Considering some simple topological properties of vorticity vector, the frozen-in property of vorticity herein is revis- ited. 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 se- vere 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.
With the definition of generalized potential temperature, a new generalized frontogenesis function, which is expressed as the Lagrangian change rate of the magnitude of the horizontal generalized potential temperature gradient, is derived. Such a frontogenesis function is more appropriate for a real moist atmosphere because it can reflect frontogenesis processes, in which the atmosphere in a frontal zone is typically characterized by neither completely dry nor uniform saturation. Furthermore, by derivation, the expression of generalized frontogenesis function includes both temperature and humidity gradients, which is different from and superior to the traditional frontogenesis function in moist processes, which also uses equivalent potential temperature. Diagnostic studies of real cases are performed and show that the generalized frontogenesis function in non- uniformly saturated moist atmosphere indeed provides a useful tool for frontogenesis, compared to using the traditional frontogenesis function. The new frontogenesis function can be used in situations involving either a strong temperature or moisture gradient and is closely correlated with precipitation.
Requested by the authors, the article entitled ＂Optical pumping nuclear magnetic resonance system rotating in a plane parallel to the quantization axis＂, published in Chinese Physics B, 2017, Vol. 26, Issue 9, Article No. 093301, has been withdrawn from the publication. The authors found that the axes in the rotating frame xy＇z are not all time-invariant, so Eq. （12） obtained from Eq. （11） is incorrect, and the conclusion is inaccurate.
A new frontogenesis function is developed and analyzed on the basis of a local change rate of the absolute horizontal gradient of the resultant deformation. Different from the traditional frontogenesis function, the newly defined deformation frontogenesis is derived from the viewpoint of dynamics rather than thermodynamics. Thus, it is more intuitive for the study of frontogenesis because the compaction of isolines of both temperature and moisture can be directly induced by the change of a flow field. This new frontogenesis function is particularly useful for studying the mei-yu front in China because mei-yu rainbands typically consist of a much stronger moisture gradient than temperature gradient, and involve large deformation flow. An analysis of real mei-yu frontal rainfall events indicates that the deformation frontogenesis function works remarkably well, producing a clearer mei-yu front than the traditional frontogenesis function based on a measure of the potential temperature gradient. More importantly, the deformation frontogenesis shows close correlation with the subsequent（6 h later） precipitation pattern and covers the rainband well, bearing significance for the prognosis or even prediction of future precipitation.
Potential vorticity(PV)has been widely applied as a tracer because of its property of conservation in frictionless,dry adiabatic flow.However,PV itself is more effective in describing the slow-manifold flow at large scale.Therefore,we wish to find a materially conserved invariant other than PV to diagnose severe weather such as growing and mature tropical cyclones,whose velocity and dynamic pressure vary rapidly and locally.Starting from the absolute motion equation after elimination of the pressure gradient term by introducing moist entropy and moist enthalpy,the baroclinic Ertel-Rossby invariant(ERI)in moist flow is derived by the Weber transformation.Furthermore,the material conservation property of moist ERI is proven.Besides the traditional moist potential vorticity(MPV)term,the invariant includes the moisture factor that is excluded in dry ERI and the term related to gradients of pressure,kinetic energy and potential energy that reflects the"fast-manifold"property.Therefore,it is more complete to describe the fast motions off the slow manifold for severe weather than is the MPV term.The moist ERI is then applied to diagnose a triple-typhoon system,and is compared with MPV and dry ERI.Contrastive analysis shows that moist ERI is a better tool to diagnose the movements and intensity variations of several coexisting typhoons.The moist ERI can signify the movement and development of a multi-typhoon system.It has wide application prospects for a real moist atmosphere.
