I'm sure it can be animated; also by transform shader, moving the Y down or so. Probably somewhere near the end of the line(s) where the colors are finally masked in. Unless a get position is used, that should be replaced by a get position in texture.
It should have a link to the waves themselves I'd say, use the same moving speed for waves as well as foam or so. Would be a nice project for your Pixelplow experiment, Hannes!