Abstract
Abstract For party-symmetric flows of the form vr (r, t)1 r + v h where v h is an arbitrary horizontal (non-radial) component and r is the spherical radius, in a spherical electrically conducting fluid volume the evolution of the poloidal magnetic field decouples from the toroidal magnetic field. It is shown that flows of this class cannot maintain poloidal magnetic fields against ohmic decay. Specifically, , where S(r) is the spherical surface of radius r concentric with the origin and B is the magnetic induction, is shown to decay to zero monotonically and unconditionally. The proof uses a comparison theorem, established by maximum principles for one dimensional parabolic inequalities, to construct comparison function bounds, one of which decays to zero, on the absolute magnetic flux through . The result strengthens the antidynamo theorem of Ivers and James (1988) for partly-symmetric flows by relaxing the incompressibility of v h .
Published Version
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