THE 2-DIMENSIONAL VORTEX MOTIONS OF A VISCOUS INCOMPRESSIBLE FLUID

A generalization of the Helmholtz theorems concerning the conservation of vortex lines and the intensity of vortex tubes, which are well known in the hydrodynamics of a non-viscous fluid, and of Kelvin's theorem on the conservation of the circulation of the velocity along a closed fluid contour is presented for the case of unsteady planar and axisymmetrical continuous flows of a viscous incompressible fluid.