= Alfvénic degeneracy of steady planar MHD
{c}
{title2=$B_z(\mu_0k^2/\rho-1)=\mu_0k(V-U)$}
The two axial invariants in <steady planar ideal-MHD field-line invariants> give the displayed identity. When $V-U\ne0$, a finite smooth flow cannot reach horizontal <Alfvén speed>. When $V=U$, an everywhere Alfvénic branch is possible even with $B_z\ne0$: constant $\rho$ and $\mathbf u=\mathbf B/\sqrt{\mu_0\rho}$ give an example. The nondegenerate exclusion must not be applied to this branch.
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