切变基流中赤道Rossby包络孤立波

A simple shallow-water model on an equatorialβ-plane is employed to investigate the nonlinear equatorial Rossby solitons in a mean zonal flow with meridional shear by the asymptotic method of multiple scales. The cubic nonlinear Schrodinger (NLS, for short) equation, satisfied for large amplitude equatorial envelope Rossby solitons in shear basic flow, is derived. The effects of basic flow shear on the nonlinear equatorial Rossby solitons are also analyzed.     

大气中孤立波的相互作用

本文讨论无限深上层流体和有限深下层流体的两层流体系统，该系统是大气的一种近似模型。采用拉格朗日坐标系，从无粘不可压流体力学方程式出发，利用摄动方法获得了所讨论系统中界面孤立波迎撞的摄动解。结果表明，在迎撞前后每个波独立地由Benjamin-Ono方程所描述，即波的形状不发生变化，迎撞的效应由相移来体现。     

振荡型Rossby孤立波与大气阻塞

从正压涡度方程出发,在弱非线性和弱其流切变条件下,导得了描述非线性大气长波活动的推广的Ｋｄｖ方程,并得到了方程的孤立波解及其色散关系。取近似于实际大气运动的物理参数作数值计算,得到了振荡型Ｒｏｓｓｂｙ孤立波的水平结构和移动特征,其结果较这建党的Ｋｄｖ孤立波更接近于实际大气中的阻塞流型。     

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。     

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。     

切变基流中赤道Rossby包络孤立波(英文)

利用一个简单的赤道β平面浅水模式和多尺度摄动法，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维向流中赤道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波子波解，并分析基本流切变对非线性赤道Ｒｏｓｓｂｙ孤立子的影响。     

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。     

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。     

中尺度大气运动中孤立重力波特征的研究

通过对斜压大气(基本风场有垂直切变)运动中重力内波的研究发现:对于小振幅扰动(弱非线性问题),考虑波动之间的非线性相互作用以后,控制重力内波波包(调制波)的演变方程是非线性Schrodinger方程.然后通过对冷锋爆发冷涌过程的计算表明:冷涌主体前沿的宽度约10km,行进速度约为13/s,随着冷涌的增强,其宽度变窄.这些计算结果与实际的观测结果比较一致.     

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.     

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.     

线性和非线性地形罗斯贝波

本文在半地转概念下,讨论了线性和非线性地形罗斯贝波的稳定性及其解。指出:线性和非线性稳定性判据形式一致。在线性时,地形东西向及南北向坡度对稳定波动的周期和传播速度有明显影响,其解为周期函数;在不稳定时,解为非周期函数。二级近似时其解为孤立波形式——不稳定时,在地形不同位置可形成东移或西移的孤立波槽或孤立波脊;而在稳定时只形成孤立波槽。三级近似时解出现间断点。     

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。     

热力强迫的非线性奇异惯性重力内波与高原低涡的联系

利用相平面分析法,由非绝热大气运动方程组导出了与非线性惯性重力内波有关的KdV方程,然后用直接积分法得到两类有天气意义的孤立波解,重点分析了与青藏高原暖性低涡有联系的一类具有间断点的奇异孤立波解的特征,进而讨论了高原非绝热加热对高原低涡生成、移动及高原低涡暖心结构的作用。     

层结流体中具有纬向基本剪切流的Rossby波振幅的mKdV方程

In this paper,modified Korteweg-de Vries (mKdV) equations for the amplitude of solitary Rossby waves in stratified fluids with a zonal shear flow are derived by using a weakly nonlinear method.It is found that the coefficients of mKdV equations depend not only on the β effect and the Visl-Brunt frequency,but also on the basic shear flow.     

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.     

Cross-equatorial structures of equatorially trapped nonlinear Rossby waves

Analysis of the Sea Surface Height (SSH) from satellite altimeters has shown that equatorially trapped Rossby waves exhibit asymmetric cross-equatorial structures; their northern extrema are much larger in magnitude than their southern counterparts. Such asymmetry is inconsistent with the classical theory for the first baroclinic, first meridional equatorially trapped Rossby mode, which predicts that SSH and zonal velocity are symmetric in latitude and the meridional velocity is latitudinally antisymmetric (Matsuno, 1966). Chelton et al. (2003) attributed the observed asymmetry to the mean-shear-induced modifications of first meridional mode Rossby waves. The present paper examines nonlinear rectification of cross-equatorial wave structures in the presence of different zonal mean currents. Nonlinear traveling Rossby waves embedded in shears are calculated numerically in a 1.5-layer model. Nonlinearity is shown to increase the cross-equatorial asymmetry substantially making the northern extrema even more pronounced. However, nonlinearity only slightly increases the magnitude of the westward phase speed.     

非线性涡旋Rossby波的演变特征

利用多重尺度摄动法，推导出非线性涡旋Rossby波波包的演变方程是非线性Schroedinger方程。对该非线性Schroedinger方程的周期波动解及其稳定性进行了研究，得到了有关稳定和不稳定的判据。数值计算表明：非线性涡旋Rossby波的相速值为10^0m／s量级，这和台风中的螺旋雨带实测移速的量级是一致的，可以从涡旋Rossby波说中较好地解释台风中的螺旋雨带的形成和维持。