The vorticity, ω, of a flow is a vector quantity which is a measure of the rotation of a flow. It is defined by the relation:
It should be emphasized that vorticity corresponds to changing orientation of microscopic fluid elements, rather than just movement in a curved path. A useful equation in fluid mechanics is the vorticity transport equation. For an incompressible fluid in a system with conservative body forces, this equation is:
where D is kinematic viscosity.
The first term on the right represents the interaction of vorticity with velocity gradients and the second term represents viscous diffusion through the fluid. The concept of vorticity is discussed further in Massey (1989) and Tritton (1977).
Massey, B. S. (1989) Mechanics of Fluids. Van Nostrant Reinhold, London.
Tritton, D. J. (1977) Physical Fluid Dynamics. Van Nostrand Reinhold, Wokinghan, UK. Leading to: Vortices