HEAT SOURCE-INFLUENCED FINITE AMPLITUDE ULTRALONG WAVE*

Discussed in this paper is finite amplitude ultralong wave under the influence of heat sources.The conditions are first investigated for the existence of periodic and solitary ultralong waves of finite amplitude in the Burger model with the aid of Hamilton function and variation of total energy and then the wave analytical expression is formulated by means of the functional approximation and the Hamilton function as the motion invariant in nature.Results show that the finite amplitude ultralong wave influenced by heat sources is unlikely to generate a solitary wave solution and imposes no constraints on horizontal divergence as opposed to the case with the effect of heat sources available.     

有热源影响的有限振幅超长波

研究了有外界热源作用下的有限振幅超长波，首先利用Ｈａｍｉｌｔｏｎ函数及总能量变化方法讨论了有限振幅周期性和孤立性超长波的存在条件。然后用Ｈａｍｉｌｔｏｎ函数为运动不变量性质与函数逼近法求得波的解析式。同时指出，不考虑热源影响的有限振幅超长波不会产生孤立波解，对水平散度也无约束；但引入热源后，由能产生孤立波解，并且对水平散度有一定约束。     

阻塞高压建立的非线性机理探讨

文中建立了一个考虑斜压大气的超长波、长波与纬向气流相互作用的动力系统 ,其中把热力强迫和摩擦耗散作为外参数 ,采用相轨线图、流函数图和Poincar啨图综合分析的方法 ,绘制了外参数平面上的系统状态和环流型式的分布图。结果表明 :用Galerkin方法时 ,在一定范围内截谱阶数的增加对系统状态分布和环流型分布的影响不大 ,但在一定程度上增加了复杂性 ;加热分布的改变对系统影响很大 ;阻塞高压与环流振荡、经向度强烈发展有密切的联系 ,而天气波的发展有利于激发振荡。     

与海南岛秋季暴雨有关的一类热带中尺度涡旋的动力学分析

对惯性重力内波方程组分别通过线性和非线性求解探讨造成2010年10月海南岛一次特大暴雨中一类热带中尺度涡旋生成发展的动力、热力机制,研究发现:（1）在副热带高压和大陆冷高压南侧反气旋性纬向水平风切变大值区、静力不稳定大气层结、积云对流潜热释放、低空急流、适当强度的冷空气有利于热带中尺度涡旋的形成和发展;（2）非线性惯性重力内波的孤立波解与这类热带中尺度涡旋有很好的联系,在静力不稳定的大气层结下,热带中尺度涡旋的形态主要由对流凝结潜热加热所决定,即潜热加热下的孤立波解要求热带中尺度涡旋在垂直方向是一个浅薄的涡旋系统;另外强盛的对流凝结潜热对热带中尺度涡旋垂直运动振幅的增强起主要作用,更有利于涡旋的发展和维持。基于天气事实分析的理论研究为深化影响海南的热带中尺度涡旋乃至南海中尺度对流系统的机理认识进行了探索。      

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。     

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.     

The stability of a coupled wave-turbulence system in a parallel shear flow

The dynamic stability of a statically stable parallel shear flow is modulated by the presence of a finite amplitude wave. This can cause turbulent breakdown of the flow in the regions of reduced stability. The fluxes of momentum and heat driven by the turbulence interact with the initiating wave, and in favorable circumstances this leads to growth of the wave amplitude so that the wave-turbulence system is explosively unstable. Such interaction seems to be possible within the night-time inversion of the atmosphere.National Oceanic and Atmospheric Administration/University of Colorado.     

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.     

外源与孤波的相互作用对阻塞形成的影响

利用准地转涡度方程导出包括外源和摩擦耗散的强迫广义KdV-Burgers方程,分析表明,外源和耗散的存在是孤波质量和能量变化的原因,耗散使孤波质量和能量随时间呈指数减小。数值计算结果指出,移动性孤波和外源的相互作用,使孤波移速减小,振幅增大;在无耗散情况下,失谐参数α较小时,由于孤波迅速离开外源强迫区,因此不利于阻塞的形成;小耗散的存在,迫使相互作用过程中孤波在外源强迫区附近来回振荡传播,大大增加相互作用时间,可能是造成外源区附近局地阻塞的一种重要机制。     

A Numerical Study Of Nocturnal Wavelike Motion In Forests

In this paper, we use a two-dimensional eddy-resolved model to investigate the instability of a parallel shear flow in a stably stratified boundary layer whose lower domain is occupied by a canopy. The results support our contention that wave motion in the canopy is initiated by shear in an air layer near the treetops. Significant modification by the wave motion of the mean velocity and temperature fields is found even before the wave reaches saturation. The wave fluxes of momentum and heat are not constant with height. Downwind tilting braids are found at the finite amplitude stage of the wave growth and could persist after wave breaking; these downwind tilting structures are believed to be the same as the temperature microfronts reported in the literature. We also present an analysis of the velocity and temperature fields of an observed wave event in the time-height domain and show that the simulation has captured the broad features of the observation.     

局地热力强迫与准定常大振幅扰动的形成

文中导得了包括热力强迫和耗散的非线性强迫ＫｄＶ－Ｂｕｒｇｅｒｓ方程,并作了数值求解。计算结果表明,热力强迫和耗散是孤波质量和能量变化的主要原因,耗散使孤波质量能量随时间指数衰减;热力强迫与地形一样,都能在强迫区产生定常孤波,但前者产生的上游扰动振幅更大,而后者产生的下游扰动更为明显;加热和地形一样都能使孤波发生位相漂移,减小其移速,阻挡孤波的移动,从而增加与孤波的相互作用时间;适当大小的耗散与热力强迫的组合迫使移动性孤波在强迫区附近来回振荡,大大增加与热力强迫的相互作用时间;在耗散与热力强迫同时存在的非线性系统中,移动性孤波与热力强迫的相互作用可能是产生阻塞等长生命周期的局地准定常系统的重要因子。     

mKdV Equation for Solitary Rossby Waves with Linear Topography Effect in Barotropic Fluids

The modify Korteweg-de Vries (mKdV) equations, governing the evolution of the amplitude of solitary Rossby waves, are derived from quasi-geostrophic vorticity equation by using the perturbation method. The result manifests that the linear topography effect with the change of latitude can induce solitary Rossby wave.     

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。     

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。     

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 dynamics of baroclinic and barotropic solitary eddies

We derive exact nonlinear solutions to the inviscid quasigeostrophic two-layer equations. The solutions represent isolated eddies with an amplitude that decays rapidly away from the eddy. They translate steadily either to the east (if there is a barotropic component in the fringes of the eddy) or either to the east or rapidly to the west (if the exterior field has only a baroclinic mode structure). They are strong in the sense that all of the fluid within a finite radius from the center is carried along with the eddy as it translates. The solutions have a characteristic north-south antisymmetry with the nonlinear vortex pair interactions being an essential feature of the dynamics. However, we also show that radially symmetric perturbations of a special form but arbitrary amplitude can be superimposed on the basic solutions; thus the antisymmetric structure may to some extent be masked. We show nondimensional dispersion relationships: atmospheric and oceanic planetary wave phenomena do fall in the range of parameters where theory predicts solitary eddy solutions can exist.     

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.     

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.     

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.