On the physical significance and use of a set of horizontal and vertical helicity budget equations

ABSTRACT

For better understanding the variation of helicity and its governing mechanisms, based on the primary momentum equation under the local Cartesian coordinate, a set of horizontal and vertical helicity equations are derived in this study. On this basis, a storm-relative helicity budget equation is derived, the main factors that govern the variation of helicity are discussed, and the key mechanisms underlying the helicity variation are illustrated by using schematic images. Both scale analysis and real case diagnosis are used to compare the relative importance of different factors on the variation of helicity. For a meso-α system, it is found that: (i) horizontal helicity is much larger than vertical helicity, and they show significantly different variation mechanisms; (ii) for the vertical helicity, the vertical perturbation pressure gradient force, buoyancy, the divergence-related effect, and the conversion between vertical and horizontal helicity govern its variation (whereas, the conversion is negligible for the evolution of horizontal helicity); and (iii) baroclinity is crucial for the variation of horizontal helicity, but it is only of secondary importance for the vertical helicity variation.

GRAPHICAL ABSTRACT

摘要

本文基于大气运动方程组推导得到了水平与垂直螺旋度收支方程组，在此基础上，本文还率先推导了风暴相对螺旋度的收支方程组。本文利用物理图像揭示了不同影响因子（特别是水平与垂直螺旋度转化项）影响螺旋度变化的机理。利用经典的尺度分析与实际个例收支相结合的方法，本文着重讨论了中-α尺度天气系统水平与垂直螺旋度的演变，并确定了其各自的主要影响因子。这为相关的研究与预报提供了参考。

KEYWORDS:

• Horizontal helicity
• vertical helicity
• baroclinity
• kinetic energy

关键词:

• 水平螺旋度
• 垂直螺旋度
• 斜压性
• 动能

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the National Key R&D Program of China [grant number 2018YFC0809400], the Strategic Priority Research Program of the Chinese Academy of Sciences [grant number XDA17010105], the Key R&D Program of Jiangxi Province of China (Grant/Award Number: 20171BBG70005), and the National Natural Science Foundation of China [grant number 41775046].