On E/ J for general steady states
J. L. Collett, Donald Lynden-Bell · Monthly Notices of the Royal Astronomical Society · 1987
For barotropic fluids and stellar dynamical systems the energy, E, is stationary in steady states at fixed angular momentum. When the angular momentum is changed keeping the circulations fixed, |$\partial{E}/\partial{J}={\Omega}_{p}$| the angular velocity with which the figure or pattern rotates. This result is true even for complicated flows where no definite rotation can be defined for the fluid itself.