>The stratosphere is called the stratosphere because the layers are stratified and the 30 hPa layer is considered the strongest QBO effect.

I have no idea how much stratification is going on in the atmossphere. I dont know but I could imagine that this Laplace equations have some connections with a set of equations which describe thicker layers (which may eventually be stratified) similar to how Eulerian fluids appear in Navier-Stokes (a very good overview is given by Tim van Beeks posts). I didnt fully read what you wrote in your post but it seems to be related to this fluid dynamics mechanism of simplification.

It may of course be the case that the images I saw or my perception of them were somehow erranous, but what I saw is a clear downward movement. So I currently imagine the QBO as being somekind of vortex line whose timeevolution is going down just as in the video you showed in 190. Hence in order to describe that the Laplace equations seem not sufficient.