Revisit to frozen-in property of vorticity

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.     

An Approximation of the Steady Gravity Wave Induced by Mountainous Topography

An approximation of the orography gravity wave, which is induced by mountainous topography, is considered in this study. By assuming that the horizontal wind is a linear function with respect to the height, the approximating equation for the orography gravity waves is obtained. Four topography functions are considered in this study and the orography gravity wave are obtained. The dynamics of the orography gravity wave is then discussed by considering the effect of the surface topography and background horizontal wind.     

Image of local energy anomaly during a heavy rainfall event

A clear and interesting image of local total energy anomaly(EA) is depicted for a heavy rainfall event in this study.Before the convection development, it exhibits a positive local EA, implying local total energy(TE) experiences heaping up to prepare for the future system development. As the convection grows, it transforms into an opposite spatial modality with negative EA dominant, which means that the local TE is consumed to feed the convection growth in the middle and lower levels. The local total EA has consistent variation regular in intensity with severe weather system evolution. By utilizing the local TE budget equation in variable density fluid, the flux divergence of energy and its components are investigated, which could account for the local TE variation better. To relax the restriction and complexity introduced by identifying sporadic and alternative positive/negative signals of EA, the method taking the absolute-value operator on energy flux divergence is used to further simplify analyses. The derived characteristic signal of absolute EA is clearer and cleaner than before.Thus, the EA could be illustrated based on the active degree of energy supply/consumption in a generalized sense whatever positive or negative anomaly should be it, which could be used easily to identify and even predict the system development for operational application. Note that, although two sets of methodologies are used to define EA herein, they play absolutely different roles in nature throughout the whole context. For example, the taking-perturbation method provides a diagnostic tool to portray a preliminary sketch and to give sufficient necessity of this research, while tendency equation of local TE illuminates more predictive sense and accounts for future local EA related to following system evolution. Therefore, the latter could be a more effective tool to routine usage.