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This question discusses how wake turbulence can affect planes flying in formation. It got me wondering, how do aircraft (the wings in particular) form wake turbulence to begin with? It can't be as simple as tip vortexes right?

As a follow up, how can you design an aircraft to minimize wake turbulence? And what are the trade offs in doing so?

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  • $\begingroup$ any object that moves through a medium creates wake turbulence $\endgroup$ – ratchet freak Oct 2 '14 at 13:52
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    $\begingroup$ FAA has a nice document about it. $\endgroup$ – Farhan Oct 2 '14 at 13:56
  • $\begingroup$ @ratchetfreak: Is that really true? Can't the wake destruct itself? I mean if the object has the shape of a water drop, at subsonic speed, will it create a wake (no taking into account the volume very close to the object). $\endgroup$ – mins Feb 4 '16 at 11:46
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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).

roll-up of wake

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.

table of vortex characteristics

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:

  1. Infinite wing span (meaning infinite mass flow, so no deflection is necessary for any lift)
  2. Infinite speed (again, gives infinite mass flow)
  3. 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).

Interference with ground

Photographic evidence

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

B-747 with contrails

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.

A-340

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.

enter image description here

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

MD-11 on a moist day

MD-11 on a moist day, flaps set for landing. 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!

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    $\begingroup$ I like the NASA image, pretty colors and all that: commons.wikimedia.org/wiki/File:Airplane_vortex_edit.jpg $\endgroup$ – Nick T Oct 3 '14 at 0:12
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    $\begingroup$ @Peter Kämpf, it seems some of your pictures got taken offline, would you mind finding similar ones that are still working? Thanks :) $\endgroup$ – ROIMaison Feb 28 '17 at 9:04
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    $\begingroup$ @ROIMaison: They all load on my side. Please look up the imgur URL in the source and try to load them directly. Maybe a server was overloaded - they should all still be online. $\endgroup$ – Peter Kämpf Feb 28 '17 at 16:43
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    $\begingroup$ @PeterKämpf, I tried exactly that, and it wasn't working. The images are working now, so I guess it was a temporary thing. Thanks! $\endgroup$ – ROIMaison Feb 28 '17 at 16:58
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    $\begingroup$ @ROIMaison: I had this happen to me just now. On the second attempt (reloading the whole page) the missing imgur file loaded as well. I guess they need to work on their bandwidth. $\endgroup$ – Peter Kämpf Feb 28 '17 at 18:34
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It is as simple as "tip" vortices, but that is a misnomer.

The wing vortices are not really caused by the "tips". They are inherent effect of generating lift over finite wingspan. To generate lift (a force on the plane), the aircraft applies force on the surrounding air (by Newton's third law). Since the air is free to move, this force accelerates it (according to Newton's second law) downward. Due to the way fluids work the force affects air both above and below the wing (to height comparable to wingspan), but not to the sides.

Wing vortex ring; from the excellent online book "How It Files"

So directly behind the plane we have air that is moving down and on the sides air that remains still. And this is the wing vortices. See also John S. Denker: How It Flies, section 3.14.

There is slight updraft just outside the wingtips caused by the transverse flow around the wing tip, but it only contributes a tiny fraction (at most couple of percent) of the circulation and associated drag. There is also some turbulence caused by simply moving through the air at sufficient speed, but that is comparably minor as well.

The inertia the aircraft has to impart to the air over unit of time is proportional to the aircraft weight. Therefore turbulence behind heavier aircraft is stronger.

If the aircraft flies faster it affects more air per unit of time, so it suffices to accelerate it to lower speed. Therefore turbulence behind slower flying aircraft (e.g. during take-off or landing) is stronger.

If the aircraft flies higher the air is less dense (has lower mass per unit of volume) so it needs to be accelerated to higher speed. Therefore turbulence behind aircraft flying higher is stronger. Fortunately when flying high aircraft also fly fast.

