Kuzmin-Osledets Formulations of Compressible Euler Equations

Kuzmin-Oseledets formulations of compressible Euler equations case are considered. Exact results and physical interpretations are given. One such exact result for the compressible barotropic case is the potential helicity Lagrange invariant. In recognition of the fundamental physical implications of this Lagrange invariant clarified here, this invariant is shown to hold for compressible non-barotropic cases as well upon using a stronger gauge condition. Symmetry restoration taking place at the Lagrangian level in the Kuzmin-Oseledets formulation is pointed out. The Kuzmin-Oseledets formulation in the compressible barotropic case is shown to admit an exact solution that physically describes a density wave on a steady irrotational flow with the Kuzmin-Oseledets velocity q growing monotonically with it and hence specifying some information about the fluid impulse that is needed to set up the flow in question.