A Mathematical Framework for the Description of Convection in Meso-scale Synoptic System

Abstract. By introducing an appropriately-defined imbalanced vortical flow as the basic state, our previous study has extended conventional instability theories of balanced flows for meso-scale convection. It considered not only the apparent instability of the imbalanced basic state but also the two-way interaction between convection/IGWs and this imbalance. This paper reports our new progresses of such framework. A regular perturbation method on the nonlinear case is performed to have an insight into the triggering mechanism of convection. It seems convection can be triggered in resonance either with imbalance forcing or with nonlinear interaction among different modes. Even if all these cannot happen, an imbalance forcing with strong enough magnitude may eventually trigger convection. These are essentially different from the concept of Liyapunov instability, in which an initial disturbance is necessary. In some simplified but relatively general setting, all modes that may contribute to the structures of meso-scale convection are investigated, including free modes of convection and forced modes of convection/IGWs by imbalance. Particularly, the influences of arbitrary distribution of stratification on qualitative properties of free and forced convection/IGW modes are discussed. Also, approximate forms of forced convection/IGW modes suitable for application are given for horizontally uniform stratification. Finally, to demonstrate the potential application of our theory, the concept of imbalance forcing and balanced flow adjustment is shown to be useful in the understanding of key issues in typhoon study, such as its possible role in typhoon's self-organization, Fujiwhara effect and the relationship between typhoon’s asymmetric structure and its track recurvature.