大气非线性波动方程的解

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。     

线性和非线性风应力对海-气耦合波的影响

在略去Ｒｅｙｌｅｉｇｈ摩擦和Ｎｅｗｔｏｎ冷却的条件下，采用定常的线性大气模式和半地转近似的非线性海洋模式，讨论了线性和非线性风应力对海－气耦合Ｒｏｓｓｂｙ波的影响，结果表明，当耦合波处于非线性不稳定的情况下，线性和非线性风应力均可产生孤立波，不同之处在于，非线性风应力所产笺波图像具有间断特点，波能的急剧聚集有可能使波的性质发生变化。     

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。     

CISK 影响下的线性和非线性惯性重力波

利用板对称的大气动力学方程组，考虑线性和非线性两种CISK加热过程，由行波法和非线性常微分方程定性理论，讨论了CISK影响下的线性和非线性惯性重力波的稳定性，以及CISK对惯性重力孤波强度和宽度的影响。结果指出，线性CISK既影响孤立波的强度，又影响孤立波的宽度，而非线性CISK只影响孤立波的强度。     

Plumb三维波作用通量和EP剖面图——对定常波模式输出结果的诊断分析

本文利用Plumb(1985年)所导出的线性、准地转定常波的三维波作用通量和Eliassen-Palm(EP)剖面图,对于一个线性和一个非线性的关于大气定常波的斜压初始方程三维谱模式的若干输出结果进行了诊断分析。分析结果表明,Plumb通量和EP剖面图,不仅可以用来诊断波作用在三维空间的传播、波动与纬向平均气流之间的相互作用,而且也可以用来诊断非线性作用的显著性,在利用它们对于观测资料进行诊断分析时,应当充分注意到非线性作用的影响。     

中尺度对称不稳定和横波不稳定的波动性质

使用纬向线性以及非线性切变基流下中尺度扰动的Boussinesq近似方程组，讨论了两种典型的中尺度扰动发生对称不稳定或者横波不稳定时，其不稳定的一些特征以及扰动的波动性质。研究结果表明：（1）对于扰动的等位相面平行于基本气流方向的对称性扰动来说，对称不稳定的波动实质是沿着与基本气流方向相垂直的方向传播的重力惯性内波的不稳定。基流二次切变对于中尺度对称扰动来说是一个不稳定因子，并且驱动不稳定的中尺度对称扰动在南北方向传播；（2）对于扰动的等位相面垂直于基本气流方向的横波性扰动来说，在基本气流为常数或者只具有线性切变的情况下，此时根本不存在涡旋Rossby波，横波不稳定的波动实质则是沿着基本气流方向双向传播的重力惯性内波的不稳定。如果考虑基本流场的风速存在二次切变或者非线性切变时，此时就会产生一支新的波动（涡旋Rossby波），涡旋Rossby波相对于基本气流^-U0是单向传播的，涡旋Rossby波产生的物理根源是基本流场的风速^-U二次切变（β＊=^-Uzz≠0），此时横波型不稳定可能是混合的涡旋Rossby——重力波的不稳定。实际大气中，涡旋Rossby波对于中够尺度对流云核、暴雨团等天气系统的发生、发展和演变的物理机制具有极其重要的意义。     

半地转近似下的混合Rossby－重力椭圆余弦波

在半地转近似［１］下，利用层结大气中的涡度方程、散度方程、连续方程和绝热方程结合行波解的方法得到了关于垂直速度的单一变量方程。这是与ＫｄＶ方程相应的非线性常微分方程，可得到椭圆余弦波或弧立波。此波动的频率有两种，表明层结大气中存在着两种性质不同的非线性波动。其一是东传的惯性重力椭圆余弦波，另一是混合Ｒｏｓｓｂｙ－重力椭圆余弦波，其性质介于Ｒｏｓｓｂｙ椭圆余弦波与西传的惯性重力椭圆余弦波之间。这两种非线性波的相速不但与波数和振幅有关，而且与β因子和静力稳定度有关，即纬度越低，则传播越慢；大气越稳定，则传播越快。     

