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1.
大气非线性波动方程的解 总被引：3，自引：5，他引：3
本文从非线性大气运动方程出发,用比较简洁的方法,求得了大气非线性惯性波、非线性重力内波和非线性Rossby波的周期解,这些解反映了非线性大气波动的特色。分析指出:对有限振幅的惯性波和重力内波,振幅大的波传播越快,而有限振福的非线性Rossby波,振幅大、波长长的波传播越慢;本文还分析了这些解的某些可能的实际意义。 这些非线性波的研究提供了解非线性方程的新的途径,而且,它可以与大家熟悉的线性波动进行比较。对于天气预报和大气湍流的研究都有一定的意义。 相似文献
2.
Nonlinear waves in barotropic model 总被引：2，自引：0，他引：2
In this paper, from the system of equation describing a barotropic atmosphere using the method of Taylor expansion for the nonlinear terms, the periodic solutions of the nonlinear inertio-surface gravity waves and Rossby waves have been obtained.The finite-amplitude nonlinear inertio-surface gravity waves and Rossby waves with horizontal divergence satisfy all the KdV equation. The solutions are all the cnoidal function, i, e, the cnoidal waves which in-clude the linear waves and form the solitary waves under certain conditions. For the finite-amplitude Rossby waves with horizontal divergence, we find the new dispersive relation including both the wave number and the amplitude parameter. In case of small amplitude it is reduced to the Yeh formula. It is shown that the larger the amplitude and width, the faster the finite-amplitude inertio-surface gravity waves and the slower the finite-amplitude Rossby waves with horizontal divergence propagate. The blocking or cut-off system in which the amplitude and width are large may be considered as Rossby solitary waves. 相似文献
3.
非线性正压Rossby波的精确解 总被引：1，自引：0，他引：1
本文从半地转近似下的正压大气运动方程组出发,导出了非线性正压Rossby波所精确满足的KdV方程,求得了椭圆余弦波解和孤立波解,并讨论了非线性波动的波速公式及其振幅与其它波参数间的关系。同时指出,在对大气模式进行数学简化时必须尽可能保证原模式所具有的一些守恒关系,否则有可能使原问题的解受到歪曲。 相似文献
4.
半地转近似下的非线性波 总被引：1，自引：4，他引：1
本文应用半地转的概念分析和求解了正压和斜压的大气运动。指出:(1)在水平无辐散或准地转条件下求单波解无法表现非线性作用的困难,可以应用半地转的假定来解决。为了避开上述困难,不得已仅保留部分非线性项,但为了准确表征大尺度运动,最好应用半地转假定,保留全部非线性项。(2)准地转的假定可以滤去快速波动,半地转的假定同样也可以滤去快速波动,而且半地转条件下的Rossby波具有充分的非线性特征。所以,它为讨论非线性问题提供了一个途径。 相似文献
5.
冬季风期间南海地区冷涌的动力学分析 总被引：3，自引：0，他引：3
利用一个部分非线性的二维经向重力内波动力模式，通过求行波解，对冬季风期间南海冷涌的传播形式，传播特征和传播速度进行了分析，并讨论了大尺度经向环流及其垂直结构、热力作用、层结稳定状况和初始扰动条件对冷涌传播的作用。主要结论是：冷涌的传播表现为具有非线性效应的无频散或弱频散的重力行波，其向南传播速度远大于平流速度而接近于重力内波波速；不同流场和位温的初始扰动状况决定了冷涌将以周期重力行波或者以孤立重力 相似文献
6.
