A high resolution shallow-water model is designed to study the roles which the topographical parameter and latitudinal basic flow play in the propagation of vortex Rossby waves and typhoon tangential velocity changes. With no latitudinal flow, the horizontal scale effects of island terrain on the vortex Rossby waves propagation show that the disturbance vorticity follows a clockwise island-circulating path more significantly, the local maximum wind speed amplitude reduces more sharply, the maximum mean azimuthally tangential wind spins down more substantially, when the topographic horizontal scale augments. With the latitudinal basic flow, the evolution of local wind and mean velocity are affected by the distance changes between TC and the terrain and the time length of topographic action: the local wind amplitude intensifies and the mean velocity diminishes while the distance is shortening; the opposite is true while TC is away from the terrain gradually.
This paper reviews the main theoretical progress of mesoscale weather dynamics since 2003, including： （1） The dynamic mechanisms of balanced and unbalanced flow are applied to study the genesis and development problems of mesoscale circulation. The symmetric instability and transverse-wave instability are analyzed in line and vortex atmosphere convection, and further research has been done on nonlinear convective symmetric instability. The interaction between forced convection and unstable convection and the wave characteristics of mesoscale motion are also discussed. （2） Intermediate atmosphere dynamic boundary layer models are developed. The complicated nonlinear interaction is analyzed theoretically between the atmospheric boundary layer and the free atmosphere. The structure of the topography boundary layer, atmospheric frontogenesis, the structure and circulation of the low-level front and other boundary layer dynamic problems are discussed. （3） The formation and development of meso-β-scale rainstorms under the background of the East-Asia atmosphere circulation are diagnosed with the variation of MPV （moist potential vorticity） anomalies. And some physical vectors are modified and applied in the moist atmosphere.
