In a cyclone, the pressure gradient force (PGF) and the Coriolis force sustain the spinning motion and causes the direction of spin (counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere). Are there vortices in the atmosphere which are sustained only by the pressure gradient force?
Tornadoes, land/waterspouts and supercell thunderstorm mesocyclones are examples of vortices where Coriolis is unimportant. Tornadoes are in cyclostrophic balance. Land and waterspouts (as well as non-supercell tornadoes) arise from horizontal convergence of vertical vorticity. The supercell mesocyclone spin originates as horizontal vorticity that is tilted and stretched into vertical vorticity. These vorticies can spin in either direction in either hemisphere.