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Suppose you have a pipe with x amount of air flowing through it. Suppose the flow is nice and laminar throughout the pipe, it's velocity distribution will look something like this.

https://files.catbox.moe/ysa5y8.jpg

The flow near the walls will be slower because the drag from the wall's boundary layer and the moving flow slows it down, while it moves faster near the center of the pipe because the greatest mass of air is moving uniformly carrying its momentum forward with no wall to obstruct it.

Now, what happens if we put a vortex in the middle of that pipe?

https://files.catbox.moe/yk9slc.jpg

The vortex itself is occupying the middle of the pipe, as long as the vortex maintains its integrity, the air cannot pass through the vortex it must go around it. Therefore the vortex is acting like a flow restriction, reducing the cross sectional area of the pipe. The shear stress of the vortex squeezes the air against the walls of the pipe, and reduces the cross sectional area of the pipe. In order to maintain continuity, the flow speeds up, and the pressure in the pipe drops.