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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 $ρ$. It will be shown how in terms of our new variable the Euler and continuity equations can be integrated in the stationary case.