论Rossby波在东、西风带中传播与频散Ⅰ——谐波扰动Rosshy波和指数扰动Rosshy波

RESEARCH ON THE ROSSBY WAVE ON PROPAGATION AND DISPERSION IN THE WESTERLIES AND EASTERLIES,PART Ⅰ:HARMONIC PERTURBATION ROSSBY WAVE & EXPONENTIAL PERTURBATION ROSSBY WAVE

传统Bossby波最初求解于局地直角坐标系(Cartesian coordinate)准地转、准水平无辐散正压大气运动微扰方程,在所谓"卢平面"近似下,归于求解一个关于经向风扰动的二阶常微分方程,它存在可在卢-平面经向-纬向传播的简谐波解,其物理机制是,扰动气流在科氏参数随纬度变化(所谓"β效应")作用下的绝对涡度守恒。本文先讨论传统Rossby波二阶常微分方程"经向谐波扰动-纬向简谐波"(谐波扰动Bossby波)通解,指出传统Rossby波只被描述为谐波扰动Bossby波,即在扰动区内形成谐波扰动可在扰动区外作经向-纬向简谐波的连续传播;又讨论数学上存在的"经向指数扰动-纬向简谐波"(指数扰动Bossby波)另一通解,并且分析与比较两个通解的纬向波速与群速诊断方程。认为,谐波扰动和指数扰动"传播"与"频散"可以在相邻边界上保持为分段"零阶"连续且为有界。从而Bossby波定义为:大气运动受到连续或分段"零阶"连续谐波扰动和(或)指数扰动和(或)其它函数扰动、在β效应与绝对涡度守恒作用下、可以在全球(东、西风带)传播与频散的波动,作"纬向简谐波"传播是Bossby波的唯一识别特征。最后,作为对传统Rossby波的补充,单纯用指数扰动Rossby波波速和群速方程,对西风带中的长-中-短波槽脊传播、阻塞高压建立与后退、大槽建立与寒潮,以及气候上的遥响应,做出新的解释,更对东风带中的东风波(倒槽)与台风传播、副热带高压西进与东退,做出传统Bossby波尚不能解释的初步解释。

The classical Rossby wave is sought for solution from atmospheric perturbation equations for the quasihydrostatic, quasi-geostrophic, horizontal quasi-nondivergent, and barotropic motions in the Cartesian coordinates. The solution of ＂meridional- zonal propagating harmonic wave＂ was obtained by solving a second-order ordinary differential equation, under the β-plane condition, from a second-order partial differential equation of a disturbance in meridional wind field. The classical Rossby wave owes its existence to the variation of the Coriolis parameter with latitude （ the so-called ＂β effect＂ ） and holds its absolute vorticity conservation. In this paper, first a general solution of ＂meridional harmonic perturbation- zonal harmonic wave＂ （harmonic perturbation Rossby wave） is presented by solving the traditional Rossby wave equation of a second-order ordinary differential equation, which is equivalent to the traditional Rossby wave in that the harmonic perturbation Rossby wave formed in disturbance domain could continuously travel, as the meridional-zonal propagating harmonic wave, outside the domain. Likewise, the other general solution of ＂meridional exponential perturbation-zonal harmonic wave＂ （exponential perturbation Rossby wave ） is introduced and compared with the harmonic perturbation Rossby wave with both phase speed and group velocity for their functional characteristics. So, we can redefine the Rossby wave just as zonal harmonic wave propagating and dispersing in the westerlies and easterlies with the effect and absolute vorticity conservation, which proceeds from an initial disturbance in the form of some harmonic, exponential and/or linear perturbation（s） that can be zero-order continuous or sectional-continuous each other in meridional wind field. Furthermore, just in terms of the formulae of phase speed and group velocity of the exponential perturbation Rossby wave, we give some preliminary analysis to interpret their motions of troughs and ridges as long, middle or short waves in the westerlies, including the blocking high＇ s formation and de- cline, long trough establishment and cold wave, generation of convective system and climate teleconnection, and to study the motions of easterly waves （ inverted troughs）, typhoon wave propagating and subtropical ridge moving westward/eastward in the easterlies. In general, all of the weather systems could exist as Rossby waves correlated with their perturbations of harmonic and/or exponential function form （s） in the meridional wind field.