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。     

地形与纬向切变基流中的非线性Rossby波

在半地转近似下,用相角函数方法得到了含地形强迫作用与纬向切变基流的非线性常微分方程.利用微分方程解的几何定性理论,直接得到该方程存在有限振幅的周期波与孤立波解的存在条件.利用函数逼近法求得波解的显式解,得到了一些有意义的结果。     

热带气旋解析解与数值解的比较

对热带气旋波谱分析正确性的验证进行了讨论。通常可找一个能解析求解的特例,并对该特例求数值解,然后比较两者的结果。在保证解析解正确的前提下,若两者结果不一致,则数值求解肯定有问题。这里给出了热带气旋波谱分析验证的具体步骤,还求得了基流趋于零时热带气旋尺度涡旋中正压原始方程特征值问题的解析解。通过比较解析解和数值解的频率可知,两者的差别并不大,最大相对误差小于10％。这表明数值计算的方案设计和编程至少在基流趋于0时是没有问题的。此时仅存在一对重力惯性波,并得到了其频率方程,其特征函数可用Bessel函数来表示。因该函数是基流趋于0情况下扰动的解,故其不可能再是典型基流下的解。该情形下求取数值解看来是唯一的办法。     

低频球面正压大气行星波的频散特征及大气环流遥相关型形成的物理机制

本文研究了非均匀基本纬向流中低频球面正压大气行星波的能量频散特征,讨论了波射线,求得了波射线路径的近似方程。此外,还讨论了沿波射线波包振幅和能量的变化。所得结果可给出大气环流遥相关型水平结构形成及其演变的基本物理图象。      

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。      

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。     

旋转二维可压缩流动的谱和特征函数——Ⅱ:谱和谱函数结构的分析

本文第一部分(Ⅰ)已给出了线性化旋转二维可压缩流动方程的谱分布,并作了初步分析。本部分(Ⅱ)对这些谱及谱函数作进一步的分析讨论。设基流是低速流,此时可用摄动法求得谱和谱函数,将它们与用差分法所得结果进行比较,表明二者吻合得很好。摄动法中的离散谱初级近似就是无基流时的相应的谱,而连续谱对应的谱函数初级近似则与准地转模式的结果一致。由初级近似和一级修正项可以清楚地说明计算所得的谱和谐函数的许多重要性质。 在低速基流情况下:(1)重力一惯性波为准简谐波,基流和可变的Coriolis参数只给以较小的修正。(2)由于基流在Coriolis力作用下使自由表面有一坡度,Kelvin波必定具有横穿波射线的速度分量,同时顺传和逆传的Kelvin波不再在形态上相似;当基流愈强时上述两性质愈明显;Coriolis参数随空间的变化也改变了顺传和逆传波的相似性,此外,Kelvin波是准非频散的。(3)不为零的基流或科氏参数的变化使慢波离散谱变为非简并的即分立的,它们或者有无穷多个且基流流速为相速的聚点(当基流为常数时),或者只有有限个,甚至不存在;而当基流有切变时则有连续谱。对应于离散谱的谱函数为准简谐波;而对应于连续谱的谐函数则为广义解,但有有限能量。 本问题的谱函数与其伴随算子的谐函数正交,满足同样边界条件     

强迫二维Rossby波传播特征的数值试验

Bjerknes提出了大气对外界强迫响应的概念。大量研究已证明这一遥响应机制的存在,且大气对强迫源的遥响应及其低频活动的共同特征都表现为类似大圆路径的波列,Hoskins的理论研究揭示了这现象的实质,他把叶笃正所提出的Rossby波的频散理论推广到球面上。黄荣辉曾利用波折射指数平方与EP通量系统地研究了北半球冬夏准定常行星波的传播规律。邹晓蕾、叶笃正、吴国雄提出了中高纬的相关链、定常地形波链,并指出北美与东亚相关型的差异与两区域地形准定常波在不同纬向流中传播的差异有关。观测分析亦表明,青藏高原是大气低频振荡的强迫源,且在此区域可产生向北、向南或向东、向西传播的波列。     

线性和非线性正压不稳定

本文从无摩擦的、无辐散的非线性正压涡度方程出发,利用行波解,在相平面上对方程的平衡点分别导得线性和非线性正压不稳定判据,与传统的不稳定判据作了比较分析。还求得了线性和非线性不稳定波的解析解,计算结果表明,若初始时刻两者波幅相等,则以后非线性不稳定波幅的增长值总小于线性不稳定波幅的增长值。非线性效应有使线性不稳定指数型增长减缓的作用。不稳定使得振幅比初始时刻增大一倍所需要的时间,对于线性不稳定大约是6h,对于非线性不稳定大约是18h,后者与实际大气中的观测事实是一致的。     

近共振热力强迫作用下多重平衡态的激发、建立和转换(一)——多重平衡态的渐近解

本文通过一个含有近共振热力强迫和耗散、基本流有常数切变的二层准地转β-平面纬向周期性窄通道斜压模式,运用多尺度方法导出一投影在T—X时空平面的、包含强迫波—自由波—自由波非线性相互作用的、关于定常热强迫波上扰动的偏微分方程组.借助奇异摄动法解析地求得了此方程组的平衡态渐近解.结果得到,在很大的参数范围内都可存在多重平衡态.     

