Is it possible to accelerate air to supersonic speeds? What would it look like? The speed of sound is the rate that disturbances in air propagate through it.
Is it possible to have a wind that itself is moving at supersonic speeds relative to stationary winds around it?
Or perhaps a fluid flowing through a pipe at a speed greater than the speed of sound within it.
If so, what would it "look" like?  What kind of phenomenon would occur?
 A: It's possible and in fact easy to do: take a tube filed with air and move a piston down it faster than the speed of sound in the surrounding air (doing this is just a matter of having enough force available). The air exiting the tube will be moving faster then the speed of sound in the air around it. OTOH it will be at a much higher pressure and as a result the speed of sound in the air exiting the tube will be higher than the speed of the air its self.
If you want to see this in action, you need only watch a rife be fired.
Also of interest is the De Laval nozzle.
A: Read something about Laval nozzles. In a narrow part of the nozzle the air attains the sound velocity and in a divergent part (diffuser) it is accelerated even more. 
Deceleration of such supersonic flow is only possible in a shock wave (suddenly), not gradually! There are plenty of pictures of supersonic flows from nozzles with visible shock wave disks or "shock diamonds" (in military aircrafts, cosmic jet engines, etc.).
A: The facility to accelerate wind to supersonic speed is called wind tunnel. Here is the pamphlet of a hypersonic (Mach 7 and 8) wind tunnel in Japan. It is explained how it works and you can even see some photos of hypersonic flow.
