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Axisymmetric magnetohydrodynamic wind

If $r^2|B_p|\to F$ and $u_p\to u_\infty$ along an open magnetic surface, then
$$
B_\phi\sim-\frac{\omega F}{u_\infty r},
\qquad
|v_{A\phi}|\to\omega\sqrt{\frac{F}{\mu_0ku_\infty}}.
$$
When enthalpy and gravity vanish asymptotically, the Bernoulli invariant becomes
$$
\epsilon=\frac12u_\infty^2+\frac{\omega^2F}{\mu_0ku_\infty}.
$$


Asymptotic energy of a radial magnetohydrodynamic wind

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 314 / 4 / c / Solution

Asymptotic energy of a radial magnetohydrodynamic wind

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Asymptotic energy of a radial magnetohydrodynamic wind

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