I've been trying to figure out for several hours now how to achieve a particular effect for a newspaper icon I've been working on. The idea was originally to make a newspaper page as a flat, perspective-less square and then apply some transformation to it later to achieve a somewhat "warped" or "rippled" look. Being fairly unfamiliar with more technical terminology, I think a picture would be best to show what I'm going for:

I've tried many related tools such as envelope distortions, pattern along path, node shaping, and using the tweak tool, but none of those quite gave the effect I wanted. Basically, I just want to shift everything in my shape (or path) vertically by a dynamic amount.
Thanks very much in advance, and my apologies if what I'm looking for isn't very clear.