Hi willc2,
Unfortunately, I think this is a job for OpenGL. You could achieve the same affect in Quartz by slicing the image up vertically and drawing segments with different vertical offsets... but I don't think you'd be able to achieve good enough performance to animate it. (At least, with 1px or 2px wide slices)
You could also leave the image stationary, and use Quartz to animate a masking path that would create the waving edges. That probably wouldn't look too natural, though.
As far as I know, Core Animation on the iPhone isn't capable of doing this, either. On the Mac it comes with some more advanced filters, but I think you'd probably see a lot more stuff like this if the iPhone filters could do it :-)
OpenGL does have quite a learning curve, but here's what you'd want to do to achieve the effect: Create a flat rectangle in OpenGL with several verticies along it's length. Point the camera at the rectangle so that it appears flat. Then, use a sine() function of some sort to animate the verticies back and forth in place.
This approach is also used to achieve the rippling-water effect, and you might be able find an example or two of it.
Sorry to bring bad news :-) Hope that helps!