Cavitation is something that came to mind as well. However I can’t think of any way we can stretch things to include the OP’s “in our atmosphere” bit. Maybe with a hypersonic projectile.
Air mostly behaves as a fluid, so fluid dynamics apply within some useful regions of physics. But its low density and viscosity make some effects hard. Then it starts to compress as we push things further and it all gets evil.
Perhaps the radiative pressure from a nuke can clear a region of air reasonably effectively. You have other problems than lack of air if you are there.
A fast-moving meteor entering the atmosphere must be creating a little bit of cavitation in its wake, surely.
Not actually the atmosphere, because its under water…
Fast moving water in rivers may contain vacuums when the water flows over a sharp hard edge ? eg rock or cliff (waterfall).
At the drop off, the water is experiencing pressure, but water was a density of 1 kg per litre, and so the pressure on water can only result in a certain acceleration. When the slope of the drop off is more than the slope that the acceleration curve can meet, a vacuum occurs.
Its not a perfect vacuum, because water vapour will move much faster, but thats its way less than 1% density …quite a serious vacuum. This is the popping in bubbling brooks ?
In the atmosphere… no storms may reduce the pressure 10%… eg from 1000 milliBars to approx 900 mB, but over many km … whats the pressure inside a tornado ? well turns out its also only as low as 100 mB less than the surrounding atmosphere, but over the thickness of the wall, eg 5 metres, its a steep change, just not an extreme in absolute pressure change, no where near vacuum.