… but what can I say, I have not seen any such effect in modern games.
Military games are full of them. I especially remember the ones in the Battlefield series, because they look really great. Here you can see a setup they used with such an pillar:
Afaik: They capture a smoke sim as a flipbook with a 6-way “lightmap” and then use particles with those flipbooks.
You can look at this thread on how such an setup works:
I can recommend Embergen for realistic smoke, because they can export everything you need at once. If you are using UE4 and want more styalized looking smoke, I can recommend Fluid Ninja.
Another Method would be to use a big mesh with tessellation and animated WPO (just like you’d do it with oceans), if it should look very thick.