grid warp move

I want to warp a wave so it appears bigger.
I have a grid warp looking good on the first frame and now i want to move the grid warp center so it follows the wave as it moves across the frame.

But when I animate the center parameter it moves the whole image.
How do I move just the grid?

If I understand you correctly you have to animate the center of the 'source' grid first to follow the wave (which makes sense since the source determines what part you're going to warp)
Then you have to animate the center of the 'destination' as well to follow along.
The best way to do that is to connect the two centers together so they will always line up their movement.

Thanks,