# Vortex formation in an airfoil

Physics Asked by PATRICK on August 4, 2020

How is a starting vortex formed when an airfoil (i.e cross-section of wings of a plane) starts to move?

As an airfoil with a positive angle of attack begins to move, slowly at first, a rear stagnation point establishes itself part way forward along the upper surface.

As the plane gathers speed, the stagnation point moves back. The air flow running back from it develops two bound or attached vortices, each rotating in opposite directions. I will call them the near and far vortices, although from what I have read their exact positions seem a bit vague.

The near vortex initially flows down to the trailing edge and forward along in the boundary layer and loops back when it meets the stagnation point. As the stagnation point moves back, part of the rear vortex is squeezed out below the trailing edge and begins to establish a circulation flow round the whole airfoil.

The far vortex is somewhat further back and rotates in the opposite sense. Overall, angular momentum must be conserved, so (save for secondary effects) the vortices have equal and opposite angular momentum.

When the stagnation point reaches the trailing edge (the Kutta condition), the near vortex now wholly surrounds the wing. According to the circulation theory of lift, this amplifies the wing lift and is the normal flight condition.

However the far vortex, having steadily gained energy as the speed increased, has also been steadily pushed back with the stagnation point. It suddenly gets shed and stays behind as the starting vortex. If litter gets caught up in a strong starting vortex, you can see how the top of the vortex spins forwards and the bottom backwards.

Theoretically a vortex cannot end and these two vortices join up with the tip vortices also being created to form a closed toroidal vortex. Of course, once the starting vortex is shed, the whole thing dissipates until the theoretical toroid quickly becomes meaningless.

Answered by Guy Inchbald on August 4, 2020