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    $\begingroup$ I liked that you addressed that turbulence is stronger behind slower aircraft, which is non-intuitive. $\endgroup$ – RoboKaren Oct 2 '14 at 17:55
  • $\begingroup$ Could possibly expand the section on how a slow flying plane creates more wake turbulence that a fast flying one? I feel like I'm poking the edges of understanding that but... I could use some clarification. $\endgroup$ – Jay Carr Oct 2 '14 at 19:50
  • $\begingroup$ Are wingtips at all relevant here? Do they affect the vortices significantly or no? $\endgroup$ – raptortech97 Oct 2 '14 at 20:02
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    $\begingroup$ @raptortech97: Not significantly. There is a tiny bit of upward flow around the tip, but it is very small compared to the downwash behind the wing. The various winglet designs have more to do with lift distribution and bending moment than saving any induced drag and corresponding energy of the wake vortex. See this answer for detailed explanation of winglets. $\endgroup$ – Jan Hudec Oct 2 '14 at 21:13
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    $\begingroup$ There is nothing wrong in this answer, but the picture is misleading: There is a sheet of vortices leaving the wing, not just two isolated ones at the wingtips. Anyway, using the mechanics of the Biot-Savart law to explain lift makes the topic needlessly convoluted. $\endgroup$ – Peter Kämpf Oct 2 '14 at 22:20
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To understand the formation of wing-tip vortices, and how that leads to wake turbulence, we must first understand how the wings of an aircraft generate lift.

Lift due to Pressure Differential

This form of lift works according to the Bernoulli's Principle; the basic idea is that fast moving air creates low pressure. This is where the structure of the wing becomes important.

Thanks to the shape of the airfoil, a low pressure forms right above the wing, and the high pressure underneath the airfoil, pushes the wing (and therefore the whole aircraft) upwards. This is can be clearly understood with the help of an image:

Image borrowed from rgsphysics.files.wordpress.com

Wing-tip vortices

A wing's lift is primarily created by the pressure differential between the lower and the upper surfaces of the wing. Air molecules underneath are already under pressure, and those close to the wing-tip escape around the wing and make their way outwards, upwards, and inwards, creating wing-tip vortices.

The wing-lets on many modern airliners also serve the purpose of somewhat preventing the formation of wing-tip vortices, by not letting the air molecules spiral in, after escaping from under the wing.

Image borrowed from NYTimes.com

Image borrowed from Boldmethod.com

Wake Turbulence

Wake Turbulence is a disturbance in the atmosphere that forms behind an aircraft as it passes through the air. It includes various components, the most important of which are wingtip vortices and jetwash.

So wake turbulence is nothing but atmospheric disturbance caused by wing-tip vortices and to a smaller extent, jet engine exhaust.

Image borrowed from *flightradar2.com*

EDIT: Removed section elaborating Impact Lift, as no such thing exists - Courtesy of Peter Kämpf

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    $\begingroup$ Oh please - not that long ago discredited impact lift theory. It was proposed by a certain Isaac Newton (who also was an avid alchemist, trying to produce gold form mercury). This theory is plain wrong. $\endgroup$ – Peter Kämpf Oct 22 '17 at 8:37
  • $\begingroup$ Really? But the sticking-out your hand really works! Could you please elaborate? Thanks! $\endgroup$ – ClobberXD Oct 22 '17 at 12:10
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    $\begingroup$ It works for the same reason that a flat plate with angle of attack produces lift: Pressure difference. This picture of collisions is total bunk. $\endgroup$ – Peter Kämpf Oct 22 '17 at 13:48
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    $\begingroup$ You can use impact lift as a crude approximation in hypersonic flow, when the impulse of the air molecules starts to dwarf all other parameters. But the principle is wrong, especially in subsonic flow. Yes, I would leave it out if I were you. Don't believe everything you find on the Web. $\endgroup$ – Peter Kämpf Oct 23 '17 at 6:39
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    $\begingroup$ Unfortunately, you are still perpetuating the equal transit-time fallacy. en.wikipedia.org/wiki/… $\endgroup$ – sdenham Oct 31 at 18:26

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