Research On Linear And Nonlinear Mesoscale Symmetric Instability Theory

In the mesoscale dynamic model, some problems on linear and nonlinear Mesoscale Symmetric instability theory have been studied in terms of different mesoscale models . In this thesis ,There are three parts . First, we make the Boussinesq approximation and study the effects of non-thermal wind and its spatial distribution on the superiority development of Mesoscale symmetric disturbance . After comparing superiority development under thermal wind balance to that under non-thermal wind, we find that non-thermal wind strengthens the superiority development of Mesoscale symmetric disturbance. At the same time ,the dynamic reasons for emerging non-thermal wind are noticed . Second , we discuss the influence of environmental referance potential temperture and thermal wind on Mesoscale symmetric instability .we find the expression of disturbance stream function and criterion of symmetric instability by analytical method and conclude that change caused by environmental referance potential temperture with height and thermal wind make critical Richardson number and disturbance critical half-wave length of symmetric instability larger ,That is to say ,they benefit the occurance of symmetric instability .Third , we study nonlinear perturbation analysis of mesoscale vertical circulation and evolution equation by means of f-plane .non-hydrostatic balance and filiter model. In this part , outstanding nonlinear characteristic of mesoscale. disturbance in vertical direction ,we obtain nonlinearsymmrtric disturbance eqution and disturbance amplitude' s evolution eqution by use of multi-scale and singular perturbation technique .The equation is an extensiveSchrodinger one. what s more ,we find it s solution.The work was supported by the National key program for developing Basic Sciences "Research on the Formation Mechanism and prediction Theory of Heavy climate and synoptic Disasters in China"(No. G1998040907).