The compressibility of the earth's core and the anti-dynamo theorems

Todoeschuck, John Peter (1979) The compressibility of the earth's core and the anti-dynamo theorems. Masters thesis, Memorial University of Newfoundland.

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Abstract

Anti-dynamo theorems are proofs that certain combinations of magnetic and velocity fields cannot produce the dynamo action needed to sustain the magnetic field. They can be divided into two classes. One class applies only to magnetic fields that are constant in time. The second is concerned with the more general case of magnetic fields that are allowed to vary in time. -- The previously accepted proofs of this second class are not generally valid in a compressible fluid. An anti-dynamo theorem can be applied in a particular case only if the parameter Rmc is much less than one. This parameter is given by - Rmc = CRm -- where Rm is the magnetic Reynolds number or the ratio of the importance of transport processes to ohmic diffusion and C is the Smylie-Rochester compressibility number which gives the fractional compression of material. -- For large scale processes involving substantial radial motion in the core of the Earth C is about 0.2 while Rm is about 200. Thus an anti-dynamo theorem for time-dependent axisymmetric velocity and magnetic fields does not apply to the core of the Earth. Another theorem for non-radial velocity fields is probably applicable as the density difference on any surface of constant radius in the core is not likely to be large. A third theorem on two-dimensional fields is hard to apply to the Earth because the system considered in the theorem is of infinite extent along one axis. -- The theorems of the first class are not affected by the introduction of compressibility.

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