ON MAGNETIC FIELD GENERATION BY A CONDUCTIVE FLUID FLOW
WITH AN INNER SCALE
V. A. Zheligovsky
Abstract
Magnetic field generation by the motion of an incompressible
conductive fluid in a bounded axisymmetric cavity embedded in a
dielectric is studied as a model for the Earth's dynamo. The case is
considered where the velocity of the conductive fluid experiences
spatial fluctuations of finite amplitude along the azimuthal direction,
while the amplitude of the mean velocity field and the magnetic
diffusion are infinitely small. The ratio of the amplitudes of the
fluctuating and mean component of the velocity is chosen to increase
as the square root of the inner spatial scale of the velocity. A
complete asymptotic expansion of magnetic induction operator
eigenvalues and associated eigenvectors is constructed, providing a
solution to this problem. It is shown that the $\alpha$effect takes
place in the system under consideration, with the magnitude of the
coefficient of generation controlled by the helicity of the velocity
vector potential. In the particular case of axial symmetry the
magnetic field is shown to obey Braginsky's equations of generation.
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Seismology,
Vol. 1.