Philip D. Thompson 《Meteorology and Atmospheric Physics》1988,38(1-2):89-94
Summary In this note we find special solutions of the nonlinear shallow-water equations. From the first integrals of the potential vorticity and energy equations for steady flow we derive a single equation in the streamfunction. In the limiting case of very small Froude number, that equation has no solutions corresponding to gravity waves. Under a nonlinear transformation of dependent variable, it becomes a linear equation whose solutions are related to Haurwitz's solutions for nondivergent barotropic flow in spherical surfaces. The distinguishing feature of these solutions is that the streamlines coincide with contours of the free surface: thus, although the height of the free surface varies, the motions of the fluid are horizontal, and the flow is nondivergent.The solutions are easily modified to correspond to Rossby waves propagating eastward or westward without change of shape.The National Center for Atmospheric Research is sponsored by the National Science Foundation.This paper is dedicated to the memory of my scientific mentor and old friend, Bernhard Haurwitz. 相似文献
7.
Wang Xingbao 《Acta Meteorologica Sinica》1995,9(4):488-500
Effects of topography on the propagation and development of inertia gravity waves areinvestigated by means of WKBJ method.The equation of wave action conservation is obtained.It isfound that the inertia gravity wave tends to propagate to the higher elevation area,meanwhile theamplitudes of the waves increase.While the inertia gravity waves propagate to a lower elevation area,their amplitudes decrease. 相似文献
8.
《Dynamics of Atmospheres and Oceans》1998,28(2):107-125
Experiments are performed in a 13-m cylindrical tank to study the generation of interfacial internal waves by barotropic sinusoidal waves passing over a slope. At each tidal cycle, there are two waves generated, one propagating onshore and the other propagating offshore. The amplitude of the waves increases with increasing forcing and evolves as nonlinear waves if the shelf width is smaller than the wavelength of the baroclinic tide. Rotation does not modify the generating mechanism but the amplitude of the generated waves decreases with increasing rotation rate; also no internal waves are generated when the forcing period is larger than the inertial period, and at high rotation rate, there are only dispersive waves propagating from the shelf break region. The experiments covered a large range of internal Froude number, Rossby number and temporal Rossby number and compare well with in situ observations. 相似文献
9.
A review on the progress in the research of nonlinear atmospheric waves, especially the nonlinear Rossby waves is made in this paper. Many results reported here have been obtained in Peking University. 相似文献
10.
利用佛山地区2017年1月至2019年10月高精度微压计数据,统计分析佛山地区不同类型雷暴天气的大气重力波频谱特征,结果表明:雷暴天气与重力波的生成、发展密切相关,长周期（90～270 min）、短周期（1～90 min）重力波在不同类型雷暴天气有明显的差异。不同类型雷暴期间,都有大振幅（≥110 Pa）、宽周期范围的长周期重力波,但是强雷暴期间长周期重力波的振幅更大、周期范围更宽,中心振幅大于130 Pa的重力波发生的比率更高;不同类型雷暴激发的短周期重力波具有共同特征,表现为周期10～90 min、中心振幅11～47 Pa,但是大部分强雷暴都会激发10～90 min短周期重力波,发生的比率高于弱雷暴,并且强雷暴更易激发更短周期（1～20 min）重力波,更利于振幅较大（≥50 Pa）的短周期重力波发生。近距离雷暴比远距离雷暴对长、短周期重力波有更积极的影响。部分雷暴发生前约114～168 min,会有长、短周期重力波先兆活动,其中,长周期（90～270 min）重力波平均中心振幅84～106 Pa、短周期（30～90 min）重力波平均中心振幅12～43 Pa;相比远距离雷暴,近距离雷暴的重力波先兆活动发生比率更高;雷暴强度对重力波先兆活动也有影响,强雷暴过程振幅更大、短周期（20～30 min）的重力波先兆活动发生率更高。重力波先兆活动这一特征可能对雷暴预警有意义。 相似文献
11.
本文研究了基本气流具有线性弱切变的非线性Rossby波,得到了一个非线性发展方程为Kubota方程,在一定的条件下,可变为Benjamin-Ono方程,并指出当代数Rossby孤立波的振幅越大时,代数Rossby孤立波的传播速度越小,基流切变越强,代数Rossby孤立波越慢,同时我们还指出在代数Rossby孤立波的振幅满足一定的条件下,代数Rossby孤立波才随纬度的增高(β减小)而减慢。并且代数Rossby孤立波的结构与大气中的偶极子阻塞是一致的。 相似文献
12.
