How does an aircraft form wake turbulence?
Origin of the vortices

Wake turbulence is easy to understand once you know how a wing creates lift: By deflecting the air flowing across it downwards. In this answer, I had used the simplification of just accelerating downwards all the air flowing through a circle with a diameter equal to the wingspan, and leaving all other air unaffected.

This helps to understand the principle of lift creation, but is too simple, of course, because the downward movement of air will create a void above it, and the air below has to make place for that downward moving streamtube. Also, the pressure field around the wing will affect the air in the vicinity of the streamtube as well, and in consequence air from below will be pushed sideways already by the wing, and the air above will start to flow towards the low pressure area over the wing. This sideways movement will become more pronounced aft of the wing, such that air will continuously be pressed outwards below the wing's wake, move up left and right of it and inwards above the wake. The inertia of the downwash keeps it moving downwards for several minutes, continuously displacing the air below it and sucking more air into the space above, and that will result in two vortices swirling behind the wing. This is the rolling up of the wake (see the sketch below, taken from this source).



The vortices are just a consequence of the downward movement of the wake, and this in turn is a consequence of lift creation. Please note that the cores of the vortices are closer together than the wingspan! This by itself should make clear that they are not caused by air flowing around wingtips, a hard to extinguish misconception. The table below gives calculations of this vortex spacing.



The table is also from the Carten paper of 1971; note the inclusion of Boeing's 2707 project!

Strength of the vortices

If we again come back to the simplified streamtube approximation, lift is proportional to the mass of air flowing through it per unit of time times the deflection angle. If lift is equal to the aircraft's mass (as it should be), heavy aircraft need to either accelerate more air (wider span) or accelerate air more (higher deflection angle) than light aircraft at the same speed. A higher deflection angle will produce more powerful vortices. For that reason, a heavy aircraft at low speed and with a small wingspan will produce the strongest vortices.

Since more air flows through the streamtube at higher flight speed, flying faster will require less deflection, making the wake vortices weaker. If the aircraft climbs, air becomes less dense with altitude, and less mass flow over the wing is available, so the vortices grow stronger if the flight speed does not change. Normally, aircraft accelerate when climbing, and the vortex strength will stay the same if the aircraft flies at constant dynamic pressure.

Vortices can be avoided in three ways:


Infinite wing span (meaning infinite mass flow, so no deflection is necessary for any lift)
Infinite speed (again, gives infinite mass flow)
No weight of the aircraft. Flying a zero-g parabola does indeed produce almost no wake turbulence.


End of the vortices

Inertia will keep the wake moving downwards and the vortices spinning, but friction will let those air movements die down within a few minutes. If the aircraft flies high, the wake is dissipated long before it hits the ground. The wake of low flying aircraft, however, does hit the ground and is deflected. The vortex tube now acts like a wheel and starts moving outward, and if there is a sufficient crosswind, the windward vortex can be arrested as in the right sketch below (also from the Carten report).

 

Photographic evidence

There are far too many pretty pictures around of wake vortices to not include some, so I will add a few here:



You can see that the outer contrails of this Boeing 747's engines wrap around the contrails of the inner engines. This shows how the air is pushed down in the wake of the wing and that the centers of the vortices are slightly inboard of the outer engines.



The condensation traces originating at the winglet tips of this A340 move in- and upward, again showing that the vortex does not originate from the tips but forms behind the wing and with a distance between the two vortex cores of substantially less than the wingspan.



These two pictures show how the downwash of the wake is cutting a furrow in the clouds.



KLM MD-11 on a moist day, flaps set for landing (source © Erwin van Dijck). One, it shows how insignificant the tip vortex is compared to vorticity shed at the flap tips, and Two it shows how the tip vortex moves inward and starts to be sucked into the wake vortex. Note also the tip vortices from the tail!