Vorticity addition method

Abstract

It is shown that in the general case it is not possible to propose the Lagrangian viewpoint on the vorticity evolution, which would be unique for the entire flow, using the existing analogs of the Helmholtz theorems. This is related to the fact that, as distinct from the Helmholtz theorem oneself, these analogs are valid only for nonzero vorticity zones. New analogs of the Helmholtz theorems are proposed for the general case of flows (from incompressible fluid to viscous gas). They describe the vorticity evolution at all the points including the points of nonzero vorticity.