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Abstract
Barotropic flows are described in terms of mass preserving velocity fields of the vortex lines and non-barotropic flows by mass preserving velocity fields that move with the entropy and the potential vorticity. In these representations, all locally conserved quantities of inviscid flows are a priori given functions of the positions of the elements of fluid.
The Hamiltonian action for these “isocirculational” flows is also given and is suitable for studying motions around given steady states. Stability conditions of stationary flows with respect to perturbations that are not necessarily small but that do not change the values of the conserved quantities including the circulations are obtained by minimizing the potential terms of the Lagrangian functional.
