Vorticity Dynamics

In the momentum equations for incompressible flow, this chapter focuses on velocity and pressure. In many instances it is advantageous to interpret the flow events in terms of the vorticity and the dynamic events that are interacting to give a certain vorticity distribution. The existence of vorticity generally indicates that viscous effects are important. This occurs because fluid particles can only be set into rotation by an unbalanced shear stress. The vorticity equation indicates that as one follows a material particle, vorticity is intensified by vortex line stretching and turning and is slowly diffused by viscosity. Pressure does not play a direct role in the equation governing vorticity dynamics. This viewpoint emphasizes viscous effects. Helmholtz's laws, allows to think of vortex lines as stringing together a set of material particles, are applicable whenever viscous diffusion is negligible.