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
GU Xu-zan
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.
Keywords：Rossby waveHaurwitz waveperturbation equationsecond-order partial differential equationharmonic perturbationexponential perturbationβeffect
Publication Date：2016-01-01
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：12( 622-633 )