Alan Baker wrote:
...

As the air the plane has forced downward encounters more air, the
momentum is diffused so that a greater and greater mass of air moves
downward at smaller and smaller velocities (net)...

...until it encounters the ground.

Yikes! Eventually, ALL of the air will be on the ground!

And eventually, that downward deflection makes it way until it -- very
diffusely -- impacts upon the surface of the earth. That is the only
thing that finally stops it.
That assertion is not true in general. What appears to happen instead is
that any downward deflection is quickly reversed, leading to what is
known as a shed vortex. Here are some links on the subject:

http://www.grc.nasa.gov/WWW/K-12/airplane/shed.html

Sorry, but the vortex is an edge effect. The net flow is downward.

Mankind needs to set up fans IMMEDIATELY to move air back up into the sky!