  On the basis of gauge principle in the field theory, a new variational
formulation is presented for flows of an ideal fluid. The fluid is defined
thermodynamically by mass density and entropy density, and its flow fields are
characterized by symmetries of translation and rotation. A structure of
rotation symmetry is equipped with a Lagrangian $\Lambda_A$ including
vorticity, in addition to Lagrangians of translation symmetry. From the action
principle, Euler's equation of motion is derived. In addition, the equations of
continuity and entropy are derived from the variations. Equations of conserved
currents are deduced as the Noether theorem in the space of Lagrangian
coordinate $\ba$. It is shown that, with the translation symmetry alone, there
is freedom in the transformation between the Lagrangian $\ba$-space and
Eulerian $\bx$-space. The Lagrangian $\Lambda_A$ provides non-trivial topology
of vorticity field and yields a source term of the helicity. The vorticity
equation is derived as an equation of the gauge field. Present formulation
provides a basis on which the transformation between the $\ba$ space and the
$\bx$ space is determined uniquely.
