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。     

EFFECTS OF TOPOGRAPHY ON SOLITARY ROSSBY WAVES IN A BAROTROPIC ATMOSPHERIC MODEL

The influences of topography on solitary Rossby waves are discussed by using a barotropic atmosphericmodel.The results show that the topography is an important factor exciting solitary Rossby waves,and itseffects are different with different height scales.Two different patterns of solitary Rossby waves are obtainedby using numerical calculation.     

大地形与正压Rossby孤立波——弱二次切变基本气流

基本气流的经向切变对Rossby孤立波的形成具有重要的作用,不同强度的切变形成不同的孤立波流型;可变坡度地形也是形成Rossby孤立波的重要因子。弱切变基本气流和坡度变化不大的地形形成的主要是经向波数为1和2的孤立波。     

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。     

大地形与正压Rossby孤立波

文中讨论了地形对正压Rossby孤立波的影响,指出,当基本气流没有切变时,地形是产生Rossby孤立波的重要因子;不同高度的地形,其作用有很大的不同;计算得到了两类不同的孤立波流型。     

The north-south elongated solitary Rossby wave

As far as the author knows, the previous models of solitary Rossby wave have been restricted to the case of the east-west elongated one. However, now, it is shown by Yano and Tsujimura that the north-south elongated KdV-type solitary Rossby wave is also possible. In this note, a typical example of the north-south elongated elongated KdV-type solitary Rossby wave in the shallow water β-plane model is examined.The conventional east-west elongated solitary Rossby wave is governed by the KdV equation in the longitudinal direction at each latitude. The same is true for the case of the north-south elongated solitary Rossby wave. The main difference is that, however, the KdV-soliton defined at each latitude has drifted by the local phase velocity, which is different for each latitude. Hence, the wave pattern is deformed continuosly with time in the latitudinal direction, and the separable solution is not possible as is in the case of the east-west elongated solitary wave.     

N层模式大气中的斜压孤立Rossby波

文中导得了N层模式的KdV方程,作为例子计算了三层模式的孤立Rossby波流型。基本气流的垂直切变、水平切变和Froude数对孤波流型都有重要影响;不同模态的孤波具有不同流型,不同高度位面上的孤波流型一般是不同的。     

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.     

副高与阻高形成的Rossby孤立波理论Ⅱ:存在临界层

研究了存在临界层的非均匀纬向流中的Ｒｐｓｓｂｙ孤立波。在求出振幅函数满足的ＫｄＶ方程或修正ＫｄＶ方程（ＭＫｄＶ）后，选择Ｃｈｅｂｙｓｈｅｖ多项式作为展开基函数，用假谱方法，求解本征值和本征函数。对理想风场的计算表明，在临界层存在与否两种情况下，都能得到在东西风界面处的反气旋式副高型Ｒｏｓｓｂｙ孤立波，同副高有一致的演变规律：当东风带相对强于西风时，向西移动；当西风相对强于东风时，则向东移动。在西风带，则得到阻高型Ｒｏｓｓｂｙ孤立波，与阻高也有同样的演变规律。另外，我们还用连续谱方法计算了临界层附近的连续谱及离散谱，也得到与假谱方法较一致的结论。     

热带大气运动的Rossby孤波

广东热带海洋气象研究所     

Equatorial solitary waves of tropical atmospheric motion in shear flow

Starting from the primary equations, the author derives the KdV equation which describes solitary Rossby waves in the tropical atmosphere, and indicates that, because these waves are ageostrophic, they differ from the quasigeostrophic solitary Rossby waves studied by Redekopp et al. Owing to nonlinear action, these waves are also different from traditional linear waves of the tropical atmosphere. The author believes that the stationary tropical atmospheric waves reflect the characteristics of solitary waves in that the energy does not disperse.     

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.     

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。     

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.     

旋转正压大气中的Rossby孤立波和偶极子阻塞

大气中的阻塞动力学一直是大气动力学中所要解决的重要问题之一,随着数学的发展,阻塞动力学的研究也取得了较大的进展。大气中的阻塞可以分为两类:一类是单个非偶极子阻塞(只存在高压或低压),另一类是偶极子阻塞(高压的南侧存在闭合的低压)。关于偶极子阻塞的动力学研究是在80年代以后才进行的。为了解释大气中所出现的偶极子阻塞,Mcwilliams(1980)提出了Equivalent     

The solitary waves of the barotropic quasi-geostrophic model with the large-scale orography

Starting from a modified barotropic quasi-geostrophic model equation, considering the actual situation of the large-orography of the Tibetan Plateau, neglecting its slope in x direction, and using the reductive perturbation method, then the solitary waves are obtained. The results show that the orography is essential factor exciting solitary Rossby waves in a flow without shear.     

考虑β随纬度变化下的Rossby孤立波与偶极子阻塞

利用文献[4]得到的推广的β平面近似式为f=f0+β0 y—（δ0/2）y2,研究由δ0项所引起的一类Rossby孤立波，而不考虑基流切变和地形等因子的作用。经过计算可以发现，当经向波数为1时，这种孤立波具有显著的南低北高的偶极子阻塞结构，它主要存在于弱西风气流中，并且偶极子的能量随着纬度的增高更容易集中(即高纬偶极子结构趋于局地化)，因而，β随纬度的变化可能是中高纬度地区偶极子阻塞产生的原因之一。     

含大地形的准地转正压模式的孤立波解

该文由修正过的含大地形的准地转正压模式方程出发,考虑青藏高原大地形的实际情况,忽略其东西向地形坡度,再利用约化摄动方法,求其孤立波解,并得到结论:当基本气流无切变时,地形是产生Rossby孤立波的必要因子。     

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.     

Oscillatory Rossby Solitary Waves in the Atmosphere

The linear Rossby wave frequency expression is expanded at higher accuracy based on the scale difference char?acteristics of atmospheric long waves in the and directions. That the nature of the waves represented by the expan?sion is identical to that of the original ones is demonstrated both in phase velocity and wave energy dispersion speed , followed by the derivation of the nonlinear expression describing atmospheric long wave behaviors with the associated approximate analytic solution obtained. Then, for the first time atmospheric’ oscillatory Rossby solitary wave’ with its dispersion relation is obtained by numerical calculation with the aid of physical parameters of the real atmosphere. The solitary wave is found to be very close to such longwave systems as blocking highs and cut-off de?pressions in the actual atmosphere.