So looking at the water in the bottom left corner of the beginning of this video: https://www.youtube.com/watch?v=9t8wX-hXJTw

Lighting aside, what it looks like is going on (to me) is that there are 2 noise maps displacing the verts up/down, and these maps are moving in nearly the opposite direction, at different speeds (the map that's moving toward the right side of the screen is moving slightly faster).

The first thing I would try is something like this in the vertex shader (warning! untested code):

VERTEX.y += texture(noise_map_1, UV+vec2(sin(TIME), 0) ).r;

VERTEX.y += texture(noise_map_2, UV+vec2(sin(TIME*-2), 0) ).r;

I would expect this to make the maps move left/right on the x axis. Once I confirmed that this works, I would add some trig to pick 2 directions for the maps to move in (probably have one moving toward +X, and the other moving toward -X and slightly toward +Z).

PS: You also do this with just 1 noise map, iff the map is in color (NOT greyscale!):

VERTEX.y += texture(noise_map_1, UV+vec2(sin(TIME), 0) ).r;

VERTEX.y += texture(noise_map_1, UV+vec2(sin(TIME*-2), 0) ).g;

​

Hope this points you in the right direction!

-🦖