Basic ideas
It might be said that the term boundary layermeans different things to different people. To someone observing fluid flowing past a flat plate, it might seem that there are two distinct regimes of motion. Far from the plate, the flow might seem too fast for the eye to follow, markers carried by the fluid appearing blurred as they speed past the plate; near the plate however the flow is so sluggish that it is easily followed by eye. The observer may call this the boundary layer, and the region beyond the free‐stream or the mainstream, and he may feel that the interface between the two is reasonably sharp, so that he can call it the edge of the boundary layer. The theoretician will see no such sharp interface but will employ a mathematical technique, sometimes called matched asymptotics that similarly distinguishes an inner region near the plate from the outer region beyond. For him, the edge of the boundary layer is a region where the two solutions are required to agree...
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Bibliography
Backus, G.E., 1968. Kinematics of geomagnetic secular variation in a perfectly conducting core. Philosophical Transactions of the Royal Society of London, A263: 239–266.
Braginsky, S.I., and Meytlis, V.P., 1992. Local turbulence in the Earth's core. Geophysical and Astrophysical Fluid Dynamics, 55: 71–87.
Desjardins, B., Dormy, E., and Grenier, E., 2001. Instability of Ekman‐Hartmann boundary layers, with application to the fluid flow near the core‐mantle boundary. Physics of the Earth and Planetary Interiors, 124: 283–294.
Dormy, E., Jault, D., and Soward, A.M., 2002. A super‐rotating shear layer in magnetohydrodynamic spherical Couette flow. Journal of Fluid Mechanics, 452: 263–291.
Dormy, E., and Soward, A.M. (eds), 2007. Mathematical Aspects of Natural Dynamos. The Fluid Mechanics of Astrophysics and Geophysics, CRC/Taylor & Francis.
Gilman, P.A., 1971. Instabilities of the Ekman‐Hartmann boundary layer. Physics of Fluids, 14: 7–12.
Gilman, P.A., and Benton, E.R., 1968. Influence of an axial magnetic field on the steady linear Ekman boundary layer. Physics of Fluids, 11: 2397–2401.
Greenspan, H.P., 1968. The Theory of Rotating Fluids., Cambridge: Cambridge University Press.
Hide, R., and Stewartson, K., 1972. Hydromagnetic oscillations of the earth's core. Reviews of Geophysics and Space Physics, 10: 579–598.
Hollerbach, R., 1994a. Magnetohydrodynamic Ekman and Stewartson layers in a rotating spherical shell. Proceedings of the Royal Society of London A, 444: 333–346.
Hollerbach, R., 1994b. Imposing a magnetic field across a nonaxisymmetric shear layer in a rotating spherical shell. Physics of Fluids, 6(7): 2540–2544.
Hollerbach, R., 1996. Magnetohydrodynamic shear layers in a rapidly rotating plane layer. Geophysical and Astrophysical Fluid Dynamics, 82: 281–280.
Kleeorin, N., Rogachevskii, A., Ruzmaikin, A., Soward, A.M., and Starchenko, S., 1997. Axisymmetric flow between differentially rotating spheres in a magnetic field with dipole symmetry. Journal of Fluid Mechanics, 344: 213–244.
Kuang, W., and Bloxham, J., 1997. An Earth‐like numerical dynamo model. Nature, 389: 371–374.
Leibovich, S., and Lele, S.K., 1985. The influence of the horizontal component of the Earth's angular velocity on the instability of the Ekman layer. Journal of Fluid Mechanics, 150: 41–87.
Lilly, D.K., 1966. On the instability of the Ekman boundary layer. Journal of the Atmospheric Sciences, 23: 481–494.
Loper, D.E., 1970. General solution for the linearised Ekman‐Hartmann layer on a spherical boundary. Physics of Fluids, 13: 2995–2998.
Müller, U., and Bühler, L., 2001. Magnetofluiddynamics in Channels and Containers. Berlin: Springer.
Pedlosky, J., 1979. Geophysical Fluid Dynamics. Berlin: Springer.
Proudman, I., 1956. The almost rigid rotation of a viscous fluid between concentric spheres. Journal of Fluid Mechanics, 1: 505–516.
Roberts, P.H., 1967. An Introduction to Magnetohydrodynamics. London: Longmans.
Rosenhead, L. (ed.), 1963. Laminar Boundary Layers. Oxford: Clarendon Press.
Schlichting, H., and Gersten, K., 2000. Boundary Layer Theory. Berlin: Springer.
Soward, A.M., and Hollerbach, R., 2000. Non‐axisymmetric magnetohydrodynamic shear layers in a rotating spherical shell. Journal of Fluid Mechanics, 408: 239–274.
Stewartson, K., 1957. On almost rigid rotations. Journal of Fluid Mechanics, 3: 299–303.
Stewartson, K., 1966. On almost rigid rotations. Part 2. Journal of Fluid Mechanics, 26: 131–144.
Vempaty, S., and Loper, D., 1975. Hydromagnetic boundary layers in a rotating cylindrical container. Physics of Fluids, 18: 1678–1686.
Vempaty, S., and Loper, D., 1978. Hydrodynamic free shear layers in rotating flows. ZAMP, 29: 450–461.
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Dormy, E., Soward, P.H.R.A.M. (2007). Core, Boundary Layers. In: Gubbins, D., Herrero-Bervera, E. (eds) Encyclopedia of Geomagnetism and Paleomagnetism. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-4423-6_44
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