Derivation of baroclinic Ertel-Rossby invariant-based thermally-coupled vorticity equation in moist flow

doi:10.1088/1674-1056/23/11/119201

Abstract For the potential vorticity (PV) invariant, there is a PV-based complete-form vorticity equation, which we use heuristically in the present paper to answer the following question: for the Ertel-Rossby invariant (ERI), is there a corresponding vorticity tendency equation? Such an ERI-based thermally-coupled vorticity equation is derived and discussed in detail in this study. From the obtained new vorticity equation, the vertical vorticity change is constrained by the vertical velocity term, the term associated with the slope of the generalized momentum surface, the term related to the horizontal vorticity change, and the baroclinic or solenoid term. It explicitly includes both the dynamical and thermodynamic factors' influence on the vorticity change. For the ERI itself, besides the traditional PV term, the ERI also includes the moisture factor, which is excluded in dry ERI, and the term related to the gradients of pressure, kinetic energy, and potential energy that reflects the fast-manifold property. Therefore, it is more complete to describe the fast motions off the slow manifold for severe weather than the PV term. These advantages are naturally handed on and inherited by the ERI-based thermally-coupled vorticity equation. Then the ERI-based thermally-coupled vorticity equation is further transformed and compared with the traditional vorticity equation. The main difference between the two equations is the term which describes the contribution of the solenoid term to the vertical vorticity development. In a barotropic flow, the solenoid term disappears, then the ERI-based thermally-coupled vorticity equation can regress to the traditional vorticity equation.

Keywords: vorticity equation derivation Ertel-Rossby invariant

Received: 11 February 2014
Revised: 13 May 2014
Accepted manuscript online:

PACS:	92.70.Gt	(Climate dynamics)
	92.70.Cp	(Atmosphere)
	92.60.Qx	(Storms)

Fund: Project supported by the National Basic Research Program of China (Grant No. 2013CB430105), the Key Research Program of the Chinese Academy of Sciences (Grant No. KZZD-EW-05-01), the National Natural Science Foundation of China (Grant Nos. 41375054 and 41375052), and the Special Scientific Research Fund of the Meteorological Public Welfare of the Ministry of Sciences and Technology, China (Grant No. GYHY201406003), and the Opening Foundation of the State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences (Grant No. 2012LASW-B02).

Corresponding Authors: Yang Shuai
E-mail: ys_ys@126.com

Cite this article:

Yang Shuai (杨帅), Gao Shou-Ting (高守亭) Derivation of baroclinic Ertel-Rossby invariant-based thermally-coupled vorticity equation in moist flow 2014 Chin. Phys. B 23 119201

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Derivation of baroclinic Ertel-Rossby invariant-based thermally-coupled vorticity equation in moist flow

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