切变气流中地形强迫激发的非线性长波

经推导得到了包括地形和耗散的ＦＫｄＶ－Ｂｕｒｇｅｒｓ方程,利用数值解讨论了地表强迫激发的弧波演变以及移动性孤波与地形的相互作用,结果显示,对于α〉０或α〈０,不论是在气旋式切变气流还是反气旋式切变气流中,地形都能在强迫激发出定常孤波,在其下游产生调制椭圆余弦波列的背风波,当α＝０时,在反气旋式切变气流中强迫区产生的是大振幅定常孤波,气旋式切变气流中强迫区产生的是复杂的非定常孤波,地形强迫产生的ｍ＝     

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。     

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。     

近共振地形强迫Rossby孤立波

利用扰动展开和时空伸长变换导得了包括地形强迫的非齐次ＫｄＶ方程，讨论了近共振地形强迫Ｒｏｓｓｂｙｙ孤立波的产生，及其与自由孤立波的相互作用，得到了一些有意义的结果，显示出地形对扰动具有明显的增幅作用，在某种程度上可以解释局地地形在阻塞高压形成中的作用。     

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。     

INTERACTION OF TOPOGRAPHY WITH SOLITARY ROSSBY WAVES IN A NEAR-RESONANT FLOW

An inhomogeneous KdV equation including topographic forcing is derived by usingperturbation expansions and stretching transforms of time and space.The generation of forcedsolitary Rossby waves by topography in a near-resonant flow and their interactions with freesolitary waves are discussed,and some interesting results are obtained.The numerical resultsshow that the topography has obvious effect on enhancing the amplitude of disturbances,and itmay explain to some degree the formation of blocking by localized topography.     

热带平流层多尺度波动分离方案的研究：多站点高分辨率无线电探空联合分析

利用太平洋地区台风过境期间6个热带气象站的高分辨率无线电探空资料,结合扩展经验正交函数（EEOF）展开,对热带下平流层行星波和重力波扰动进行了分离,给出了一种热带地区提取重力波扰动的新方案。对观测数据做EEOF展开后,选择表征行星尺度波动模态的特征向量和相应权重进行气象要素场的重建。结果显示,在不同的台风过程期间,温度、纬向风和经向风的重建扰动量显示出不同的动力学偏振关系:在准两年振荡（QBO）东风位相时与赤道开尔文波的偏振关系一致,而在准两年振荡西风位相时与混合罗斯贝-重力波（MRG）的偏振关系一致。把行星尺度波动模态从原始观测中剔除,得到新的扰动廓线,对其进行重力波垂直波数谱的谱型拟合。结果发现,与以往方法提取的重力波扰动相比,新方法所得谱型参数中特征垂直波长λ*在不同时期不同站点变化很小,稳定在1.7 km左右,且低频波数段谱斜率s的数值与理论假设1十分接近。综合其研究结果可以推测,用新方法提取的热带重力波扰动更加符合当前的理论垂直波数谱模型。      

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。     

旋转正压大气中的Rossby波射线

本文将缓变介质中波动的传播理论应用于Rossby波。在基流和不同走向地形假设下，计算了Rossby波射线路径及沿射线波数的变化。结果表明大尺度地形对Rossby波射线有显著影响。     

Topography and the non-linear Rossby wave in the zonal shear basic flow

Under semi geostropical approximation, by means or phase angle function the non-linear ordinary differential equation is derived involving topography and zonal shear basic flow. Conditions for the existence of limited amplitude periodical and isolated wave solutions are directly obtained based on the qualitative theory of the ordinary differentical equation. Analysis is thus made of the influence of topography and zonal shear flow on the existence of wave solution. Finally, explicit wave solutions are determined by function approaching with the result that topogra-phy and zonal shear flow affect not only the existence but also the form of waves, indicating the non-linear features of waves and the effect of topography and shear basic flow on undulation.     

