Cherbn-Simons reduction and non-Abelian fluid mechanics

We propose a non-Abelian generalization of the Clebsch parametrization for a vector in three dimensions. The construction is based on a group-theoretical reduction of the Chern-Simons form on a symmetric space. The formalism is then used to give a canonical (symplectic) discussion of non-Abelian fluid mechanics, analogous to the way the Abelian Clebsch parametrization allows a canonical description of conventional fluid mechanics.