垂直切变流中非线性重力波及其相互作用

利用多重尺度摄动法，推导出斜压大气中(基本风场具有垂直切变)两个非线性重力波相互作用方程，这两个方程联立组合为耦合非线性schrǒdīnger方程组。两个重力波相互作用时可激发出重力驻波。数值计算表明：两个孤立重力波相遇，相追会使波振幅增大，波宽变窄。强烈对流天气突然爆发的可能原因之一是中尺度重力波非线性相互作用的结果。     

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。     

斜压切变基流中横波型扰动的特征波动──Ⅰ:谱点分析

文中对谱点的分布作了定性分析和数值计算。结果发现：当基流存在切变时,无论是重力惯性波还是涡旋波都存在连续谱。在通常的环境下,对天气尺度的扰动,3支波动的连续谱不重叠,3支波动明显可分;当扰动尺度小于临界波长l0时,可出现涡旋波和一支重力惯性波的两波连续谱区的重叠,当扰动尺度小于l0／2时,可出现涡旋波和一对重力惯性波的三波连续谱区的重叠,此时两种波动不可分。当出现重叠谱时,若出现不稳定扰动,其频率的实部落在重叠谱区。     

The structure and propagation of stationary planetary wave packet in the barotropic atmosphere

Monthly or seasonally mean anomalies of large-scale atmospheric circulation are better represented by wave packets or their combination. Both qualitative and quantitative analyses of equations of wave packet dynamics, which are obtained by the use of WKB approximation, are very helpful for the understanding of structure, formation and propagation of stationary and quasi-stationary planetary wave packet patterns in the atmosphere. Indeed, these equations of wave packet dynamics can be directly solved by the method of characteristic lines, and the results can be simply and clearly interpreted by physical laws. In this paper, a quasi-geostrophic barotropic model is taken for simplicity, and the wave packets superimposed on several ideal profiles of the basic current and excited by some ideal forcings are investigated in order to make comparison of the accuracy of calculation with the analytical solution. It is revealed that (a) the rays of stationary planetary wave packet do not coincide with but go away from the great circle with significant difference if the shear of the basic zonal flow is not too small; (b) being superimposed on a westerly jet flow with positive shear (Uλ/y>0), the stationary wave packets excited by low-latitudinal forcing are first intensified during their northeastward propagation in the Northern Hemisphere, then reach their maximum of amplitude at some critical latitude, and after that weaken again; (c) the connected line of extremes (the positive and negative centres) of wave packet does not coincide with but crosses the ray by an angle, the larger the scale of external forcing, the larger the angle; and (d) the whole pattern of a trapped stationary wave packet is complicated by the interference between the incident and reflected waves.     

垂直切变基流中东西向地形对惯性重力波稳定性的影响

利用分层浅水波方程和小参数(WKB)方法，考虑具有垂直切变的基流和地形的作用，求得惯性重力波的局地频率方程，并根据此方程分析讨论了在多种环境条件下波动的稳定性情况。     

The nonlinear interaction between different wave components and the process of index cycle of general circulation

By using a two-level quasi-geostrophic truncated spectral model taking account of the nonlinear in-teraction between different wave components (i. e. basic current, ultra-long waves and long waves), the index cycle of general circulation is investigated. The calculated results show that the circulation index has a, quasi-periodic vacillation with a period of 8 to 16 days, which can be created by the nonlinear interaction and that the nonlinear interaction between different wave components may cause the tilted-trough vacillation, amplitude vacillation of wave pattern and quasi-periodic change of wave number of flow pattern.     

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.     

Properties and stability of a meso-scale line-form disturbance

By using the 3D dynamic equations for small- and meso-scale disturbances, an investigation is performed on the heterotropic instability (including symmetric instability and traversal-type instability) of a zonal line-like disturbance moving at any angle with respect to basic flow, arriving at the following results: (1) with linear shear available, the heterotropic instability of the disturbance will occur only when flow shearing happens in the direction of the line-like disturbance movement or in the direction perpendicular to the disturbance movement, with the heterotropic instability showing the instability of the internal inertial gravity wave; (2) in the presence of second-order non-linear shear, the disturbance of the heterotropic instability includes internal inertial gravity and vortex Rossby waves. For the zonal line-form disturbance under study, the vortex Rossby wave has its source in the second-order shear of meridional basic wind speed in the flow and propagates unidirectionally with respect to the meridional basic flow. As a mesoscale heterotropic instable disturbance, the vortex Rossby wave has its origin from the second shear of the flow in the direction perpendicular to the line-form disturbance and is independent of the condition in the direction parallel to the flow; (3) for general zonal line-like disturbances, if the second-order shear happens in the meridional wind speed, i.e., the second shear of the flow in the direction perpendicular to the line-form disturbance, then the heterotropic instability of the disturbance is likely to be the instability of a mixed Rossby–internal inertial gravity wave; (4) the symmetric instability is actually the instability of the internal inertial gravity wave. The second-order shear in the flow represents an instable factor for a symmetric-type disturbance; (5) the instability of a traversal-type disturbance is the instability of the internal inertial gravity wave when the basic flow is constant or only linearly sheared. With a second or nonlinear vertical shear of the basic flow taken into account, the instability of a traversal-type disturbance may be the instability of a mixed vortex Rossby – gravity wave.     

