纬向气流对地形Rossby波的影响

本文在半地转近似下,采用相平面方法讨论了纬向基本气流对线性和非线性地形Rossby波的稳定性及解的性质的影响。结果指出:线性和非线性稳定性判据形式一样,纬向气流及其切变对稳定性有明显影响;在非线性近似下,可形成孤立波槽和孤立波脊。     

低纬大气Kelvin波和Rossby波的非线性相互作用

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。     

The effects of zonal flow on nonlinear Rossby waves

In this paper, we using phase plane method have derived the stability criteria of linear and nonlinear Rossby waves under the conditions of semi-geostrophic approximation and have gotten the solutions and geostrophic vorticity of corresponding solitary Rossby waves. It is pointed out that the wave stability is connected with the distri-bution of zonal flow and when the zonal flow is different the solitary wave trough or ridge is formed.     

On the low-frequency,planetary-scale motion in the tropical atmosphere and oceans

Scale analyses for long wave, zonal ultralong wave (with zonal scale of disturbance L1~104 km and meridional scale L2~103 km) and meridional ultralong wave (L1~103 km, L2~104 km) are carried out and a set of approximate equations suitable for the study of these waves in a dry tropical atmosphere is obtained. Under the condition of sheared basic current, frequency analyses for the equations are carried out. It is found that Rossby waves and gravity waves may be separated for n ≥ l where n is the meridional wave number, whereas for n = 0 and L1~1000 km, the mixed Rossby-gravity wave will appear. Hence it is confirmed that the above results of scale analyses are correct. The consistency be-tween frequency analysis and scale analysis is established.The effect of shear of basic current on the equatorial waves is to change their frequencies and phase velocities and hence their group velocities. It increases the velocity of westward travelling Rossby waves and inertia-gravity and mixed waves, but decelerates the eastward inertia-gravity waves and the Kelvin wave. The recently observed low-frequency equatorial ocean wave may be interpreted as an eastward Kelvin wave in a basic current with shear.     

Wave dynamics of super cloud clusters over the tropical region

A wave dynamics for the super cloud clusters associated with the tropical intraseasonal oscillation is constructed. Under the present framework, the basic state of super cloud clusters is considered to be a large-scale convergence of the zonal wind. This convergence is created by a nonlinear diabatic Kelvin wave front, which moves eastward slowly without change of shape. When interacting with free equatorial waves with n=−1, 0, 1 and 2, this basic flow will suppress those waves which move eastward except for free Kelvin waves, and permit westward propagating modes such as the mixed Rossby-gravity wave, the inertio-gravity waves with n=1 and 2 to appear in the large-scale convergent region. Among these waves, only fast modes, that is, inertio-gravity waves with n=1 and 2 are regarded to be responsible for the presence of cloud clusters which move westward within a super cloud cluster, while the multiplicity of the occurrences of super cloud clusters, which move eastward within the large-scale convergent region, is due to the superposition of free Kelvin wave upon these inertio-gravity waves.     

大气中40—60天低频振荡形成的数值试验

观测资料的分析表明,40—60天的低频振荡,除了在赤道附近有向东的传播外,在副热带和高纬度带还存在向西传播的现象.本文利用正压原始方程的谱模式,加以与运动(辐散)相联系的强迫(相当于加热场),模拟这类低频振荡发现有两类波存在:一类是周期约为10—20天向东传播的行星波,另一类是周期为40—60天向西传播的低频波,它是前一类行星波的波包相速度,每天5—6经度,纬向波数为1.这类低频波的出现可能是行星波与加热场非线性相互作用的结果. 这里之所以没有得到东传的40—60天的低频波,可能是由于模式格点较疏,使赤道Kelvin波不能明显激发出来.     

Nonlinear waves in barotropic model

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.     

层结大气中非线性椭圆余弦波和孤立波的研究

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。     

A numerical method for solving the evolution equation of solitary Rossby waves on a weak shear

In this paper an evolution equation in integral-differential form for finite amplitude Rossby waves on a weak shear is presented and an efficient method for its numerical solution is set up. It is shown that a propa-gation of solitary wave is possible whenever a proper weak shear in basic flows acts with the nonlinear effects and dispersion of the media, both in the atmosphere and in the ocean. To test the numerical method for solving the evolution equation, a series of experiments are carried out. The results indicate that the solitary solutions do exist and interact with each other in quite a succinct, manner. Therefore the method is successful and efficient for solving initial value problems of the above equation. The time decoupling problem arising in the numerical scheme and the related filtering technique are discussed. A variety of interesting phenomena such as the interaction of solitary Rossby waves, damping, dispersion and the development of nonlinear wave train are numerically studied.     

INFLUENCES OF TOPOGRAPHY ON BAROCLINIC SOLITARY ROSSBY WAVES IN A MULTILEVEL MODEL

The KdV equation with topography included in an N-level model is derived. It is shown that if the topography ex-ists. the KdV equation may describe the solitary Rossby waves in the case of basic current without vertical shear, and itis no necessary to introduce the MKdV equation. The results of calculations show that the change of horizontal shearpattern of basic flow may cause an important change of the streamline pattern of the solitary waves with the oddmeridional wavenumber m, and has no effect for the even meridional wavenumber m. The vertical shear increases thesteepness of the barotropic solitary modes, and it has a complicated effect on the baroclinic modes. The influences oftopographic slope on the solitary waves are very great. The southern and northern slopes of topography may cause dif-ferent solitary wave patterns, with the effect of northern slope greater. The effect of Froude number on the solitarywaves is generally to steepen the solitary waves, however, the effect also depends on the meridional wavenumber m andthe modes of solitary wave.     

