 1983. Hydromagnetic waves in a differentially rotating sphere. Journal of Fluid Mechanics, 128: 1–20.
Finlay, C.C., and Jackson A., 2003. Equatorially dominated magnetic field change at the surface of Earth's core. Science, 300: 2084–2086.
Hide, R., 1966. Free hydromagnetic oscillations of the Earth's core and the theory of geomagnetic secular variation. Philosophical Transactions of the Royal Society of London Series A, 259: 615–647.
Hide R., and Stewartson K., 1972. Hydromagnetic oscillations in the Earth's core. Reviews of Geophysics and Space Physics, 10: 579–598.
Jackson, A., Jonkers, A.R.T., and Walker, M.R., 2000. Four centuries of geomagnetic secular variation from historical records. Philosophical Transaction of the Royal Society of London, 358: 957–990.
Jones, C.A., Mussa A.I., and Worland S.J., 2003. Magnetoconvection in a rapidly rotating sphere: the weak field case. Proceedings of the Royal Society of London Series A, 459: 773–797.
Kerswell, R.R., 1994. Tidal excitation of hydromagnetic waves and their damping in the Earth. Journal of Fluid Mechanics, 274: 219–241.
Korte, M., and Constable, C., 2005. Continuous global geomagnetic field models for the past 7 millennia II: CALS7K.1. Geochemistry, Geophysics, Geosystems, 6(1): doi:10.1029/2004GC00801
Lehnert B., 1954. Magnetohydrodynamic waves under the action of the Coriolis force. Astrophysical Journal, 119: 647–654.
Malkus, W.V.R., 1967. Hydromagnetic planetary waves. Journal of Fluid Mechanics, 90: 641–668.
Moffatt H.K., 1978. Magnetic Field Generation in Electrically Conducting Fluids. Cambridge: Cambridge University Press.
Proctor, M.R.E., 1994. Convection and magnetoconvection. M.R.E., and In Proctor, Gilbert, A.D. (eds.), Lectures on Solar and Planetary Dynamos. Cambridge: Cambridge University Press, 97–115.
Roberts, P.H., and Loper, D.E., 1979. On the diffusive instability of some simple steady magnetohydrodynamic flows. Journal of Fluid Mechanics, 90: 641–668.
Roberts, P.H., and Soward, A.M., 1972. Magnetohydrodynamics of the Earth's core. Annual Review of Fluid Mechanics, 4: 117–153.
Roberts, P.H., and Stewartson, K., 1974. On finite amplitude convection in a rotating magnetic system. Philosophical Transactions of the Royal Society of London, 277: 287–315.
Soward, A.M., 1979. Convection‐driven dynamos. Physics of the Earth and Planetary Interiors, 20: 281–301.
Walker, M.R., Barenghi, C.F., and Jones C.A., 1998. A note on dynamo action at asymptotically small Ekman number. Geophysical and Astrophysical Fluid Dynamics, 88: 261–275.
Zhang, K., and Gubbins, D., 2002. Convection‐driven hydromagnetic waves in planetary fluid cores. Mathematical and Computer Modelling, 36: 389–401.
Zhang, K., and Schubert, G., 2000. Magnetohydrodynamics in rapidly rotating spherical systems. Annual Review of Fluid Mechanics, 32: 409–443.
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Finlay, C. (2007). Magnetohydrodynamic Waves. In: Gubbins, D., Herrero-Bervera, E. (eds) Encyclopedia of Geomagnetism and Paleomagnetism. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-4423-6_202
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