I animate the wave or ripples shader natural function in bump or displacement, it has completion, perpetration etc that can be oscillated for continual movement and centre H and V that can be translated for directional movement.
I was trying this out and looks promising.
Can the wave loop? Completion goes from 0 to 100 for the waves, but I’m not clear on if that means one cycle, or what.
0 would be at the beginning of the scene and 100 at the end. As Wendy mentioned you can use an oscillate tweener (or maybe a noise tweener for more randomness). If the scene is long and the wave action is slow, take a look to see if there’s a speed setting in the shader as well. If not, then the oscillate or noise tweeners are the way to go.