How to calculate the radius of wing tip vortices?

Question

Is it possible to find the radius of wing tip vortices?

Answer 1

A vortex in free air does not have any sharp boundary, so it does not have an obvious definition of radius.

To get some general idea, consider how the vortex is formed: the wing accelerates the air downward, over all of its span—that is how it generates lift. Since the air outside the span is not moving down, the boundary becomes a vortex line and it starts at the wingtips. This is the wingtip vortex.

So the two wingtip vortices “touch” from the start, and therefore have radius of half span. As the air below gets pushed out, the outside part of the vortices starts moving up in width comparable to the inner part, though not as fast—the vortex as a whole moves down and a little bit inward.

This upward flow on the outside is used by many large migratory birds to save a bit of effort by flying in the V formations. The wing vortex of each follower partially cancels with the wing vortex of the predecessor, saving them a bit of energy. For the leader it is neither advantage nor disadvantage, but when it gets tired, it can fall back to the end of the flock and the next one becomes a leader.

Internal friction of air makes the vortex slow down over time, but also pulls in more air, so the affected area grows in size. There is no specific limit, it grows until it can't be detected anymore.

It is possible to calculate something precisely—so long as you can decide what to calculate (and what is it useful for so it is worth calculating)—but it requires powerful computer as the equations describing fluid motion, Navier–Stokes equations, don't have analytical solution.