1.8 Vorticity and Its Dynamics

Insights into fluid dynamics come from many sources. The integrated, control volume analysis of 1.6.1 gives a coarse-grained view of the conservation laws. The parallel flow approximation of 1.5 gives some flavor of viscous effects. Vorticity is another important notion.

Many aspects of fluid motion and convective mixing can be understood in terms of vorticity, its dynamics, and its associated velocity field. For instance, vortex dynamics might provide conceptual insights into features seen in CFD simulations. These might take the form of interpreting flow patterns in terms of vortices and their motion; it might take the form of computing vorticity, to provide a concrete structure to visualize.

The flow field associated with vortical structures can loosely be described as velocity that whirls around the vortex, in the locally perpendicular plane. This is shown schematically in Figure 1.12. Sometimes we can understand convective mixing thus: vortices form in the flow; they convect fluid round themselves; they thereby transport material from one place to another. A striking example is Figure 1.13. Smoke has been released into the wing-tip vortex of a small airplane. It is swept round by the circulatory flow. The cloud of smoke is spread by advection. A by-product of the advective transport is a nice visualization of the tip vortex. As another example, streamwise vortices parallel to a wall have a tendency to increase heat transfer to, or from, the wall. In that case, they increase advective transport perpendicular to the...