# Why do co-rotating vortices coalesce, but not counter-rotating ones?

In studying the aerodynamics of modern aircraft equipped with high-lift devices, I have discovered that quite a number of distinct trailing vortices are present in the immediate wake of an airplane in flight (e.g. off the outboard edge of the flap, the wingtip, etc). However, they always manage to roll-up into a solitary pair of vortices after only a few seconds have elapsed (see below).

Why do the individual vortex cores in close proximity merge together? This phenomenon appears to occur only when the vortices rotate in the same direction.

• Not enough for a full answer -- consider the pressure field between the vortex pair and the pressure outside of it. You get a Venturi type effect -- the same reason two boats moving side by side get sucked together. Commented Jul 13, 2014 at 20:59
• This clearly cannot be the entire story (if any of it), because counter-rotating vortices do not merge. Commented Jul 13, 2014 at 21:01
• What the heck is going on in that picture? Commented Jul 14, 2014 at 5:28
• @user2357112 A scale model of an airplane moves along a rail in a tunnel. Within the air are dispersed tiny particles which are illuminated by a laser sheet perpendicular to the direction of motion. Commented Jul 14, 2014 at 14:01
• @user2357112 See these videos: youtu.be/HfFfbOdUT0k?t=1m28s youtube.com/watch?v=nZMcypFErdE youtube.com/watch?v=L_8tQKVLzE0 youtu.be/zW4PmUE151c?t=1m45s Commented Jul 14, 2014 at 22:59

If you have counter rotating vortices they have zero net angular momentum (to first order). If they merged they would have to have no motion -> where did the energy go. In between the two axes of rotation the fluid moves in the same direction and has no mechanism for dissipation.

By contrast for two vortices with the same direction of rotation the fluids in between travel in opposite directions. They cancel and that leave you with only the vorticity around the outside of the two of them, which makes them merge.

As I said - intuitive start of an answer: I hope someone else can build on it.

• "They cancel and that leave you with only the vorticity around the outside of the two of them, which makes them merge." This is the part that I am looking for a deeper insight into. Helmholtz's theorem can very accurately predict the net vorticity/angular momentum of the merged vortex, but why do they come together? Commented Jul 13, 2014 at 22:52
• Also I think that if one vortex is considerably stronger than the other, the larger one can convect the smaller one around itself during the process whereby the two merge. Commented Jul 14, 2014 at 14:25
• I am giving Floris the nod (sadly I can give only one), but Mike definitely gets an assist on this one. Thanks to MSalters as well!!! Commented Jul 14, 2014 at 16:16

Because where they come close together the air in between circulates in such a way as to join them in a single path.

Floris is right, but maybe this picture helps.

• Any how precisely does that cause one vortex to be subsumed by the other? And what happens if they are of the same strength? Commented Jul 14, 2014 at 0:03
• @BrysonS. Forget subsumption. They simply merge, because each little parcel of air follows a path. Commented Jul 14, 2014 at 0:06
• Also, look at the area between the two vortices. In Mike's example, there's tremendous shear. The downward motion on the right happens very close to the upward motion on the left. That's not a stable situation. The two currents will interfere, slow each other, become turbulent, and as a result the air there becomes stationary - the core of the new single vortex. In the original question, the flow in the middle is unambiguously downwards and this is a stable pattern. Commented Jul 14, 2014 at 6:57
• @MSalters I believe "viscous shearing" is exactly what the OP is looking for; you should post it as an answer.
– user10851
Commented Jul 14, 2014 at 9:08
• I am giving Floris the nod (sadly I can give only one), but Mike definitely gets an assist on this one. Thanks to MSalters as well!!! Commented Jul 14, 2014 at 16:16