On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the third-class initial value problem with typ- icality and application is analyzed. The calculational method and concrete expressions of analytical solution about the well-posed initial value problem of the third-kind are given in the analytic function classes. Near an appointed point, the relevant theoretical and computational problems about analytical solution of initial value problem are solved completely in the meaning of local solution. Moreover, for other type ofproblems for determining solution, the computational method and process of their stable analytical solution can be obtained in a similar way given in this paper.
Nowadays, the nested grid model is widely used to increase the resolution of numerical model. An attempt to investigate the influence of the newly developed nesting technique of WRF model on the mesoscale numerical simulation of severe storm is described in this article. The results of sensitivity tests infer that the WRF model give more accurate and vivid prediction of severe storm with nesting scheme. As is shown in the tests, simulating value of the precipitation centers using nesting scheme are larger than those without using nesting scheme, which indicates that the simulating precipitation of nested storm is closer to the real rainfall. And there is obvious improvement of distribution of rain area and position of precipitation centers. According to the high resolution output data of the WRF model, deep and detailed analysis of characters of the mesoscale system that triggers the rainstorm is reported in this article, and the thermal and dynamical characters of this Meiyu front severe storm are also discussed.
The topological characteristics for the basic system of equations of atmospheric motion were analyzed with the help of method provided by stratification theory. It was proved that in the local rectangular coordinate system the basic system of equations of atmospheric motion is stable in infinitely differentiable function class. In the sense of local solution, the necessary and sufficient conditions by which the typical problem for determining solution is well posed were also given. Such problems as something about ＂speculating future from past＂ in atmospheric dynamics and how to amend the conditions for determining solution as well as the choice of underlying surface when involving the practical application were further discussed. It is also pointed out that under the usual conditions, three motion equations and continuity equation in the basic system of equations determine entirely the property of this system of equations.
