I've got a 2D image and I want to transform it into something that looks like a single frame from an animation of that logo on fabric catching just a bit of breeze. I'm not an artist so don't have Photoshop or Illustrator, just free stuff like GIMP and Inkscape (under Windows)
I know it's some kind 3D transform (or a cheap simulation using filters) - but I don't know the technique. Honestly, I don't know what keywords to use to search Google/YouTube to find what I need.
Ideally, something like this (though less drastic) from a flat image:
But something even more fake/subtle like this would be OK: 
Perhaps techniques for both?
Update Here's a photo with some of my results using the water simulator mentioned in the selected answer:
