= Toroidal-velocity anti-dynamo theorem
= Toroidal flow theorem
{synonym}
For a bounded conducting sphere with uniform <magnetic diffusivity> and an insulating exterior, an <incompressible flow> tangent to concentric spheres cannot sustain <dynamo action>. Neither the <velocity> nor the <magnetic field> needs to be axisymmetric. The radial magnetic scalar has a homogeneous advection-diffusion equation, so the poloidal field decays. Once it is absent, the toroidal magnetic potential also has a homogeneous scalar advection-diffusion equation. This is a theorem about spherical flow geometry, not about a general cylindrical flow with an axial component.
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