Canonical formulation for nonrelativistic Euler fluids and Schwinger type conditions

We present a new approach, based on Noether's energy-momentum tensor, to construct the lagrangian for nonrelativistic nonisentropic Euler fluids. An advantage of this approach is that it naturally provides a generalised Clebsh decomposition for the fluid velocity. This is used to develop a hamiltonian formulation inolving a noncanonical algebra. This algebra is very simply obtained from the symplectic structure. It is used to show that the components of the Noether's energy-momentum tensor satisfy certain Schwinger-type relations. These relations, which are reminiscent of corresponding relations in relativistic field theory, are new.