基于螺旋度的中尺度平衡方程及非平衡流诊断方法

在回顾大尺度准地转平衡理论、各种平衡方程、平衡模式及非平衡流诊断工具的基础上,对平衡方程、非平衡方程给出了具体的定义.并在此基础上,进一步考虑中尺度强对流天气系统的特征,指出中尺度也有平衡运动的存在.但是由于中尺度对流系统中强烈的辐散风效应以及不可忽略的垂直运动的作用,以散度方程为基础的各种近似平衡方程不足以描述中尺度强对流天气系统的平衡运动,进而提出了从能够同时考虑旋转、辐散及垂直运动作用的螺旋度方程出发,寻找中尺度的平衡方程.在所得的平衡方程基础上,给出了相应的平衡模式和非平衡方程.并进一步将非平衡方程分解,用来诊断非平衡过程的平衡破坏和平衡恢复两个阶段,同时将它们与水平螺旋度和垂直螺旋度联系起来.

Mesoscale Balance Equation and the Diagnostic Method of Unbalanced Flow Based on Helicity

By retrospecting large-scale quasi-geostrophy theory and many kinds of balance equations and models,including some methods of the diagnosis of unbalanced flow,the authors make the concrete mathematics definitions for balance equations and imbalance equations as well as point out their physical meanings.Furthermore,the authors analyze many mesoscale strong-convective systems and conclude that there also exist balanced motions in the mesoscale convective system.But in the mesoscale strong-convective system the divergent wind is strong and the vertical motion cannot be neglected,so all those balance equations based on divergent equation are not adapt to be used in the analysis of mesoscale balanced or unbalanced motion.Thus it is presented to construct a kind of new balance equation which includes the divergence,vorticity and vertical motion simultaneously.After the scale-analysis of helicity equation,the authors find a balance equation which meets well that condition.On the basis of this,the authors infer horizontal divergence equation,vertical vorticity equation,continuity equation and thermal dynamic equation under the same approximations.All these equations form a set of new balance model.As to the new balance equation,the imbalance equation is to retain all other relative small terms in the primitive equation,thus it is equal to the helicity equation.If the unbalanced process is divided into two periods,the imbalance equation can be decomposed into two equations.Furthermore,it is found that the two periods of the unbalanced flow can separately be connected to the horizontal helicity and vertical helicity,that is,the horizontal helicity and vertical helicity can be taken as the tools of diagnosing unbalanced flow.