Wave/wave interaction producing horizontal mean flows in stably stratified fluids

We show that internal wave/wave interactions in stratified fluids are able to produce strong horizontal mean currents. A simple analytical model allows us to estimate the amplitude of the time-periodic horizontal mean flow induced by the interaction of two monochromatic waves. This model shows that in some cases, the mean flow velocity can overgo a threshold beyond which critical layers and intense energy transfers from the waves to the mean flow are expected. This prediction is confirmed by direct pseudo-spectral simulations of the Navier–Stokes equations under the Boussinesq approximation. Such interactions may help to further understand the presence of strong vertical shear observed in the final stage of stratified flows in oceans and atmospheres.     

Stationary Rossby wave propagation in a shear flow along a reflective boundary

Summary This study investigates the impact of lateral boundary conditions on the propagation and dispersion of locally excited Rossby waves in a zonally periodic, barotropic, quasigeostrophic channel model on the β-plane. We use basic flows with either a linear meridional shear or a jet-like profile. On the southern boundary of the channel we impose either a rigid wall or a radiation condition, whereas the northern sidewall is permeable for Rossby waves. We compare the numerical solutions found for a reflecting southern boundary in a weakly dissipative flow to the solutions obtained from a WKB-analysis for the corresponding unforced nondissipative situation. Furthermore, we compare the generalized Eliassen-Palm flux vectors to the ray paths of Rossby wave packets, obtained from WKB ray tracing. In particular, we focus our investigation on the two-dimensional structure of trapped modal waves and wavetrains in a simple linear numerical model. Summarizing our results, we find that along the reflective wall, trapped modal wave structures as well as reflected wavetrains occur with characteristics (e.g., wavenumbers, turning latitudes) similar to the ones computed using asymptotic methods. In a linear sheared flow wave packets are trapped for all zonal wave numbers in contrast to a jet-like mean flow which has a selective effect on the waves; i.e., a turning latitudes phenomenon between the coast and the flow maximum occurs for short waves, while long waves can propagate freely across the zonal mean flow. This comes out clearly when studying the stream lines of the Eliassen-Palm flux vectors of the numerical model simulations. Furthermore, due to the reflected wave activity, the dispersion of Rossby waves is influenced by the southern boundary condition not only in the vicinity of the border but also in regions away from the boundary. These results appear to be important on the one hand for the existence of trapped Rossby waves in large-scale oceanic shear flows along a zonally oriented coast. And, on the other hand for large-scale boundary waves in conceptional atmospheric channel models which can lead to unwanted resonance effects. Received July 18, 2000/Revised June 9, 2001     

低空急流和非均匀层结条件下重力惯性波的传播与发展

本文从基流背景下线性化Boussinesq方程组出发,采用WKBJ方法,首先求得重力惯性波的广义波作用量变化方程及波参数随波包的变化方程,讨论了基流切变对重力惯性波传播和发展的影响;然后用Runge-Kutta方法讨论了不同层结(含降水影响)下重力惯性波的传播路径。得到了降水强度大、静力稳定度小的区域对重力惯性波有“吸引”作用,因而引起重力惯性波能量的集中,进而触发和强化对流天气的结论。      

