Revisit to frozen-in property of vorticity Project supported by the Special Scientific Research Fund of the Meteorological Public Welfare of the Ministry of Sciences and Technology, China (Grant No. GYHY201406003), the Open Research Fund Program of Plateau Atmosphere and Environment Key Laboratory of Sichuan Province, China (Grant No. PAEKL-2015-K3), and the National Natural Science Foundation of China (Grant Nos. 41375054, 41575064, 91437215, 41405055 and 41375052)

• Published in: Chinese physics B 2017-08, Vol.26 (8)
• Main Authors: Yang, Shuai, Zuo, Qun-Jie, Gao, Shou-Ting
• Format: Article
• Language: English
• Subjects: baroclinic fluid; frozen-in property; material line element; vortex
• ISSN: 1674-1056
• DOI: 10.1088/1674-1056/26/8/089201

Considering some simple topological properties of vorticity vector, the frozen-in property of vorticity herein is revisited. A vortex line, as is analogous to velocity vector along a streamline, is defined as such a coincident material (curve) line that connects many material fluid elements, on which the local vorticity vector for each fluid element is also tangent to the vortex line. The vortex line evolves in the same manner as the material line that it is initially associated with. The vortex line and the material line are both oriented to the same directions, and evolve with the proportional magnitude, just like being 'frozen' or 'glued' to the material elements of the fluid under the barotropic assumption. To relax the limits of incompressible and barotropic atmosphere, the frozen-in property is further derived and proved in the baroclinic case. Then two effective usages are given as examples. One is the derivation of potential vorticity conservation from the frozen-in property in both barotropic and baroclinic atmospheres, as a theory application, and the other is used to illuminate the vorticity generation and growth in ideal cases and real severe weather process, e.g., in squall line, tornado, and other severe convection weather with vortex. There is no necessity to derive vorticity equation, and this method is very intuitive to explain vorticity development qualitatively, especially for fast analysis for forecasters. Certainly, by investigating the evolution of vortex line, it is possible to locate the associated line element vector and its development on the basis of the frozen-in property of vorticity. Because it is simple and visualized, it manifests broad application prospects.