Vorticity in high Reynolds number flows

The Helmholtz vorticity transport equation (1.95) dictates that an aerodynamic flow which is uniform up­stream will have zero vorticity everywhere, except in boundary layers and wakes where the action of viscous stress is significant. As sketched in Figure 1.9, at high Reynolds number these vortical regions are thin com­pared to the body dimensions, which makes them natural candidates for lumping into sheets or filaments with only a small loss of accuracy. Figure 2.12 shows such an approximate representation of an airfoil flow-field via a variable-strength vortex sheet placed on the airfoil surface. In this vortex sheet model, the irrotational inviscid flow extends all the way to the surface. Note also that in the 2D case there is no need to place a vortex sheet on the wake, since the net vorticity integrated across the wake is essentially zero. Chapter 3 will examine this flow-field model in more detail, and improve it for cases where the viscous layer is not particularly thin.