正压模式中的非线性波动

本文从非线性大气运动正压模式方程组出发,用我们所设计的将非线性项在平衡点附近作Taylor展开的方法,求得了非线性有限振幅的惯性-重力外波和有辐散的Rossby波,均满足著名的KdV方程,它的解为椭圆余弦波,它包含线性波动,在一定的条件下形成孤立波。对有限振幅的但有辐散的Rossby波,它包含线性的有辐散的Rossby波(即叶笃正波),而且建立了包含叶笃正公式在内的新的色散关系,它含有振幅因子。分析表明:对有限振幅的惯性-重力外波,振幅大、宽度大的波传播越快,但对有限振幅的有辐散的Rossby波,振幅大、宽度大的波传播越慢,阻塞、切断系统可能属于Rossby孤立波。     

纬向切变基流中的非线性正压Rossby波

在半地转近似下，用相角函数方法得到了包含纬向基流及其切变的非线性常微分方程。利用常微分方程解的拓扑性质的定性理论，直接得到该方程存在有限振幅的周期波解与孤立波解即非线性正压Ｒｏｓｓｂｙ波解存在的条件，由此分析了纬向切变基流对波解存在的影响。最后利用函数逼近法求得了非线性正压Ｒｏｓｓｂｙ波解的显式表达式。结果表明，纬向切变基流对波的影响不仅表现在波的存在方面，而且还表现在波的形态方面，反映了波的非线性特点和基流对波动的作用。     

准地转动量近似下风速切变线上的波动

利用准地转动量近似下的斜压两层大气的非线性方程组及非线性边界条件，研究了切变线上波动的稳定性，导出了切变线上孤立波解。较好地解释了切变线上易产生低涡等天气系统现象。     

Equatorial solitary waves Part 4. Kelvin solitons in a shear flow

It is shown that a mean flow with shear makes the Kelvin wave dispersive. This in turn modifies its nonlinear behavior and makes it necessary to replace the one-dimensional advection equation derived in an earlier work of the author's by the Korteweg-deVries equation instead. The frontogenesis predicted in the earlier paper will still occur, but the wave breaking will not. Instead, once a steep front has formed, it will disintegrate into a train of solitary waves. These then propagate towards the east at a faster-than-linear rate. It is also shown that Kelvin solitary waves will have much smaller zonal widths than Rossby solitons of the same height; “round” Kelvin solitary waves (equal zonal and latitudinal width) are to be expected, and are fully consistent with the small amplitude, weak dispersion theory. An interesting implication of the Korteweg-deVries model is that the peak signal from a nonlinear Kelvin wave packet may be roughly double that of a linear Kelvin wavetrain.     

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。     

A further study on an extended nonlinear ocean-atmosphere coupled hydrodynamic characteristic system and the abrupt feature of ENSO events

An extended ocean-atmosphere coupled characteristic system including thermodynamic physical processes in ocean mixed layer is formulated in order to describe SST explicitly and remove possible limitation of ocean-atmos-phere coupling assumption in hydrodynamic ENSO models. It is revealed that there is a kind of abrupt nonlinear characteristic behaviour, which relates to rapid onset and intermittency of El Nino events, on the second order slow time scale due to the nonlinear interaction between a linear unstable low-frequency primary eigen component of ocean-atmosphere coupled Kelvin wave and its higher order harmonic components under a strong ocean-atmos-phere coupling background. And, on the other hand, there is a kind of finite amplitude nonlinear characteristic behaviour on the second order slow time scale due to the nonlinear interaction between the linear unstable primary eigen component and its higher order harmonic components under a weak ocean-atmosphere coupling background in this model system.     

SOUTHERN BOUNDARY FORCING RELATIVE TO GENESIS,MAINTENANCE AND OSCILLATION OF A SUBTROPICAL HIGH

A nonlinear critical layer and a Kelvin cat's eye excited thereupon are simulated through fourschemes in the context of a nonlinear quasi-geostrophic barotropic vorticity equation model withforced stationary wave acting along the southern boundary to investigate effects of tropical steadyforcing on the genesis,maintenance and oscillation of a subtropical high(STH).Evidence suggeststhat the southern forcing is responsible for the planetary quasi-steady anticyclonic Kelvin cat's eye-form flow field inside the nonlinear critical layer,with the eye shifting,vigor and shape changingquite similar to the behaviors of a summer STH,in striking contrast to the northern stationaryforcing.As such,the southern boundary-caused cat's eye is likely to be an even more importantmechanism for STH genesis and evolution.In addition,a physical mechanism is introduced forquasi-steady planetary wave moving through the critical layer at subtropical latitudes.     

