The theory of interaction between wave and basic flow
Ran Ling-Kun(冉令坤)a)† and John P. Boydb)
aLaboratory of Cloud-Precipitation Physics and Severe Storms (LACS), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China; bDepartment of Atmospheric, Oceanic, and Space Science, University of Michigan, Ann Arbor, Michigan, USA
Abstract This paper investigates the interaction between transient wave and non-stationary and non-conservative basic flow. An interaction equation is derived from the zonally symmetric and non-hydrostatic primitive equations in Cartesian coordinates by using the Momentum--Casimir method. In the derivation, it is assumed that the transient disturbances satisfy the linear perturbation equations and the basic states are non-conservative and slowly vary in time and space. The diabatic heating composed of basic-state heating and perturbation heating is also introduced. Since the theory of wave--flow interaction is constructed in non-hydrostatic and ageostrophic dynamical framework, it is applicable to diagnosing the interaction between the meso-scale convective system in front and the background flow. It follows from the local interaction equation that the local tendency of pseudomomentum wave-activity density depends on the combination of the perturbation flux divergence second-order in disturbance amplitude, the local change of basic-state pseudomomentum density, the basic-state flux divergence and the forcing effect of diabatic heating. Furthermore, the tendency of pseudomomentum wave-activity density is opposite to that of basic-state pseudomomentum density. The globally integrated basic-state pseudomomentum equation and wave-activity equation reveal that the global development of basic-state pseudomomentum is only dominated by the basic-state diabatic heating while it is the forcing effect of total diabatic heating from which the global evolution of pseudomomentum wave activity results. Therefore, the interaction between the transient wave and the non-stationary and non-conservative basic flow is realized in virtue of the basic-state diabatic heating.
Received: 21 May 2007
Revised: 29 July 2007
Accepted manuscript online:
Fund: Project
supported by the National Natural Science Foundation of China
(Grant Nos 40405011, 40575025 and 40475006).
Cite this article:
Ran Ling-Kun(冉令坤) and John P. Boyd The theory of interaction between wave and basic flow 2008 Chin. Phys. B 17 1138
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