I think most of us know how lift is created. Air is deflected downward because of the shape of an airfoil.
How long does downwash last, is the air going to flow downward forever or will it climb back up to leveled degree? If so how long would it take for the air to get back on its normal flow path, which is not downward?
Like everything else, air will be accelerated either upwards or downwards if a force is applied to it. The aircraft's wing applies a downward force to the air mass thus accelerating it in that direction. However, nothing applies an upward force to that mass of air, so it can be assumed it will not climb back up. (I am neglecting the formation of vortexes and possible differences in air density)
The velocity of the mass of air will be reduced by friction with and the inertia of the surrounding air until it comes to rest.
What you call the "normal flow path" of the air is it simply being still before an aircraft flies through it.
The forces that slow the air movement are proportional to the velocity of the movement, so the vortex decays slower the smaller it is and never decays completely. But of course after some time it decays to slower than turbulence caused by other reasons and then we can say it no longer exists for any practical purpose.
I don't know how quickly exactly the vortex decays. However, rough idea can be obtained from the separation requirements for aircraft.
The required separation for heavy and super behind same class is 4 NM, which for those aircraft is usually 1 to 1½ minute. After that time, the vortex has decayed enough to allow aircraft of similar weight as the one that made it, but not smaller ones.
For the biggest difference, small behind super, 8 NM is needed. Small aircraft are usually also slower, so say 3 to 4 minutes. After that time, the vortex has decayed so that it is no longer dangerous even to small aircraft, but probably still noticeable.
Now super is 30 times heavier than the largest small (A380 is 575t, small is up to 19t) and the vortex has to decay on similar order for the number to make sense. Probably even more, because the quantity that matter is moment of inertia and that grows faster than weight.
Since exponential means it decays by the same fraction every n minutes, after another couple of minutes it will be another two orders of magnitude down and likely no longer measurable.
So my wild guess is from under a minute behind small aircraft to maybe 10-15 minutes behind A380—and depending on speed; the vortex is weaker when flying fast.
