= Flux expulsion
Flux expulsion is redistribution of <magnetic flux> out of the interiors of persistent circulating flows into their edges and surrounding regions. In two-dimensional <incompressible flow>, a magnetic flux function obeys $\partial_t A+\mathbf u\cdot\nabla A=\eta\nabla^2 A$. At large but finite <magnetic Reynolds number>, circulation stretches gradients of $A$, enabling resistive smoothing and weak interior <magnetic field> with strong field near the circulation boundary. Finite <magnetic diffusivity> is essential to the eventual rearrangement; exact ideal <magnetic flux freezing> alone does not justify a flux-free steady cell. Magnetic back reaction can limit the process.
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