Theoretical studies of motions in the Earth's fluid (liquid) metallic outer core, where the main geomagnetic field is produced by self‐exciting dynamo (q.v.) action, are based on the nonlinear partial differential equations (PDEs) of magnetohydrodynamics (MHD) (q.v.) that govern the flow of electrically conducting fluids. The equations are mathematical expressions of the laws of mechanics, thermodynamics and electrodynamics applied to a continuous medium.
The equations of electrodynamics are not needed when dealing with fluids of low electrical conductivity, for effects due to Lorentz forces associated with the flow of electric currents are then negligible, as in dynamical meteorology and oceanography. In these highly developed areas of geophysical fluid dynamics a key role is played by the concept of potential vorticity(PV). This pseudoscalar quantity—defined as the reciprocal of the density of the fluid multiplied by the scalar product of the vorticity vector and the gradient of...
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Hide, R. (2007). Potential Vorticity and Potential Magnetic Field Theorems. In: Gubbins, D., Herrero-Bervera, E. (eds) Encyclopedia of Geomagnetism and Paleomagnetism. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-4423-6_268
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