  A rigorous method for introducing the variational principle describing
relativistic ideal hydrodynamic flows with all possible types of
discontinuities (including shocks) is presented in the framework of an exact
Clebsch type representation of the four-velocity field as a bilinear
combination of the scalar fields. The boundary conditions for these fields on
the discontinuities are found. We also discuss the local invariants caused by
the relabeling symmetry of the problem and derive recursion relations linking
invariants of different types. These invariants are of specific interest for
stability problems. In particular, we present a set of invariants based on the
relativistic generalization of the Ertel invariant.
