This paper investigates the interaction between transient wave and non-stationary and non-conservative basic flow. An interaction equation is derived from the zonally symmetric and non-hydrostatic primitive equations in Cartesian coordinates by using the Momentum-Casimir method. In the derivation, it is assumed that the transient disturbances satisfy the linear perturbation equations and the basic states are non-conservative and slowly vary in time and space. The diabatic heating composed of basic-state heating and perturbation heating is also introduced. Since the theory of wave-flow interaction is constructed in non-hydrostatic and ageostrophic dynamical framework, it is applicable to diagnosing the interaction between the meso-scale convective system in front and the background flow. It follows from the local interaction equation that the local tendency of pseudomomentum wave-activity density depends on the combination of the perturbation flux divergence second-order in disturbance amplitude, the local change of basic-state pseudomomentum density, the basic-state flux divergence and the forcing effect of diabatic heating. Furthermore, the tendency of pseudomomentum wave-activity density is opposite to that of basic-state pseudomomentum density. The globally integrated basic-state pseudomomentum equation and wave-activity equation reveal that the global development of basic-state pseudomomentum is only dominated by the basic-state diabatic heating while it is the forcing effect of total diabatic heating from which the global evolution of pseudomomentum wave activity results. Therefore, the interaction between the transient wave and the non-stationary and non-conservative basic flow is realized in virtue of the basic-state diabatic heating.
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.
