Simplified Variational Principles for Barotropic Fluid Dynamics
  We introduce a three independent functions variational formalism for stationary and non-stationary barotropic flows. This is less than the four variables which appear in the standard equations of fluid dynamics which are the velocity field $\vec v$ and the density $\rho$. It will be shown how in terms of our new variable the Euler and continuity equations can be integrated in the stationary case. 
Asher Yahalom and Donald Lynden-Bell