Abstract: The development of vertical vorticity under adiabatic condition is investigated by virtue of the view of potential vorticity and potential temperature(PV-θ) and from a Lagrangian perspective. A new concept of generalized slantwise vorticity development(GSVD) is introduced for adiabatic condition. The GSVD is a coordinate independent framework of vorticity development (VD) which includes slantwise vorticity development (SVD) when a particle is sliding down the concave slope or up the convex slope of a sharply tilting isentropic surface under stable or unstable condition. The SVD is a special VD for studying the severe weather systems with rapid development of vertical vorticity. In addition, the GSVD clarifies VD and SVD. The criteria for VD and SVD demonstrate that the demand for SVD is much more restricted than the demand for VD. When an air parcel is moving down the concave slope or up the convex slope of a sharply tilting isentropic surface in a stable stratified atmosphere with its stability decreasing, or in an unstable atmosphere with its stability increasing, i.e., its stability θz approaches zero, its vertical vorticity can develop rapidly if its CD is decreasing.The theoretical results are employed to analyze a Tibetan Plateau(TP) vortex (TPV) which appeared over the TP then slid down and moved eastward in late July 2008, resulting heavy rainfall in Sichuan Province and along the middle and lower reaches of the Yangtze River. The change of PV2 contributed to the intensification of the TPV from 00:00 UTC to 06:00 UTC 22 July 2008 when it slid upward on the upslope of the northeastern edge of Sichuan basin, since the changes in both horizontal vorticity ηs and baroclinity θs have positive effects on the development of vertical and vorticity. At 06:00 UTC 22 July 2008, the criterion for SVD at 300 K isentropic surface is satisfied, meaning that SVD occured and contributed significantly to the development of vertical vorticity. The appearance of the stronger signals concerning the VD and SVD surrounding the vortex indicates that the GSVD concept can serve as a useful tool for diagnosing the development of weather systems.