地形强迫对偶极型阻塞形势的影响分析

本研究运用多尺度变换和摄动法简化具有地形强迫的正压准地转涡度方程,得到带有扰动项的非线性Shr?dinger方程,在此基础上,采用孤立子直接微扰理论研究地形强迫对偶极型阻塞结构的作用。研究表明:地形强迫对偶极型阻塞发展具有增强和持续作用,其增长率与大地形山体的斜率成正比。      

旋转球面上行星波的共振相互作用

本文从球面非线性位涡方程出发,应用多重尺度法导出了三波共振的耦合方程.求得非线性耦合方程的通解可以用椭圆函数表示,因而扰动的能量及其变化是有界的.同时,还探讨了共振三波组的守恒律以及共振激发过程中能量的转换.指出在一定的初始条件下,非线性相互作用是可逆的;且就纬向波数谱而言,大波数模态的初始扰动能量在共振激发过程中可以完全转化为较小波数模态的能量.并揭示了旋转大气中非线性行星波动的孤立子性质.     

旋转正压大气中的非线性Schrödinger方程和大气阻塞

本文利用WKB方法导出了旋转正压大气中的非线性Rossby波所满足的立方Schrödinger方程,指出在1≤m≤2的情况下,非线性Schrödinger方程具有包络孤立波解,同时我们还对大气中的包络Rossby孤立波的流场进行了计算,结果得到了阻塞高压和切断低压等结构,并且这些阻塞系统能够维持五天以上。     

旋转正压大气中的非线性Schrödinger方程和大气阻塞

本文利用WKB方法导出了旋转正压大气中的非线性Rossby波所满足的立方Schrödinger方程,指出在1≤m≤2的情况下,非线性Schrödinger方程具有包络孤立波解,同时我们还对大气中的包络Rossby孤立波的流场进行了计算,结果得到了阻塞高压和切断低压等结构,并且这些阻塞系统能够维持五天以上。     

以Schr?dinger方程为例子介绍直接解法及其在波与波碰撞中的应用

本文以描述某些中尺度系统振幅演变的Schr?dinger方程为例子，着重介绍了直接解法及其在波与波的碰撞相互作用过程中的应用。     

中尺度大气运动中孤立重力波特征的研究

通过对斜压大气(基本风场有垂直切变)运动中重力内波的研究发现:对于小振幅扰动(弱非线性问题),考虑波动之间的非线性相互作用以后,控制重力内波波包(调制波)的演变方程是非线性Schrodinger方程.然后通过对冷锋爆发冷涌过程的计算表明:冷涌主体前沿的宽度约10km,行进速度约为13/s,随着冷涌的增强,其宽度变窄.这些计算结果与实际的观测结果比较一致.     

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。     

旋转大气中有限振幅扰动波包与基本气流的非线性共振相互作用

本文应用多重尺度法研究了在旋转球面上正压大气中有限振幅扰动波包与纬向基本气流的非线性共振相互作用。首先,导出了同时包含色散效应和耗散效应的三波共振非线性耦合方程。然后,在零耗散极限和无规相位近似下,求得了不同模态波包的非线性共振耦合方程。并着重讨论了有限振幅扰动波包与纬向基本气流之间的能量输运过程。结果表明,在旋转球面上正压大气中的有限振幅扰动波包通过非线性共振相互作用能够激发出纬向基本气流,而且其能量最终都要输运给纬向基本气流,直至大气运动成为完全的带状环流为止。从而阐明了非线性共振相互作用是大气旋转适应过程的重要物理机制。     

非线性Schrdinger方程差分格式的计算稳定性

运用判定非线性发展方程差分格式计算稳定性的Hirt启发性分析方法,对一类非线性Schrdinger方程差分格式的计算稳定性进行分析,得到了保证差分格式计算稳定的必要条件.数值试验结果进一步表明,得到的稳定性判据不仅是保证差分格式计算稳定的必要条件,而且在实际中也是非常有效的.     

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.     

The dynamic mechanism of the formation of the low level jet

The ordinary multidimensional reductive perturbation method is generalized so as to apply to the general case including the dissipative factor. With this the corresponding Cubic-Schrödinger equation is deduced, and by the preliminary study of its solution, it shows that it is more admissible to consider atmospheric meso-scale systems as the nonlinear Cubic-Schrödinger waves. With suitable boundary and initial conditions, the Cubic-Schrödinger equation is numerically integrated so as to investigate the possible dynamic mechanism as well as the impacts of the nonlinear action, turbulent friction and topogrphy to the formation of the LLJ. The results indicate that the downward transfer of the momentum and the effect of the surface friction are responsible for the concentration of the momentum in the layer between 850 and 700 hPa. The location of the horizontal concentration of momentum depends on the propagation of momentum, in the process the inertia-gravity internal wave is very important, whereas turbulent friction is unfavourable for or delays the formation of the low level jet.     

切变基流中赤道Rossby包络孤立波

A simple shallow-water model on an equatorialβ-plane is employed to investigate the nonlinear equatorial Rossby solitons in a mean zonal flow with meridional shear by the asymptotic method of multiple scales. The cubic nonlinear Schrodinger (NLS, for short) equation, satisfied for large amplitude equatorial envelope Rossby solitons in shear basic flow, is derived. The effects of basic flow shear on the nonlinear equatorial Rossby solitons are also analyzed.     

