Introduction
Background
The anelastic and Boussinesq approximations are simplifications of the system of equations governing buoyantly driven flows. The Boussinesq equations were the first to appear in print. In an influential paper on thermal convection, Rayleigh (1916) attributed them, without reference, to Boussinesq and the name has stuck, even though they had previously been employed by Oberbeck (1888). Although variations in density are the very essence of buoyancy, they are neglected everywhere in the Boussinesq equations “except in so far as they modify the action of gravity” (Rayleigh, 1916), i.e., the density is assumed to be constant except in the buoyancy force. This retains the essential physics with a minimum of complexity. The Boussinesq approximation usually performs well in modeling convection in laboratory conditions in which variations in pressure scarcely affect the density of the fluid. It is, however, unsatisfactory for large systems like the Earth's core, the...
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Braginsky, S.I., Roberts, P.H. (2007). Anelastic and Boussinesq Approximations. In: Gubbins, D., Herrero-Bervera, E. (eds) Encyclopedia of Geomagnetism and Paleomagnetism. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-4423-6_6
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