文中讨论了陆架波系和赤道波系在动力学上的相似性，和赤道波系一样，陆架波系也由惯性重力波、Ｋｅｌｖｉｎ波、Ｒｏｓｓｂｙ（长、短）波和有条件的Ｒｏｓｓｂｙ－重力混合波组成。指出，当 海洋三边存在陆架而一边为赤道时（如北太平洋），则陆架波系和赤道波系中的Ｋｅｌｖｉｎ波， 将以逆时针方向携带信号绕海盆一周，而两个波系中的Ｒｏｓｓｂｙ长波，将以顺时针方向绕海盆一周，即通过陆架波和赤道波为海洋中某些信号的传播组织成一个绕海盆的环路。这种物理 过程可望用以解释发生在海洋中的某些长周期现象，如Ｅｌ Ｎｉ ｏ现象。文中进一步 讨论了陆架波的各种简化运动。 相似文献
13.
利用多重尺度摄动法,对低纬大气Kelvin波和Rossby波的波包演变进行了分析,得到两波的非线性相互作用方程为耦合的非线性复系数Landau方程组。数值计算表明两波相遇将使波振幅变化,波宽变窄;两波非线性相互作用可能是低纬强烈天气突然爆发的原因之一。 相似文献
14.
从Rossby波能量频散理论到准定常行星波动力学研究的发展 总被引：3，自引：0，他引：3
本文是为纪念叶笃正院士诞辰百周年和他对大气动力学发展的重大贡献而撰写的.叶先生在20世纪40年代所提出的罗斯贝波能量频散理论不仅至今仍广泛应用于天气预报,而且开创了准定常行星波动力学的研究.在罗斯贝波频散理论的启迪和引领下,行星波动力学和大气环流异常遥相关的研究取得重要进展.特别是关于准定常行星波在二维和三维球面大气的传播特征以及北半球夏季大气环流异常的EAP(East Asia-Pacific)型和"丝绸之路(Silk Road)"型遥相关及其机理已做出系统的研究,本文简要地回顾这些研究.并且,本文还回顾了在叶先生所提出罗斯贝波能量频散理论的引领下,近年来我们关于东亚冬、夏季风和我国气候灾害的年际和年代际变化的内动力学机理研究所取得的进展. 相似文献
15.
在前文采用半地转近似和行波法来研究层结大气中的非线性波动的基础上,进一步探讨非线性方程及其级数近似方程的解的稳定性,波动解的存在条件和波动的一些特征。研究指出,在平衡点附近,将非线性方程用其级数近似方程代替是可行的、合理的。在初始拟能满足一定的条件下,椭圆余弦波和孤立波是存在的。文中还求得了椭圆余弦波解的周期、ｘ向波长和振幅以及孤立波的宽度和振幅。并指出,孤立波的宽度和振幅不但与波速有关,还与β因子和层结稳定度有关,而且在相同的某条件下,西行的混合Ｒｏｓｓｂｙ－重力孤立波比起东行的惯性重力孤立波来,宽度要小但振幅却大。 相似文献
16.
The system of linearized shallow water equations is formulated in this paper on any rotating and smooth surface M in terms of differential geometry. The system decouples into two separate equations: a scalar one for the height deviation and a vector one for the velocity field. For low and high frequencies these equations yield asymptotic equations whose solutions are the generalizations of the Poincare and Rossby waves to smooth surface. The application of these equations to the β-plane yields both new and previously known equations for the height deviation and for the velocity components. The application of the equations to the rotating spherical Earth shows that the meridional amplitudes of Poincare and Rossby waves are both described by the prolate angular spheroidal wave functions. The asymptotic and the power series expansions of the eigenvalues of these functions yield new approximations for the dispersion relations of these waves on a sphere. The new dispersion relations are very accurate in the physically relevant range of the single nondimensional model parameter – the square of the nondimensional gravity waves’ phase speed. The invariant formulation can also be applied to other surfaces that are of geophysical interest such as an oblate ellipsoid of revolution. 相似文献
17.