南海夏季风爆发前后扰动演变及其数值研究

以球面正压涡度方程为数学模型，建立了线性和非线性的数值积分模式，通过在模式中设置不同的基本流场和初始扰动场，研究基流和初始场对扰动发展的作用，揭示在球面正压大气中扰动发展的动力学机制。数值试验结果表明:在线性模式中，扰动的移动和发展与基流的分布有着很密切的关系，基流影响着扰动纬向传播的速度和方向； 在非线性模式中，当基流稳定时，扰动的移动以及传播与线性模式的结果相同，但与线性情况的最大区别在于，此时扰动能量的增长存在上限。同时发现，扰动的发展既依赖于基本气流的分布，也依赖初始扰动的结构；南海夏季风爆发前后的基本流场是正压不稳定的，且这种不稳定在季风爆发时达到最强，这可以成为季风爆发的动力学解释。     

斜压大气中尺度扰动的有限振幅对称不稳定

本文通过一个非地转、非静力的Eady模式讨论了斜压粘性流中的非线性对称不稳定。采用具有常值水平和垂直切变的基本场,考虑扰动沿基本气流方向不变,应用摄动方法,得到了非线性情况下扰动振幅的特性方程。结果表明,当δ>0时(δ是进行稳定性分析时所选取的无量纲小参数),振幅|A(T)|存在两个有意义的平衡点|A|_(b1)=0和|A|_(b2)=(-μ_2/μ_1)~(1/2)(μ_1,μ_2是和流体性质、区域大小以及波参数有关的量),|A|_(b1)为不稳定平衡点,|A|_(b2)为稳定平衡点。因此,不论初态如何,终态都趋于稳定平衡点,出现有限振幅现象。当δ<0时,振幅|A(T)|仅有一个有意义的平衡点|A|_(b1)=0,且为稳定平衡点。线性分析所得结果为非线性结果的特例。     

Interaction between a slowly moving planetary—scale dipole envelope rossby soliton and a wavenumber— two topography in a forced higher order nonlinear Schrödinger equation

A parametrically excited higher-order nonlinear Schr dinger (NLS) equation is derived to describe the interaction of a ,slowly moving planetary-scale envelope Rossby soliton for zonal wavenumber-two with a wavenumber-two topography under the LG-type dipole near-resonant condition. The numerical solution of this equation is made. It is found that in a weak background westerly wind satisfying the LG-type dipole near-resonance condition, when an incipient envelope Rossby soliton is located in the topographic trough and propagates slowly, it can be amplified through the near-resonant forcing of wavenumber-two topography and can exhibit an oscillation.However, this soliton can break up after a long time and excite a train of small amplitude waves that propagate westward. In addition, it is observed that in the soliton-topography interaction the topographically near-resonantly forced planetary-scale soliton has a slowly westward propagation, but a slowly eastward propagation after a certain time. The instantaneous total streamfunction fields of the topographically forced planetary-scale soliton are found to bear remarkable resemblance to the initiation, maintenance and decay of observed omega-type blocking high and dipole blocking. The soliton perturbation theory is used to examine the role of a wavenumber-two topography in near-resonantly forcing omega-type blocking high and dipole blocking. It can be shown that in the amplifying process of forced planetary-scale soliton, due to the inclusion of the higher order terms its group velocity gradually tends to be equal to its phase velocity so that the block envelope and carrier wave can be phase-locked at a certain time.This shows that the initiation of blocking is a transfer of amplified envelope soliton system from dispersion to nondispersion. However, there exists a reverse process during the decay of blocking. It appears that in the higher latitude regions, the planetary-scale envelope soliton-topography interaction could be regarded as a possible mechanism of the establishment of blocking.     

Nonlinear rossby wave induced by large-scale topography

In this paper, a barotropic model is used to discuss the nonlinear Rossby wave induced by the large-scale topography. By using separate multi-scale perturbation method and matching boundary condition, the general-ized KDV equation is obtained. Especially, in consideration of the effect of the Tibetan Plateau, the distribu-tions of the disturbance stream function is given. It is proved that solitary wave induced by the large-scale topog-raphy exists indeed and it has direct influence on the weather of its lower reaches.     

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。     

The effect of barotropic shear on baroclinic instability Part II: The initial value problem

The effect of barotropic shear on baroclinic instability has been investigated using both a linear quasi-geostrophic β-plane channel model and a multilevel primitive equation model on the sphere when a nonmodal disturbance is used as the initial perturbation condition. The analysis of the initial value problem has demonstrated the existence of a rapid transient growth phase of the most unstable mode. The inclusion of a linear barotropic shear reduces initial rapid transient growth, although at intermediate times the transient growth rates of the sheared cases can be larger than in the unsheared case owing to downgradient eddy momentum fluxes. Certain disturbances can amplify by factors of 4.5–60 times (for the L₂ norm), or 3–30 times (for the perturbation amplitude maximum), as large as disturbances based on the linear normal modes. However, linear horizontal shear always reduces the amplification factors. The mechanism is that the shear confines the disturbance meriodionally and therefore limits the energy conversion from the zonal available potential energy to eddy energy. The effect of barotropic shear on the transient growth is not changed much in the presence of either thermal damping or Ekman pumping. Nonmodal integrations of baroclinic wave lifecycles show that the energy level reached by eddies is not very sensitive to the structure of the initial disturbance if the amplitude of the initial disturbance is small. Although in some cases the eddy kinetic energy level reached by the wave integrated from nonmodal disturbance can be 25–150% larger than the normal mode integrations, barotropic shear, characterized by large shear vorticity with small horizontal curvature, always reduces the eddy kinetic energy level reached by the wave, confirming the results of normal mode studies.