Axisymmetric hydrodynamic mass flux function ($\rho {\mathbf{u}}_p=\nabla \psi \times \nabla \varphi$)

For a steady axisymmetric compressible fluid flow, mass conservation permits this representation. The mass flow through an annulus between two stream surfaces is $2\pi \Delta \psi$. In a steady adiabatic wind without magnetic forces, the specific entropy, specific angular momentum and Bernoulli function are locally functions of $\psi$ on connected regular stream surfaces.