Let's take a look at the experiment results. The white dots on the screen are the neutrally floating beads.

Looking at this, a current is flowing horizontally around the water tank in addition to the short-cycle waves. Further, you can see that the current is reversing periodically from the bottom of the tank (i.e. the top of the stratosphere).

This happens because the wave does not simply oscillate back and forth but

the waves have momentum

in the direction of the phase velocity. The wave which passes through the current carries reverse momentum opposite to the current far away. This momentum reverses the current.