  A new exact solution of the hydrodynamic equations is obtained in the form of
the Burgers vortex generalization (BVG)accounting for the medium rotation as a
whole and linear uniform friction. The nonlinear dissipative-centrifugal
instability(DCI)condition, associated with some superthreshold rotation angular
velocity and nonzero friction, for solid-body rotating core of BVG is obtained.
The new effect of cyclone-anticyclone vortex asymmetry, arising during DCI of
BVG vortex core, is shown to be similar to that observed for the atmospheres of
high speed rotating planets and laboratory experiments.
