typically called a cyclone - a tornado or hurricane are great examples. In theory, you could also include the likes of "black holes" and whirlpools.
Tornadoes
Cyclone
A Typhoon.
The Tempest
A transient, sometimes violent storm of thunder and lightning, often accompanied by rain and sometimes hail.
A violent storm
Yes a typhoon is a type of storm that rotates.
A small violent storm might include a thunderstorm or a tornado. The hurricanes tend to be much larger violent storms than tornadoes or thunderstorms.
Tornadoes
Typhoon
A solar flair.
The violent storm on the sun is called prominence
Tornadoes are the most violent storms on Earth. As such a tornado will usually be the most violent part of its parent storm.
Tempest.
A bayamo is a type of violent storm in the Caribbean.
Cyclone
A Typhoon.