SOUTHERN BOUNDARY FORCING RELATIVE TO GENESIS, MAINTENANCE AND OSCILLATION OF A SUBTROPICAL HIGH*

A nonlinear critical layer and a Kelvin cat's eye excited thereupon are simulated through four schemes in the context of a nonlinear quasi-geostrophic barotropic vorticity equation model with forced stationary wave acting along the southern boundary to investigate effects of tropical steady forcing on the genesis,maintenance and oscillation of a subtropical high(STH).Evidence suggests that the southern forcing is responsible for the planetary quasi-steady anticyclonic Kelvin cat's eye-form flow field inside the nonlinear critical layer,with the eye shifting,vigor and shape changing quite similar to the behaviors of a summer STH,in striking contrast to the northern stationary forcing.As such,the southern boundary-caused cat's eye is likely to be an even more important mechanism for STH genesis and evolution.In addition,a physical mechanism is introduced for quasi-steady planetary wave moving through the critical layer at subtropical latitudes.     

Behaviour of Coupled Modes in a Simple Nonlinear Air-Sea Interaction Model

Ｂｅｈａｖｉｏｕｒ　ｏｆ　Ｃｏｕｐｌｅｄ　Ｍｏｄｅｓ　ｉｎ　ａ　Ｓｉｍｐｌｅ　Ｎｏｎｌｉｎｅａｒ　Ａｉｒ－Ｓｅａ　Ｉｎｔｅｒａｃｔｉｏｎ　ＭｏｄｅｌＬｉＣｈｏｎｇｙｉｎａｎｄＬｉａｏＱｉｎｇｈａｉ（ＬＡＳＧ，ＩｎｓｔｉｔｕｔｅｏｆＡｔｍｏｓｐｈｅｒｉ...     

南边界强迫的非线性临界层与副高的形成、维持和振荡

用非线性准地转正压涡度方程模式，在南边界取定常强迫波，采用４种方案模拟了非线性临界层及其上激发的Ｋｅｌｖｉｎ猫眼，以确定热带的定常强迫对副高的形成、维持和振荡的影响。结果表明，南边界定常强迫仍在非线性临界层内激发行星尺度的准定常反气旋的Ｋｅｌｖｉｎ猫眼流场，猫眼的移动、强度和形状变化与夏季副高比较相似．而北边界定常强迫所得结果与夏季副高差异较大。因此，南边界所激发的非线性临界层上的Ｋｅｌｖｉｎ猫眼可能是夏季副高形成、维持和振荡的一种更为重要的新物理机制。文中还提出准定常行星波穿越副热带的非线性临界层的物理机制。     

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.     

有地形坡度的非线性Kelvin行波

提出了一个考虑地形坡度的非线性Kelvin行波解的模型，在假定了地形坡度沿山脉走向不变而仅在垂直于山脉走向的方向有改变的情况下，求得了该模型的解析解，这有助于加深对沿海山地捕获波的认识。文中还将该解与经典情形(即侧边界取为垂直刚壁而底面为水平)的解作了比较，发现前者的波速与扰动振幅均较后者要小，这与我国东南沿海武夷山区的沿海山地捕获波的情况相一致。     

简单热带海气耦合模型中不同扰动形式间的耦合作用

在局地热平衡情况下研究了简单热带海气耦合模式中不同扰动形式间的耦合，依次讨论了由大气准定常Kelvin波与海洋R0ssby波、大气准定常Rossby波与海洋Kelvin波、大气准定常Kelvin波与海洋KelVin波、大气准定常Rossby波与海洋Rossby波组成的耦合系统的性质，并研究了存在于其中的耦合扰动的特征。