A low-area storm with high winds rotating about a centre of low atmospheric pressure

One word substitute is Cyclone.

Cyclone: a system of winds rotating inwards to an area of low barometric pressure, with an anticlockwise (northern hemisphere) or clockwise (southern hemisphere) circulation; a depression.
Tornado: a mobile, destructive vortex of violently rotating winds having the appearance of a funnel-shaped cloud and advancing beneath a large storm system.
Typhoon: a tropical storm in the region of the Indian or western Pacific oceans.
Hurricane: a storm with a violent wind, in particular a tropical cyclone in the Caribbean.