= Hydrodynamic transfield equation for an axisymmetric wind
{title2=$\rho^{-1}\nabla\cdot(\nabla\psi/(\rho R^2))=\varepsilon'-Ts'-\ell\ell'/R^2$}
Using an <axisymmetric hydrodynamic mass flux function>, set $s=s(\psi)$, $\ell=Ru_\phi=\ell(\psi)$ and $\varepsilon=\varepsilon(\psi)$. The azimuthal <vorticity> is $\omega_\phi=-R\nabla\cdot(\nabla\psi/(\rho R^2))$. The meridional projection of the <Crocco form of the unsteady Euler equation> gives the displayed equation. The <mass density> also satisfies the Bernoulli relation $\varepsilon=|\nabla\psi|^2/(2\rho^2R^2)+\ell^2/(2R^2)+w+\Phi$, so an <equation of state> is part of closing the system.
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