= Material advection of an axisymmetric magnetic flux function
{title2=$D\Psi/Dt=0$}
For an axisymmetric <poloidal magnetic field> $\mathbf B_p=\nabla\Psi\times\nabla\phi$, the <ideal magnetohydrodynamic induction equation> gives $\partial_t\Psi+\mathbf u_p\cdot\nabla\Psi=0$, after fixing the time-dependent additive constant in $\Psi$. A regular axial reference makes $2\pi\Psi$ the enclosed <magnetic flux>. This scalar statement of <magnetic flux freezing> holds even when rotation also produces a <toroidal magnetic field>.
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