Asymptotic energy of a radial magnetohydrodynamic wind
= Asymptotic energy of a radial 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
$$
\epsilon=\frac12u_\infty^2+\frac{\omega^2F}{\mu_0ku_\infty}.
$$