A distortion or better still a displacement map (which is built-in so is faster) would be the way to go.
See
http://www.imagemagick.org/Usage/compose/#displace
In fact it would probably turn out so nice looking you may have to blur the image a little to dirty it so it becomes more realistic
Animation it is easy, it is just set of distortion/displacement maps applied to the same image over an over. The difficult part is geting the right sequence of distortion maps
However Please let us know how you get on. I would love to see your final set of distortion maps, and hopefully include at least one non-animationed example
in IM Examples...
Think of it as the payment for this advice.
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