Finite domain viscous correction to the Kutta-Joukowski Theorem in incompressible flow

The classical relationship between lift and circulation in inviscid and irrotational flow was developed independently. Although being derived from ideal-fluid considerations with a free-slip (inviscid) boundary condition on the lifting airfoil, the Kutta Joukowski theorem has proven its applicability to high-Reynolds-number attached viscous flow, and constitutes the foundation of human understanding of aerodynamic lift. A recently published review on the development of circulation theory during the first three decades of the last century describes in some detail the complex discussions among the various experts at that time, some of whom were in favor and some opposing the circulation theory. In viscous flow, the circulation results from the vorticity generated on the no-slip wall of the airfoil. This vorticity is present throughout the wake, and subject to stretching and diffusion.