This is not concretely reallistic water shader with some collision effect(by mask with stones in video,but there is no geometry except plane-all is one shader).
And i intentionally hyperbolized the color of water to blue, I like the color.
I also increased water rebound from the stones(but there is value “Flow factor” in shader,you can change it to 10+ and water will flow more directly).
This is example of how you can organize fluid flow(liquid,mist,some atmospheric effect of planet,etc) via advanced uv animation and old gamedev trick(through several position vectors components and some math).
Methode good when there is no really need for simulation.
Because all Blender examples i`ve seen about uv animation is pretty simple,linear motion by some vector(like that https://www.youtube.com/watch?v=mMTLi4TvNzI).
Or simple noise animation via size or position and so on,if we talk about bump.
Shader has a lot of potential for tweak(and maybe the render is not the result i wanted to show, but the main target was to explain the principle).
Because by this principe you can animate not only noise maps for flow,but the input mask too(static in my example).And with combination you can achived really interesting result.
Hope you like it.
Thanks for watching.
Scene file: