On the Total Vorticity of Motion of a Continuous Medium

Abstract

A general kinematic formula for the rate of change of the total vorticity of a finite volume of a continuous medium is deduced. Two kinematic theorems follow: (1) In a motion filling all space the total vorticity is constant in time, provided that the motion vanishes at infinity to a sufficiently high order; (2) The rate of change of total vorticity within an arbitrary volume is independent of the state of motion at all interior points of the volume. The mechanism of diffusion of total vorticity is then discussed in detail for the case of a viscous, compressible fluid.