An Analytical Study on the Differential Equation of Mesoscale Symmetric Instability under Deep Convection

Yuan-hong GUAN, Hong CHEN, Jie REN, Ting-wen ZHENG

Abstract


Based on a mesoscale model with the quasi-Bossinesq approximation, we found that the disturbance stream-function would be represented by a partial differential equation, and we then obtained the analytical solution of the equation. Further, it was shown that the amplitude of instability wave changes along the direction of the characteristic line, if we consider the interaction between the change of environmental potential temperature with height and thermal wind. Besides, the interaction increases the Critical Richardson Number of Symmetric Instability (Ric  Ric0 ) , and enlarges critical half wave-length of perturbation ( 2 2 c c0 L  L ), which favors the occurrence of the Symmetric Instability ( c0 Ri and 2 c0 L here are numbers when the interaction is not considered as in previous studies).

Keywords


Differential equation, Analytical solution, Dynamical mechanism, Mesoscale symmetric instability.


DOI
10.12783/dtetr/icamm2016/7339

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