Vorticity invariants in hydrodynamics

Abstract

An invariance condition of differential forms under a flow generated by a four vector field in a four-dimensional manifold is used to obtain vorticity invariants in hydrodynamics. The manifold represents the four-dimensional Euclidean space-time continuum. Differential forms of degree 0, 1, 2 and 3 exists in three dimensional space, which lead to the existence of four types of local invariants. But in the four dimensional space-time manifold one more differential form, of degree four also, exists. The invariance condition of this form gives an additional invariant of hydrodynamics.