The noncommutativity of the conservation laws: Mechanism of origination of vorticity and turbulence

Abstract

From the equations of conservation laws for energy, linear momentum, angular momentum and mass the evolutionary relation in differential forms follows. This relation connects the differential of entropy and the skew-symmetric form, whose coefficients depend on the characteristics of gas-dynamic system and the external actions. The evolutionary relation turns out to be nonidentical that is explained by the noncommutativity of conservation laws. The properties of such nonidentical relation (selfvariation, degenerate transformation) enable one to disclose the mechanism of evolutionary processes in gas-dynamic system that are accompanied by origination of vorticity and turbulence. In this case the intensity of vorticity and turbulence is defined by the commutator on unclosed skew-symmetric form in the nonidentical evolutionary relation.