Do winds behave like waves? Like a sound wave, there are compressed and dilated regions in the air. But do compressed regions also occur in winds. If one considers squalls, they feel like a compressed region of air. Perhaps they are too great to be considered as a kind of amplitude, but is there anyway a kind of wave in wind?

In the other question/answer is not mentioned anything about forming waves. So does wind behave (perhaps only a little bit) with sound-wave compressions and dilations?
Yes, there are a lot of waves in wind. The wave you may be looking for is called a gravity wave (aka buoyancy wave). To name a few other waves
Rossby Waves, Gravity Waves, Inertio-Gravity waves, Sound Waves, Kelvin Waves

I am sure there are more than just those few waves out there.