Does that kind of thing really happen? Let's try it out in an experiment.

We made a stable stratification in a donut-shaped water tank using salt, and assumed it to be the equatorial stratosphere. In the real stratosphere, waves are transmitted from below, however, it isn't easy to cause waves at the bottom of a water tank. Instead, we turned

the model upside-down

and vibrated a rubber membrane on the surface of the water with air, and created waves (internal gravity waves) that way.

Waves are vertically symmetrical, so turning the model upside-down essentially doesn't affect the model. The problem is whether or not a one-way current will be formed by the waves oscillating symmetrically back and forth, and if that current will reverse as planned.