切变基本纬向流中赤道Rossby包络孤立波

利用多重尺度摄动法，从描写赤道Rossby波的正压大气位涡度方程中推导出在切变基本纬向流中非线性赤道Rossby波包演变所满足的非线性Schrodinger方程，并得到其单个包络孤立子波解，分析基本流切变对非线性赤道Rossby波动的影响。     

热带海气耦合Kelvin波的弱相互作用

本文在简单的热带海气耦合方程组中 ,引进基本风场和平均海流的作用以后 ,对热带海气耦合 Kelvin波的不稳定性进行了讨论 ,得到其耦合不稳定的判据条件 ,并且分析了它的传播结构特征。     

正压大气中的代数Rossby孤立波

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。     

垂直切变流中非线性重力波及其相互作用

利用多重尺度摄动法，推导出斜压大气中(基本风场具有垂直切变)两个非线性重力波相互作用方程，这两个方程联立组合为耦合非线性schrǒdīnger方程组。两个重力波相互作用时可激发出重力驻波。数值计算表明：两个孤立重力波相遇，相追会使波振幅增大，波宽变窄。强烈对流天气突然爆发的可能原因之一是中尺度重力波非线性相互作用的结果。     

大气中的包络Rossby孤立波——纬度效应的作用

本文进一步对旋转正压大气中的包络Rossby孤立波进行了研究，结果发现当Rossby波的波数m（m为纬向波数）满足1≤m≤2时，旋转正压大气中才存在包络Rossby孤立波，并且只有m＝2的包络Rossby孤立波才具有阻塞高压的结构。我们还对这种m＝２的包络Rossby孤立波随纬度变化的持续性进行了计算，得到了许多结果。     

球面正压粘性大气的运动特征

通过对球面正压粘性大气非线性扰动的研究表明:由于波动之间的弱非线性相互作用，球面小扰动的波包演变是由一种较为简单的方程形式控制，当此粘性力消失时，该方程为非线性Schr?dinger方程。研究结果还表明:非线性Schr?dinger孤立波的形成，有两个因子非常重要，一是运动的球面性，另一个则是基本风场的经向切变。前者反映了球面运动的特殊性。本文还从另一个角度证明了粘性力的作用对波动起着加强能量的耗散作用，不利于这种几率波（Schr?dinger 孤立波）的形成。     

Modulation of Convectively Coupled Kelvin Wave Activity in the Tropical Pacific by ENSO

The influence of El Nio-Southern Oscillation (ENSO) on the convectively coupled Kelvin waves over the tropical Pacific is investigated by comparing the Kelvin wave activity in the eastern Pacific (EP) El Nio, central Pacific (CP) El Nio, and La Nia years, respectively, to 30-yr (1982-2011) mean statistics. The convectively coupled Kelvin waves in this study are represented by the two leading modes of empirical orthogonal function (EOF) of 2-25-day band-pass filtered daily outgoing longwave radiation (OLR), with the estimated zonal wavenumber of 3 or 4, period of 8 days, and eastward propagating speed of 17 ms-1 . The most significant impact of ENSO on the Kelvin wave activity is the intensification of the Kelvin waves during the EP El Nios. The impact of La Nia on the reduction of the Kelvin wave intensity is relatively weaker, reflecting the nonlinearity of tropical deep convection and the associated Kelvin waves in response to ENSO sea surface temperature (SST) anomalies. The impact of the CP El Nio on the Kelvin waves is less significant due to relatively weaker SST anomalies and smaller spatial coverage. ENSO may also alter the frequency, wavelength, and phase speed of the Kelvin waves. This study demonstrates that low-frequency ENSO SST anomalies modulate high-frequency tropical disturbances, an example of weather-climate linkage.     

The domain of validity of the KdV-type solitary rossby waves in the shallow water β-plane model

The Domain, where the necessary and sufficient conditions for the existence of the KdV-type solitary Rossby waves are satisfied is defined in the shallow water β-plane model. The KdV-type solitary Rossby waves are the Rossby waves whose time-longitude dependence is determined by the KdV equation. As far as an appropriate amplitude and an appropriate ratio of the scales of the east-west and north-south directions are given, the KdV-type solitary Rossby waves can exist for every basic zonal flow. This result suggests the large validity of the soliton model in geophysical fluid dynamics. The KdV-type solitary Rossby waves are classified into four categories: (1) shear solitons studied by Long, Larsen, Benny, Redekop, and Hukuda, (2) β-divergent solitons studied by Clarke, Yamagata, and Nogami, (3) β-solitons found in the case of the strong stratification, and (4) divergent solitons which exist in the planetary-geostrophic-scale zonal flow. A remarkable result is that, in addition to the conventional east-west elongated solitons, the north-south elongated solitons can also exist for the case of the divergent solitons.