Abstract: In this study,a complete formof vertical vorticity tendency equation was deduced from the Ertel potential vorticity theory.Itincludes notonly dynamic elements,but also thermody namic elements,frictional dissipation and diabatic heating,and is applicable to three dimensional motion.It was proved that the classical vertical vorticity equation which is appropriate only for horizontal motion is merely a special case of this newly obtained complete formequation.Based upon this equation,the theory of Slant wise Vorticity Development(SVD) proposed by Wu et al.was also proved.According to this theory,when a parrel slides down a slantwise isentropic surface and the thermal par ameter CD is decreasing,its vertical vorticity develops.Toverify the theory,a θ coordinate model was employed to simulate the formation of a "southwest vortex" near the Tibetan Plateau.Results show that the vertical vorticity development due to SVD is about anorder of magnitude stronger than that due to convergence which has been traditionally emphasised.