= Magnetic concentration by an incompressible stagnation flow
The linear <incompressible flow> $\mathbf u=(-\omega x,-\omega y,2\omega z)$ compresses the transverse plane and stretches the axial direction. An axial <magnetic field> obeys $B_t-\omega rB_r=2\omega B+\eta\Delta_\perp B$. In <ideal magnetohydrodynamics>, its amplitude grows as $e^{2\omega t}$ while its transverse width decreases as $e^{-\omega t}$. Thus its <magnetic energy> per unit axial length grows as $e^{2\omega t}$, even when opposite-polarity angular sectors give zero signed <magnetic flux>. Finite <magnetic diffusivity> limits the amplification of localized finite-flux Gaussian fields.
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