波流相互作用与波动传播模态

波和流是大气中两种最基本的运动形式,两者之间的相互作用可以导致千变万化的天气现象。波流相互作用理论是大气动力学的基本理论之一,该理论的研究具有重要的理论价值和科学意义。波流相互作用的研究主要包括两方面:一方面是可以描述基本气流对波强迫作用的“波作用”（守恒）方程的研究,另一方面是可以描述波对基本气流反馈作用的E-P通量以及波形变、传播等理论的研究。波流相互作用的研究不仅在理论上已取得重要进展,例如, E-P通量的提出,剩余环流的引进,广义E-P通量的出现,三维E-P通量的建立,波作用守恒方程、波动突变、波流稳定性结构、波形变及其大圆路径、低频波遥相关等理论的发展,而且在实际应用上也取得丰硕成果,如科学地解释了赤道平流层东西风准两年振荡、极地平流层爆发性增温、瞬变波对阻高的维持和高空急流加速以及大气低频波遥相关等,特别是为预测行星波的传播,研究风暴轴和诊断分析实际大气中波能集中区和发散区提供了理论基础和科学方法。作者从小振幅和有限振幅扰动两方面回顾了国内外波流相互作用和低频波传播理论的研究进展,重点介绍了大尺度环流系统波流相互作用和波动传播模态的最新研究成果,提出了不同动力、热力背景下多尺度波流相互作用机理及其理论模型,建立了非线性大气动力学突变及其稳定性结构等理论。相对来说,热源强迫和地形强迫引起的波流相互作用中稳定性问题的研究一直比较薄弱,特别是关于大气水分循环过程和青藏高原等复杂大地形影响下不同尺度系统波流相互作用的研究,这也是未来波流相互作用研究的一个重要内容。     

Baroclinic solitary waves with radial symmetry

A model for the structure and motion of baroclinic solitary waves in the atmosphere or ocean is presented. Like gravity wave solitons, these planetary wave solutions are both weakly nonlinear and weakly dispersive. The dispersion effects, induced by β, are small because the scale of the wave is large compared to the deformation radius. The steepening effects are provided by the interaction of the wave with exterior mean shear flow, which may be either barotropic or baroclinic. The solutions have two properties which suggest that such theories may be useful in modelling solitary disturbances in the atmosphere or ocean: radial symmetry and fluid speeds which exceed the phase speed of the wave itself. As an example, we apply the model to Gulf Stream Rings.     

垂直切变和地形影响下惯性重力波的发展

采用分层浅水波方程和ＷＫＢ方法，分别讨论了在基流垂直切变和地形的影响下，二维惯性重力波的稳定性及其发展，并根据理论结果试图解释１９９２年６月２１日发生在京津冀的一次飑线演变与惯性重力波之间的关系，这可能为飑线预报提供一种思路     

斜压切变基流中横波型扰动的特征波动 Ⅱ:谱函数

“斜压切变基流中横波型扰动的特征波动Ⅰ谱点分布”一文中分析了斜压切变基流中横波型扰动的谱点分布，这里又对其谱函数进行了分析讨论。结果表明当基流在垂直方向存在切变时，重力惯性波与涡旋波的谱函数在垂直方向上均可出现临界层，临界层的高度随频率σ而变化，即重力惯性波与涡旋波都存在连续谱，但涡旋波与重力惯性波连续谱的结构却不同；对天气尺度扰动，两支重力惯性波和1支涡旋波的连续谱不重叠，此时每支波动仅有1个临界层；而对次天气尺度的扰动，重力惯性波与涡旋波的连续谱区会发生重叠，在连续谱的重叠区，重力惯性波仍只有1个临界层，但涡旋波则可以有2个或3个临界层。无论是涡旋波还是重力惯性波其连续谱的波包随时间都是衰减的，但涡旋波波包比重力惯性波波包衰减得慢。     

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。     

低纬地区超长波的三维分析

本文从原始方程组出发,在赤道β平面上采用正交模态法,对低纬超长波进行水平结构和垂直结构分析,发现低纬超长波主要出现在对流层上层和平流层低层。其次,本文还讨论了含有低纬理想热源的原始方程模式,并通过对模式求数值解得出:低纬热源强迫是对流层上层Kelvin波的形成原因之一。      

关于西风急流在强迫扰动中作用的数值试验

本文利用非线性水波方程谱模式模拟了不同基本气流对低纬和中纬地区涡源扰动的强迫响应，进而讨论西风急流在大尺度流场强迫扰动中的作用。试验分析表明，中纬度西风急流对来自低纬的扰动波列有增哟的阻 阻滞的作用，并能影响强迫扰动的波数和路径。在存在西风急流的情况下，基本气流对低纬扰源的响应比对中纬扰源的响应要强得多。     

纬向气流对地形Rossby波的影响

本文在半地转近似下,采用相平面方法讨论了纬向基本气流对线性和非线性地形Rossby波的稳定性及解的性质的影响。结果指出:线性和非线性稳定性判据形式一样,纬向气流及其切变对稳定性有明显影响;在非线性近似下,可形成孤立波槽和孤立波脊。