Axial Flow in Laminar Trailing Vortices

Abstract

The structure of laminar trailing vortices behind a lifting wing is considered. The inviscid roll up of the trailing vortex sheet is examined, and the nature of the singularity at the centre of the spiral is determined. It is shown that viscosity removes the singularity and the structure of the viscous core is obtained. The pressure in the viscous core is found and used to calculate the axial velocities produced by streamwise pressure gradients. It is found that the perturbation of axial velocity can be either away from the wing or towards the wing depending on the distribution of tip loading on the wing. For elliptic loading, the perturbation is towards the wing. The axial flow deficit in the core due to the boundary layers on the wing is also estimated. A comparison with experiment is made and reasonable agreement is found.