I'm far from an expert, but they appear to be ripple fold draperies. Some of what your seeing is because they seem to have used a type of top mounted rod similar to what one finds in many hotels.

We have this in our master bedroom, but I unfortunately don't recall the name of the rod type.

Ripple Fold, @rrah is correct

I think it's called a traverse rod

Track curtain rod

https://www.wayfair.com/Symple-Stuff--Hayhurs-Single-Curtain-Rod-X112326336-L6262-K~W001215225.html?refid=GX434712764844-W001215225_332084452_332084453&device=c&ptid=1096346910952&network=g&targetid=pla-1096346910952&channel=GooglePLA&ireid=79537642&fdid=1817&PiID%5B%5D=332084452&PiID%5B%5D=332084453&gclid=EAIaIQobChMIrs-Txcf2_AIVSMSGCh1NhAb_EAQYAyABEgK6AvD_BwE

The actual style of the drape (the way the top section waves in and out) is called ripple fold.

https://www.theshadestore.com/drapery/custom-drapes/ripple-fold-drapery