Usually we see wave crests propagating, and since the eye can’t stop following them, it is easy to assume that they transport water with them instead of leaving the water put and just transporting energy. But here is an example of a situation where bubbles as tracers for water “parcels” show that, despite large waves passing, the water itself only moves up and down, and a little back and forth, but isn’t really transported away:

Of course there is some Stokes drift, but compared to the wave speed the speed associated with that is tiny…