The solitary wave of barotropic atmosphere on a sphere

In this paper, we have investigated large scale disturbance in barotropic atmosphere on a sphere. It demonstrates that: considering nonlinear effects of interaction between waves in barotropic vorticity equation, the wave packet of the disturbance is governed by the famous equation-nonlinear Schrodinger equation. For the solitary wave, two fac-tors are very important: one is spherical effect of the disturbance and the other is meridional shear of blocking high. In comparison with the results of local Cartesian coordinates, the former factor is the individuality of spherical soliton.     

地形追随垂直运动方程在南疆极端暴雨中的诊断分析

针对2021年6月15～17日发生在昆仑山脉北坡的南疆极端暴雨过程,本文综合考虑地形对暴雨发生、发展的作用后,利用地形追随坐标控制方程并采用Boussinesq近似推导建立了地形追随坐标的非静力平衡广义垂直运动方程。诊断结果表明,经向气压梯度力耦合经向散度项（项一）、垂直气压梯度力耦合纬向散度项（项二）和非绝热加热经向梯度项（项三）是激发暴雨垂直运动发展演变的三个主要强迫项。项一体现了偏北风逐渐增强,在昆仑山脉的阻挡下导致经向辐合增强,触发了垂直上升运动。经向气流辐合始终是对流活动最主要的强迫过程,其次为纬向气流辐合。在地形追随坐标形式下,经向和垂直气压梯度能够增强项一和项二。对流发展阶段,水汽辐合与非绝热加热过程增强了非绝热加热经向梯度,促进了垂直上升运动发展。在地形的影响下,对流层中高层西风过山气流波动特征明显。重力波活动导致的高层辐散进一步促进了山脉迎风坡对流活动。经向和纬向气流辐合、非绝热加热过程以及重力波活动等多个因素共同造成了此次南疆极端暴雨。     

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.     

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。     

地形强迫对大气长波调整的可能影响

地形作为大气的外部强迫,其动力和热力作用对波动结构演变及极端天气出现都有不能忽视的作用。本文通过数值求解考虑地形强迫的β平面正压准地转位势涡度方程,探讨了地形强迫作用对大气长波调整的可能影响,结果表明:同非线性作用和纬向非均匀基流作用一样,无基流情形下具有纬向差异的地形分布影响了大气长波结构的演变,也能强迫出大气长波调整现象。大气长波调整依赖于地形的高度和地形分布,地形越高,长波越容易出现波数的调整;地形波数越大,即地形结构复杂,越不易出现波数变化。大气长波调整还与纬度有关,纬度越高,β越小,地形强迫作用越突出,长波调整容易出现;反之,低纬度以β效应为主的线性波动不易出现波数调整。大气长波调整对波动初始波动的振幅不敏感,但依赖于波动的初始结构。此外,有基流作用时,地形强迫还是诱发定常波的重要因素,且定常波流场结构依赖于地形高度分布,与波动初始结构无关。     

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。     

THE ROLES OF BOUNDARY-LAYER DYNAMICS ON THE DEVELOPMENT OF MADDEN-JULIAN OSCILLATION*

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.     

Experimental study of the generation, damping, and reflexion of a solitary wave

In a (36 m × 0.55 m × 1.30 m) channel we did numerous experiments to study the generation, propagation, damping and reflexion along a wall of a solitary wave. The data are compared with the available analytical or numerical results. From a given paddle movement, the Inverse Scattering Method is proved to provide with great accuracy the number and amplitude of the generated solitary waves. Then, studying the damping of the wave due to dispersion and viscosity, we find that the formula proposed by Keulegan describes the phenomenon well. This last result enables us to modify the KdV equation with the second term used by Kakutani and Matsuuchi, to compute the solitary wave and tail generated by a given intumescence or a given paddle movement. We notice that the computations fit well with the experimental measurements. Finally, we study the reflexion of a solitary wave from a plane vertical wall. To obtain good experimental data requires great care, but the results agree with the analytical prediction. The reflexion appears to be a rather complex phenomenon and needs further theoretical developments. We present here some experimetal data which confirm recent numerical observations (Mirie and Su, Fenton and Rienecker).     

THE ROLES OF BOUNDARY-LAYER DYNAMICS ON THE DEVELOPMENT OF MADDEN-JULIAN OSCILLATION

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.     

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。