MESOCYCLONE

A mesocyclone is a vortex of air, approximately 2 to 10 km in diameter (the  mesoscale of meteorology), within a convective storm. That is, it is air that rises and rotates around a vertical axis, usually in the same direction as low pressure systems in a given hemisphere. They are most often cyclonic, that is, associated with a localized low-pressure region within a severe thunderstorm. Such storms can feature strong surface winds and severe hail. Mesocyclones often occur together with updrafts in supercells, where tornadoes may form.
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A storm-scale region of rotation, typically around 2-6 miles in diameter and often found in the right rear flank of a supercell (or often on the eastern, or front, flank of an HP storm ). The circulation of a mesocyclone covers an area much larger than the tornado that may develop within it.
Properly used, mesocyclone is a radar term; it is defined as a rotation signature appearing on Doppler radar that meets specific criteria for magnitude, vertical depth, and duration. Therefore, a mesocyclone should not be considered a visually-observable phenomenon (although visual evidence of rotation, such as curved inflow bands , may imply the presence of a mesocyclone).