Abstract: The circulation structure of a common vortex that occurs within the planet boundary layer was studied. It is shown that under the friction of a boundary layer, a weaker vortex may lead to the obvious radial flow and cause the convergence from all around to the centre of the vortex. The convergence yields a vertical motion, the magnitude of which near the centre of the vortex approaches the order of the vertical motion in the meso-scale systems. The damping of unsteady, axisymmetrical vortex circulation was analyzed by means of multiparameter purterbation method.