Astronomy and Astrophysics – Astronomy
Scientific paper
Apr 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008geoji.173...79g&link_type=abstract
Geophysical Journal International, Volume 173, Issue 1, pp. 79-91.
Astronomy and Astrophysics
Astronomy
3
Dynamo: Theories And Simulations, Geomagnetic Excursions, Reversals: Process, Time Scale, Magnetostratigraphy
Scientific paper
In the kinematic dynamo problem Maxwell's equations are solved for the magnetic field given a prescribed fluid velocity. Although no dynamic equations are involved, it does provide an accurate link between the magnetic field and fluid velocity and can therefore be used to infer something about the flow underlying the observed geomagnetic field. In this sense it complements the commonly used frozen-flux theory for inverting secular variation for core flow, in which electrical diffusion is neglected, and can be used to show up some of the strengths and weaknesses of the frozen-flux approximation. It might be thought that kinematic models have been superceded by dynamic models that include the momentum and heat equations, but this is not the case. Even the biggest numerical simulation cannot approach the correct parameters for the Earth's core, and the classes of flows that result are, in fact, quite restricted as well as being too complex for simple physical interpretation. A variety of simple flows have been studied for dynamo action; of particular interest here are a broad class of flows, based loosely on extensions of the early simple choice of Bullard & Gellman and to some extent representative of what might be generated by convection in the Earth's rapidly rotating core: this paper reviews the implications of the solutions for geomagnetism. The non-axisymmetric flows mimic convection rolls in a rotating sphere, the axisymmetric poloidal flows describe meridional circulation, a likely secondary flow, and the axisymmetric toroidal flow is a simple differential rotation. Helicity, which seems to be important for dynamo action, is related to spiralling of the rolls. Dipole, rather than quadrupole, fields are preferred when spiralling is eastward and differential rotation westward at the surface. Magnetic flux tends to be concentrated at stagnation points of the flow, and dynamo action fails when this concentration becomes so intense that steep gradients develop so as to enhance energy loss by diffusion. On the surface these stagnation points are centres of downwelling that concentrate vertical flux. Flux concentration plays an important role in determining the magnetic field's symmetry: for example, concentration of vertical flux in high latitudes favours dipolar fields while concentration near the equator, where dipole symmetry requires a change of sign, favours quadrupole symmetry. Steady fluid flow can only produce steady or oscillatory solutions to the kinematic problem at onset of instability. Steady solutions are preferred in three dimensions, in contrast to predictions of axisymmetric mean-field dynamo theory, where oscillatory solutions are the most common. Oscillatory solutions are preferred when poloidal and toroidal field coincide, which is unlikely to happen in the Earth because poloidal field is concentrated at high latitudes around the tangent cylinder while the toroidal field is probably strongest in mid-latitudes. Geomagnetic reversals are not oscillatory in nature and, therefore, require time-dependent flow, but kinematic examples show that only a tiny change in flow is needed to produce a realistic geomagnetic reversal. Linear modes of the induction equation of all symmetries are beginning to guide work on the dynamics of the geodynamo.
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