  On the basis of the gauge principle of 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. The rotational
transformations are regarded as gauge transformations as well as the
translational ones. In addition to the Lagrangians representing the translation
symmetry, a structure of rotation symmetry is equipped with a Lagrangian
$\Lambda_A$ including the vorticity and a vector potential bilinearly. Euler's
equation of motion is derived from variations according to the action
principle. 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 $\ba$. Without $\Lambda_A$, the
action principle results in the Clebsch solution with vanishing helicity. The
Lagrangian $\Lambda_A$ yields non-vanishing vorticity and provides a source
term of non-vanishing helicity. The vorticity equation is derived as an
equation of the gauge field, and the $\Lambda_A$ characterizes topology of the
field. The present formulation is comprehensive and provides a consistent basis
for a unique transformation between the Lagrangian $\ba$ space and the Eulerian
$\bx$ space. In contrast, with translation symmetry alone, there is an
arbitrariness in the ransformation between these spaces.
