In brief, mountain waves happen when strong winds from a stable airmass at altitude blow perpendicular to a mountain range and when there is a big contrast between wind speeds at high and low altitude. When the air mass encounters a barrier and gets shoved upward…
…it falls downward, seeking equilibrium, on the lee side of the mountains. Its momentum makes it overshoot, so then it bounces up again, and overshoots again, and this repeats, making the wave. Bouncing back aloft brings it back to where wind speeds are higher, enhancing the wind speed each time.
…I think. I’m not an atmospheric scientist. But the key conditions are stable air mass with strong winds aloft that blow perpendicular to mountain ranges. When the stable air mass moves off to the east, the conditions will subside.
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