= Barotropic cylindrical rotation theorem
{title2=$\partial_z\Omega^2=0$}
= Poincaré-Wavre theorem
{c}
{synonym}
In a steady axisymmetric <barotropic fluid> with purely azimuthal velocity $r\Omega\mathbf e_\phi$ and a conservative body force, the <barotropic enthalpy function> obeys $\nabla(w+\Phi)=r\Omega^2\mathbf e_r$. Taking its curl yields the displayed cylindrical rotation law. The first integral is $w+\Phi-\int r\Omega^2dr=C$ in a connected fluid region. Baroclinic pressure and density need not satisfy this conclusion.
Back to article page
