Some vorticity theorems and conservation laws for non-barotropic fluids

Abstract

Some theorems concerning the vorticity in barotropic flows of perfect fluids are generalized for non-barotropic flows. The generalization involves replacing the velocity in certain parts of the equations by a time-dependent quantity which is a function of the velocity and thermodynamic properties of the fluid. Results which are generalized include Kelvin's circulation theorem and conservation laws for potential vorticity and helicity. It is shown how the results can be further generalized to include dissipative effects. The possibility of using some of the results in deriving a complete set of Lagrangian conservation laws for perfect fluids is discussed.