本文使用WKB方法对弱耗散作用下基本气流具有弱切变的行星大气中非线性Rossby波进行了研究,得到了弱耗散的非线性Rossby波振幅所满足的复系数非线性Schrdinger方程,并分别就无耗散和弱耗散的Rossby波的边带稳定性问题进行了讨论,得到了一些新结果. 相似文献
18.
为了分析热带海气耦合系统中不稳定扰动究竟由哪种自由波占主导地位，根据本文第I部分提出的热带海气耦合模式，讨论了取耦合系统中不同的径向模时耦合波的性质，即分别讨论了大气长Rossby波和海洋长Rossby波、大气Kelvin波和海洋长Rossby波、大气长Rossby波和海洋Kelvin波的耦合波以及考虑了大气和海洋中所有这些波动时耦合波的性质。结果指出，这些耦合波对海气耦合模式中参数的取值很敏感，不同的参数可以产生性质不同的耦合波。本文的结果也说明了海气耦合系统的性质与热带大气的性质和结构有很大关系。 相似文献
19.
In this paper,a tropical atmospheric model of relevance to shorts-term climate variations(Wang and Li 1993) is utilized for study of the development of Madden-Julian oscillation.The model contains an interactive process of boundary-layer Ekman convergence and precipitation heating.The model is solved by expanding dependent variables in terms of parabolic cylindrical functions in the meridional direction and truncating three meridional modes n=0,2,4 for equatorial symmetric solutions.The free wave solutions obtained under long-wave approximation are induced as a Kelvin wave and two Rossby waves.After considering the effect of boundary-layer dynamic process,the modified Kelvin wave becomes unstable in long-wave bands with a typical growth rate on an order of 10-6 s-1and an eastward phase speed of 10 m s-1;the most unstable mode is wavenumber one.These theoretical results are consistent with the observed Madden-Julian oscillation in equatorial area.For the two modified Rossby waves,one with a smaller meridional scale(n=4) decays except for extra long-waves;the other with a larger meridional scale(n=2) grows in short-wave bands.This may be relevant to explaining the westward propagation of super cloud clusters in the Madden-Julian oscillation.The theory suggests that the boundary-layer dynamic process is an important mechanism in the development of the Madden-Julian oscillation. 相似文献
20.
In this paper,a tropical atmospheric model of relevance to shorts-term climate variations(Wang and Li 1993)is util-ized for study of the development of Madden-Julian oscillation.The model contains an interactive process ofboundary-layer Ekman convergence and precipitation heating.The model is solved by expanding dependent variables interms of parabolic cylindrical functions in the meridional direction and truncating three meridional modes n=0,2,4 forequatorial symmetric solutions.The free wave solutions obtained under long-wave approximation are induced as aKelvin wave and two Rossby waves.After considering the effect of boundary-layer dynamic process,the modifiedKelvin wave becomes unstable in long-wave bands with a typical growth rate on an order of 10~(-6) s~(-1)and an eastwardphase speed of 10 m s~(-1);the most unstable mode is wavenumber one.These theoretical results are consistent with the ob-served Madden-Julian oscillation in equatorial area.For the two modified Rossby waves,one with a smaller meridionalscale(n=4)decays except for extra long-waves;the other with a larger meridional scale(n=2)grows in short-wavebands.This may be relevant to explaining the westward propagation of super cloud clusters in the Madden-Julianoscillation.The theory suggests that the boundary-layer dynamic process is an important mechanism in the develop-ment of the Madden-Julian oscillation. 相似文献