Mesoscale Balance Equation and the Diagnostic Method of Unbalanced Flow Based on Helicity
Mesoscale Balance Equation and the Diagnostic Method of Unbalanced Flow Based on Helicity
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发表时间：
2006
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通讯作者：
Gao Shou;Zhou Fei
中科院分区：
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作者：
Gao Shou;Zhou Fei
通过对大尺度准地转理论和各种平衡方程、模型的回顾，以及对不平衡流诊断的一些方法，对平衡方程和不平衡方程给出了具体的数学定义，并指出了它们的物理意义。作者分析了许多中尺度强-中尺度对流系统中也存在平衡运动，但在中尺度强对流系统中，对流系统辐散风强，垂直运动不可忽略，因此，基于散度方程的平衡方程不适合于中尺度平衡或不平衡运动的分析，本文提出构造一种新的平衡方程，同时考虑了散度、涡度和垂直运动的新的平衡方程。本文通过对螺旋度方程的尺度分析，找到了一个能很好地满足这一条件的平衡方程。在此基础上，在相同的近似下，推导出了水平散度方程、垂直涡度方程、连续性方程和热力学方程。所有这些方程构成了一组新的平衡模型。对于新的平衡方程，不平衡方程是为了保留原始方程中的所有其他相对小的项，因此它与螺旋度方程是等价的，如果把不平衡过程分为两个阶段，不平衡方程可以分解为两个方程，而且发现不平衡流的两个阶段可以分别与水平螺旋度和垂直螺旋度联系起来，即，水平螺旋度和垂直螺旋度可以作为诊断不平衡流动的工具。
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.