热带气象学报2016，Vol.32Issue(5)：622-633,12.DOI:10.16032/j.issn.1004-4965.2016.05.005
论Rossby波在东、西风带中传播与频散II--球面Rossby波方程与诊断分析
RESEARCH ON THE ROSSBY WAVE ON PROPAGATION AND DISPERSION IN THE WESTERLIES AND EASTERLIES,PART Ⅱ:ANALYSIS AND DIAGNOSIS OF DEDUING SPHERICAL ROSSBY WAVE EQUATION
摘要
Abstract
In this paper,from the quasi-hydrostatic,ageostrophic (with two curvature force terms in the hori-zontal momentum equations)and horizontal non-divergent (with curvature divergence term in the continuity e-quation)barotropic motions and the full perturbation equations in spherical coordinates,a partial differential e-quation,i.e.spherical Rossby wave equation,is derived.It shows that while the absolute vorticity conservation with the βeffect is still demonstrated,the constant basic state zonal velocity with its constant vorticity can take part in the βeffect.Because of that,in the partial differential equation of the spherical Rossby wave,there is no solution to the “meridional-zonal propagating harmonic wave”as in the classical Rossby wave equation. However,one of the “zonal propagating harmonic waves”obtained by separating zonal derivatives,and a sec-ond-order meridional partial differential equation of the meridional wind field remain unsolved in any known spe-cial functions,including the associated Legendre function of the Haurwitz wave.It confirms that the linear part is right as “meridional-zonal propagating harmonic wave on the β-plane”of the spherical Rossby wave.There-fore,we take the general solution of the classical Rossby wave as the specific solution (no complementary solu-tion)of the spherical Rossby wave.What we do,thorough diagnosis and analysis,shows that both the zonal phase speed and group velocity of the spherical Rossby wave can deal with the curvature (tanφ)of the Earth and some singularities are allowed.The spherical harmonic Rossby wave can be zonally symmetric about its trough and ridge,though the sine perturbation Rossby wave and cosine perturbation Rossby wave have a lot of distinctions,while the spherical exponential Rossby wave must be zonally asymmetric about its trough and ridge, just like asymmetric troughs and ridges in westerlies and typhoons in easterlies.关键词
Rossby波/Haurwitz波/微扰方程/二阶偏微分方程/谐波扰动解/指数扰动解/β效应Key words
Rossby wave/Haurwitz wave/perturbation equation/second-order partial differential equation/harmonic perturbation/exponential perturbation/βeffect分类
天文与地球科学引用本文复制引用
辜旭赞..论Rossby波在东、西风带中传播与频散II--球面Rossby波方程与诊断分析[J].热带气象学报,2016,32(5):622-633,12.基金项目
国家自然科学基金项目“全球三次样条格式数值模式动力框架与理想场试验研究”（41275106）资助 （）