Variational principle of instability of atmospheric motions

Problems of instability of rotating atmospheric motions are investigated by using nonlinear governing equations and the variational principle. The method suggested in this paper is universal for obtaining criteria of instability in all models with all possible basic flows. For example, the model can be barotropic or baroclinic, layer or continuous, quasi-geostrophic or primitive equations; the basic flow can be zonal or nonzonal, steady or unsteady.Although the basic flows possess a great deal of variety, they all are the stationary points in the functional space determined by an appropriate invariant functional. The basic flow is an unsteady one if the conservation of angular momentum is included in the associated functional.The second variation, linear or nonlinear, gives the criteria of instability. Especially, the general criteria of instability for unsteady basic flow, orographically disturbed flow as well as nongeostrophic flow are first obtained by the method described in this paper.It is also shown that the difference between the criteria of instability obtained by the linear theory and our variational principle clearly indicates the importance of using nonlinear governing equations.In the appendix the theory is extended to cases such as in a β-plane where the fluid does not possess finite total energy, hence the variational principle can not be directly applied. However, a generalized Liapounoff norm can still be obtained on the basis of variational consideration.     

NONLINEAR BAROTROPIC INSTABILITY INCLUDING FRICTION DISSIPATION,THERMAL DRIVING AND LARGE TOPOGRAPHY*

From a nonlinear quasi-geostrophic barotropic vorticity equation including frictional dissipation,thermal driving and large topography used by Charney in investigation of the multiple flow equilibria and blocking,using the Serrin-Joseph energy method and the variational principle,we found the nonlinear barotropic stability criteria of the zonal basic flow with the total energy,total enstrophy and their linear combination respectively,and compared the criteria with Charney's results.     

强迫和耗散作用下大气运动的非线性正压不稳定

本文从Charney研究多平衡态的包含摩擦耗散、热力强迫和大地形的非线性准地转正压涡度方程出发,应用Serrin-Joseph的能量方法,利用变分原理,分别用总能景和总位涡拟能导得纬向基流的非线性正压稳定性判据。      

龙卷风与旋衡风的动力学分析及其统一认识

通过对旋衡风的受力分析,验证旋衡风遵守的基本物理原理:即旋衡风旋转的气流具有的离心力与其所承受的气压梯度力平衡。提出了龙卷风与旋衡风的统一认识:即龙卷风是旋衡风超高速旋转的极端存在形式。依据旋衡风所遵守的基本原理对龙卷风(或旋衡风)建立物理模型,根据该模型对龙卷风的角速度、密度以及其旋转气流层半径进行了参数化描述。依据龙卷风的模型分析探索龙卷风的压强差梯度场,得到龙卷风中心到边缘距离的气压变化值与龙卷风半径及其旋转气流层的角速度、密度的关系,并提出相关计算的数学表达式,以及龙卷风具有的能量与龙卷风旋转气流层各参数的关系。龙卷风及旋衡风的旋转运动还受其本身角动量守恒的制约,并论证了龙卷风旋转气流层的密度与半径以及角速度的关系。     

摩擦耗散大气中切变流的非线性稳定性

本文从包含摩擦耗散的非线性准地转方程组和包含摩擦耗散与大地形作用的非线性浅水波方程组出发,使用了Serrin-Joseph的能量方法,利用变分原理,分别用总能量和总位涡拟能导得这两个方程组的切变基流的非线性稳定性判据。     

再论球面上正压准地转运动的半圆定理

进一步了球面上正压准地转运动中不稳定波的Ｈｏｗａｒｄ半圆定理，发现在某些特定的基本流分布下，该定理可以发展成圆弧定理，由此得到不稳定扰动增长率的更为精确的估计式。     

On the Nonlinear Stability of Three-Dimensional Quasigeostrophic Motions in Spherical Geometry

Nonlinear Mobility criteria for the motions geoverned by three-dimensional quasigeostrophic model in spherical geometry are obtained by using Arnol’d’s variational principle and a priori estimate method. The results gained in this paper are parallel to Arnol’d’s second theorem and better than the known results. Especially, under the approxima-tion of vertically integrated nondivergency, criteria corresponding to Arnol’d’s second theorem are first established by a detailed analysis.     

On a Non-local Parameterisation for Shear Turbulence and the Uniqueness of its Solutions

A non-local parameterisation of shear turbulence is proposed, which includes a dimensionless multiplicative constant as the sole tunable parameter. Analytical and numerical solutions in the case of plane Couette flow exhibit sheared velocity profiles with logarithmic behaviour near the boundaries, and the classical logarithmic flow profile is reproduced for a semi-infinite domain. We also prove that the families of analytical solutions obtained are locally unique: if the velocity is a strictly-increasing function of the distance from the boundary, a small perturbation of the velocity profile must be of the same functional form as the basic flow.     

Three－dimensional Global Scale Permanent－wave Solutions of the Nonlinear Quasigeostrophic Potential Vorticity Equation and Energy Dispersion

The three-dimensional nonlinear quasi-geostrophic potential vorticity equation is reduced to a linear form in the stream function in spherical coordinates for the permanent wave solutions consisting of zonal wavenumbers from 0 to n and rn vertical components with a given degree n. This equation is solved by treating the coefficient of the Coriolis parameter square in the equation as the eigenvalue both for sinusoidal and hyperbolic variations in vertical direction. It is found that these solutions can represent the observed long term flow patterns at the surface and aloft over the globe closely. In addition, the sinusoidal vertical solutions with large eigenvalue G are trapped in low latitude, and the scales of these trapped modes are longer than 10 deg. lat. even for the top layer of the ocean and hence they are much larger than that given by the equatorial β-plane solutions. Therefore such baroclinic disturb-ances in the ocean can easily interact with those in the atmosphere.Solutions of the shallow water potential vorticity equation are treated in a similar manner but with the effective depth H = RT / g taken as limited within a small range for the atmosphere.The propagation of the flow energy of the wave packet consisting of more than one degree is found to be along the great circle around the globe both for barotropic and for baroclinic flows in the atmosphere.     

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.