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

作　　者：辜旭赞[1] 

机构地区：[1]中国气象局武汉暴雨研究所,湖北武汉430074

出　　处：《热带气象学报》2016年第5期622-633,共12页Journal of Tropical Meteorology

基　　金：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

摘　　要：从球坐标(Spherical coordinate)非地转、正压水平无辐散大气运动微扰方程出发,推导出球面Rossby波方程,证明球面Rossby波的物理机制仍然是绝对涡度守恒与卢效应,但基本气流以涡度形式参与了卢效应。因球面Rossby波偏微分方程不存在经向-纬向传播的"双向简谐波(传统Rossby波)"解,则将它做经向-纬向求导分离,从而得到关于球面经向风扰动的二阶偏微分方程及与之相应的仅作纬向传播的简谐波解,但待解的二阶偏微分方程不归于数理方程中的任何特殊函数,即证明不存在以连带Legendre函数为通解的Haurwitz波。采用传统Rossby波两个通解,当作球面Rossby波两类特解,做诊断分析表明,传统Rossby波正确反映球面Rossby波的(β-平面近似)"线性部分",但球面Rossby波及其纬向波速和群速都带有地球曲率性,并且存在奇点,其中,球面谐波扰动Rossby波仍然保持槽与脊纬向对称性,但"正弦扰动"与"余弦扰动"Rossby波有一定差别,而球面指数扰动Rossby波槽与脊不具备纬向对称性,后者可以解释东、西风带槽与脊一般为纬向非对称,还可以解释台风的纬向非对称结构。In this paper, from the quasi- hydrostatic, ageostrophic （with two curvature force terms in the horizontal momentum equations） and horizontal non-divergent （with curvature divergence term in the continuity equation） barotropic motions and the full perturbation equations in spherical coordinates, a partial differential equation, i.e. spherical Rossby wave equation, is derived. It shows that while the absolute vorticity conservation with the β effect is still demonstrated, the constant basic state zonal velocity with its constant vorticity can take part in the β effect. Because of that, in the partial differential equation of the spherical Rossby wave, there is no solution to the ＂meridionalzonal 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 second-order meridional partial differential equation of the meridional wind field remain unsolved in any known special 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 fl- plane＂ of the spherical Rossby wave. Therefore, we take the general solution of the classical Rossby wave as the specific solution （ no complementary solution） 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 

分 类 号：P432[天文地球—大气科学及气象学]