Wavy animation

[wise totem]

I'm trying to make a wavy animation like the one in the clip. But when I move the deformer it moves the image instead of passing over it like in the clip. What am I missing here?

[ruby crow]

do you have the link to that clip?

[sage orbit]

(i made that) I have the flame moving downwards, so the upwards motion from the waro deformer is cancelled out