涡旋流自发辐射惯性重力波的初步解析研究  

A Preliminary Analytical Study on the Spontaneous Emission of Inertia-gravity Waves from Vortical Flows

作　　者：赵南[1,2] 甘璐[1] 沈新勇[2,3] 

机构地区：[1]中国气象科学研究院灾害天气国家重点实验室,北京100081 [2]南京信息工程大学气象灾害省部共建教育部重点实验室,南京210044 [3]马里兰大学大气海洋科学系

出　　处：《应用气象学报》2010年第1期83-88,共6页Journal of Applied Meteorological Science

基　　金：灾害天气国家重点实验室科研业务费;国家自然科学基金项目(40775033);公益性行业科研专项经费项目(GYHY200806009);国家重点基础研究发展规划项目(2009CB421503;2004CB418301);江苏省青蓝工程(2009)共同资助

摘　　要：平衡流(或粗略地说涡旋流)调整目前被认为是惯性重力波产生的一种新的机制并被称为自发辐射问题。基于f平面上正压模式,该文对涡旋流自发辐射惯性重力波这一问题进行了初步解析研究。首先,通过该模式讨论了慢流形和平衡流的概念并强调了平衡流的涡旋运动特征。假定Froude数F《1且Rossby数ε=O(1)(即近似为平衡流的涡旋流包括了梯度风和其他非地转成分),于是基本方程可以写为有关惯性重力波的非齐次波动方程,其非齐次项与涡旋流的非平衡性质有关,而对于严格平衡的涡旋流,非齐次项消失,故涡旋流的非平衡性实际上提供了惯性重力波的强迫源,通过找出该方程的格林函数给出了反映自发辐射的非齐次解。在远离波源的区域,该非齐次解可以展开为远场形式,包括单极、偶极和四极辐射,另一方面,在波源区域以内及其附近,解的近场形式可以看作是慢流形的近似表达式。结果表明:与涡旋流相伴随的辐合/辐散运动主要由两部分组成,即由它自发辐射出的惯性重力波以及从属于平衡流的缓慢变化的辐合/辐散运动。与Ford的匹配渐近展开方法相比较,尽管不能给出更高阶近似,但格林函数法得到的非齐次解形式,在描写自发辐射方面更具物理直观性。The emission of inertia-gravity waves from the adjustment of balanced flows （or, basically, vortical flows） is currently regarded as a new mechanism of the production of inertia-gravity waves and referred as the spontaneous emission. Based on f-plane barotropic model, a preliminary analytical study on the spontaneous emission of inertia-gravity waves from vortical flows is conducted. First of all, the concept of slow manifold and balanced flow are discussed via this model and vortical property of the balanced flow is emphasized. Then, by assuming that the Froude number F and Rossby number satisfy and （implying that vortical flow approximately balanced flow that includes gradient wind and other ageostrophic contributions）, the basic equations are simplified to an inhomogeneous wave equation of inertia-gravity wave, while the inhomogeneous term is related to the imbalance of the vortical flow. This inhomogeneous term vanishes when vortical flow is exactly balanced. So the imbalance of the vortical flow provides a forcing or source to the inertia-gravity wave. The Green function of this equation is found to give the inhomogeneous solution standing for the spontaneous emission. In the field far from the wave ＂source＂, this inhomogeneous solution can be expanded into far-field form, including wave emission of monopole, dipole and quadrupole types. On the other hand, within or near to the ＂source＂ field, the near-field form can serve as an approximate expression of the slow manifold. These results indicate that the convergence/divergence fields accompanied with vortical flows is composed of two main parts, i. e. , the spontaneous emission of inertiagravity waves from vortical flows and slow-varying convergence/divergence filed slaved to the adjustment of balanced flow. Although higher-order approximation solution has already been given by Ford （2000） using method of matched asymptotic expansions, the Green function solution can depict the spontaneous emission in a more physical way.

关 键 词：平衡流 慢流形 惯性重力波 自发辐射 解析研究 

分 类 号：P433[天文地球—大气科学及气象学] O174.5[理学—数学]