that sort of thing is usually done in post, Shake , After Effects, one way is using a technique called 'displacement.'

one uses the RGB values of an image to push the pixels of another image

in after effects go to effect/displacement

in the effects panel go to/ displacement map layer

choose your displacement layer (the one you have already made using grey scale values, in your case i imagine it to be 'wave like'??)

horizontal and vertical displacement (you will see the in the effects panel of your displacement effect) will work with colours (when you look at it yu will know what i mean) but with a grey scale it makes no difference.

its simple, just play with that for a while

best i can do.., got to go!!

opps, i ve been shaped so i didnt see you are using fusion.., anyway.., its the same thing. there must be a displacement node in Fusion.., not sure whats it is called.., ill look

dum de dum

yep, there it is.., warp/displace

mess with that..,