This upward and downward movement may be simply a phase relationship between the stratified layers. Almost all of the momentum is tied up in the horizontal wind, and so the vertical momentum transfer is minimal in the stratosphere. Dropping in to the troposphere, there is more drag so the wind speed will always lag there. I should add a drag term to the equations to see how it changes. It should get weaker with an accompanying phase lag.

Hard to understand these vertical movements when the horizontal movements are that strong.