Plug a Time node into a Sine Node. Multiply this by a factor of your choice. Multiply this by a Float3 with an RGB value of (0,0,1) to get a vector that = (0,0,Wave). Plug this into the World Position Offset of the material. It will now move in a sine wave pattern.
You can use anything to modulate the vector, not just a Sine wave.
A panning world space noise texture would more closely resemble your video, for example. Same story, multiply the desired offset by (0,0,1) and it will apply it only in the Z direction. This sort of panning texture is often how wind is faked when controlling grass.
The WPO expects a V3 where (R,G,B) represents an offset amount in each of those directions as (X,Y,Z). By plugging in an input with (0,0,Z) you’re telling it to offset the entire mesh in the Z direction only.
If the event you only want to move part of the mesh, such as the surface, you would also multiply the result by a mask to control how strong the effect is on a given vertex. But since you want the whole mesh to move, you will not need any mask.