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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
Research article
27 Jan 2016
Review status
This discussion paper is a preprint. It has been under review for the journal Nonlinear Processes in Geophysics (NPG). The revised manuscript was not accepted.
A Mathematical Framework for the Description of Convection in Meso-scale Synoptic System
Nan Zhao1 and Masaaki Takahashi2 1State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, 100081, China
2Atmosphere and Ocean Research Institute (AORI), University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, 277-8568, Japan
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.

Citation: Zhao, N. and Takahashi, M.: A Mathematical Framework for the Description of Convection in Meso-scale Synoptic System, Nonlin. Processes Geophys. Discuss.,, 2016.
Nan Zhao and Masaaki Takahashi
Interactive discussionStatus: closed
AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment
Printer-friendly Version - Printer-friendly version      Supplement - Supplement
RC1: 'Review', Anonymous Referee #1, 26 Feb 2016 Printer-friendly Version 
AC1: 'reply to reviewer#1', Nan Zhao, 07 Mar 2016 Printer-friendly Version Supplement 
RC2: 'Review', Anonymous Referee #2, 28 Feb 2016 Printer-friendly Version 
AC2: 'reply to reviewer#2', Nan Zhao, 09 Mar 2016 Printer-friendly Version 
SC1: 'Fujiwhara effect', Nan Zhao, 10 Mar 2016 Printer-friendly Version 
SC2: 'closed equation', Nan Zhao, 11 Mar 2016 Printer-friendly Version 
Nan Zhao and Masaaki Takahashi
Nan Zhao and Masaaki Takahashi


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Latest update: 24 Nov 2017
Publications Copernicus
Short summary
Convection in meso-scale synoptic system is usually attributed to problem of instability of balanced basic state, although no such balanced basic state can be found in real atmosphere. This paper develops a theory for unbalanced basic state, which can treat key issues of convection such as the triggering mechanism of convection and two-way interaction betwenn convection and unbalanced basic state.
Convection in meso-scale synoptic system is usually attributed to problem of instability of...