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Wake vortices are created all along the wingspan but, the vortices come together to form two tip vortices. How exacly does this happen and why does it? I know that wake vortices push air to the side. Does this sideways moving air somehow pull the vortices to the tip?

Here is a picture of what I am talking about:

enter image description here

This picture shows that there is downwash and vortices along the whole wing span but, for some reason there are only two vortices at the tips.

One theory I have is that the up wash from the vortices follows the downwash from the rest of the wing and they spin around in a circle but, I am not completely sure

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    $\begingroup$ The roll-up at the tip is because the tip is a discontinuity between air accelerated downwards, and free air stream. There are two excellent answers about tip roll-up at this question. $\endgroup$ – Koyovis Jun 26 '17 at 0:27
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The picture in your question is an oversimplification. Maybe this photo of an MD-11 on a moist day will help to illustrate the point:

MD-11 on a moist day

I also think you should not call the wake vortices "tip vortices". The tip vortices are an insignificant part of the whole wake system and can be seen in the picture above on both the winglets and the horizontal tail as thin lines of condensation. The wake vortices are the result of the vorticity shed over the wingspan rolling up. With flaps set for landing, the MD-11 has a big change in circulation at the flap tips, so here the shedding is intensified and shows as a thick line of condensation. There is more going on left and right of that thick line, but it is not visible because the gradient of circulation over span is too shallow to cause condensation in the wake (it does over the wing itself, due to the low pressure on the top side).

Maybe it will be best for understanding wake rollup if you watch it happen in a video. It should also help to confirm your theory :-). A good one is at 3:20 and again at 5:40. Also, watch how the wake changes when ground effect kicks in at around 4:00.

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You have to think of where pressure is lowest and where it is highest.

enter image description here

The wing is forcing air downward along its entire span, creating a low pressure area above the wing and high pressure below it. Higher pressure air wants to move in to fill the low pressure voids. The ambient air above and away from the wing moves downward toward the low pressure zone. This accelerating air causes lift, and the downwash.

At the wingtips, in addition to ambient air above and below, the accelerating air encounters ambient air to the outside, so the ambient air moves inward toward the low pressure zone. The high pressure below the wing pushes outward toward the ambient air. This causes a rotation. The rotation is the beginning of the vortex. It begins at the wingtips because that's the first place it can occur.

As the wings move away they leave a sheet of low pressure behind them. The low pressure zone is pulling ambient air downward and inward from above whereas the high pressure is pushing downward and outward into the ambient air. As each parcel of air moves toward the voids, the parcel behind it moves in to fill in where it was, so the whole process expands outward as it involves a larger area. The rotation that began at the wingtips spreads outward creating the rotating funnel shape.

You can see this in the photo below. As the vortices spread and the moisture of the engine contrails get caught in them you can see how they move. The inner contrails are being pushed down and out. At the top the contrail the parcels of air are being pulled in and down toward the void and the outside is being pulled up and around to fill in where the first parcels left. The sheet in the center is the low pressure area. The low pressure is causing water to condense into a fine mist that can be seen by the sheen near the top of the photo.

enter image description here

Zooming in on the wingtip you can faintly see the vortex forming at the tips.

enter image description here

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