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。     

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。     

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.     

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.     

INFLUENCES OF TOPOGRAPHY ON BAROCLINIC SOLITARY ROSSBY WAVES IN A MULTILEVEL MODEL

The KdV equation with topography included in an N-level model is derived. It is shown that if the topography ex-ists. the KdV equation may describe the solitary Rossby waves in the case of basic current without vertical shear, and itis no necessary to introduce the MKdV equation. The results of calculations show that the change of horizontal shearpattern of basic flow may cause an important change of the streamline pattern of the solitary waves with the oddmeridional wavenumber m, and has no effect for the even meridional wavenumber m. The vertical shear increases thesteepness of the barotropic solitary modes, and it has a complicated effect on the baroclinic modes. The influences oftopographic slope on the solitary waves are very great. The southern and northern slopes of topography may cause dif-ferent solitary wave patterns, with the effect of northern slope greater. The effect of Froude number on the solitarywaves is generally to steepen the solitary waves, however, the effect also depends on the meridional wavenumber m andthe modes of solitary wave.     

THE SEMI-GEOSTROPHIC ADAPTATION PROCESS WITH TWO-LAYER BAROCLINIC MODEL IN LOW LATITUDE ATMOSPHERE

In this paper, the adaptation process in low latitude atmosphere is discussed by means of a two-layer baroclinic model on the equator β plane, showing that the adaptation process in low latitude is mainly dominated by the internal inertial gravity waves. The initial ageostrophic energy is dispersed by the internal inertial gravity waves, and as a result, the geostrophic motion is obtained in zonal direction while the ageostro-phic motion maintains in meridional direction, which can be called semi-geostrophic balance in barotropic model as well as semi-thermal-wind balance in baroclinic model. The vertical motion is determined both by the distribution of the initial vertical motion and that of the initial vertical motion tendency, but it is unrelated to the initial potential vorticity. Finally, the motion tends to be horizontal. The discussion of the physical mechanism of the semi-thermal-wind balance in low latitude atmosphere shows that the achievement of the semi-thermal-wind balance is due to the adjustment between the stream field and the temperature field through the horizontal convergence and divergence which is related to the vertical motion excited by the internal inertial gravity waves. The terminal adaptation state obtained shows that the adaptation direction between the mean temperature field and the shear flow field is determined by the ratio of the scale of the initial ageostrophic disturbance to the scale of one character scale related to the baroclinic Rossby radius of deformation. The shear stream field adapts to the mean temperature field when the ratio is greater than 1, and the mean temperature field adapts to the shear stream field when the ratio is smaller than 1.     

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.     

Numerical prediction of an intense convective system associated with the July 1987 montreal flood. part I: Gravity waves and the squall line

Abstract

In this study, a 24‐h high‐resolution numerical prediction of a prefrontal squall line associated with the 14 July 1987 Montreal flood is employed to investigate the origin and role of mesoscale gravity waves in the development of the squall system. The 24‐h integration using an improved mesoscale version of the Canadian regional finite‐element model is first validated against available observations; then non‐observable features are diagnosed to reveal the relationship between deep convection and gravity wave events. It is shown that the model reproduces well many aspects of the squall line, such as the propagation and organization of the convective system, as well as its associated precipitation. It is found that gravity waves are first excited near Lake Erie, following the initiation of early convective activity. Then, these waves propagate eastward and northeastward at speeds of 20 and 35 m s^‐1, respectively. As the waves propagate downstream, deep convection radiates rapidly behind the wave trough axis, forming a long line of squall convection. Because the squall line moves with the gravity waves in a “phase‐locked” manner, deep convection has a significant influence on the structure and amplitude of the gravity waves. The sensitivity of the wave‐squall prediction to various parameters in convective parameterization is also examined.     

低空急流形成发展的一种可能机制——重力波的惯性不稳定

当斜压大气在高空急流轴附近满足条件f(f-/y)＜0时,非地转运动激发出的重力惯性波将得到进一步的发展.此时,斜压大气的地转适应过程无法实现,非热成风和垂直环流之间将发生正反馈作用, 负的非热成风将激发并加强南部上升北部下沉的垂直环流,垂直上升流的加强将导致低层低压系统的发展和低层流场的辐合,使得低层低压系统南侧的气压梯度力增大,结果在辐合区南侧形成低空急流.此外,非热成风的分布对垂直环流和低空急流的形成发展也具有非常重要的作用.     

均匀基流中非线性行波解的稳定性及其存在条件

本文利用地转动量近似＾「１」并结合行波解的方法,研究了均匀基本气流中的层结大气非线性波动,首先由绝热无磨擦的闭合方程组导得关于垂直Ｐ速度的单一变量的非线性方程,然后讨论了非线性方程解的稳定性,并求得近似的非线性方程的椭圆余弦波和孤立波解及其存在条件。     

STUDY OF NONLINEAR ROSSBY WAVES IN THE ATMOSPHERE UNDER SEMI-GEOSTROPHIC APPROXIMATION

Under semi-geostrophic approximation the nonlinear ordinary differential equations are obtained for the motion inthe barotropic and baroclinic atmospheres with the effects of zonal shear basic flow and topographic forcing included.Two constraints are acquired of finite-amplitude periodic and solitary waves in the original model with the aid of thephase-plane geometric qualitative theory of a dynamic system defined by the differential equation.The explicit solutionof the nonlinear waves is found by means of the approximation method and some significant results are achieved.     

STUDY OF NONLINEAR ROSSBY WAVES IN THE ATMOSPHERE UNDER SEMI-GEOSTROPHIC APPROXIMATION*

Under semi-geostrophic approximation the nonlinear ordinary differential equations are obtained for the motion in the barotropic and baroclinic atmospheres with the effects of zonal shear basic flow and topographic forcing included.Two constraints are acquired of finite-amplitude periodic and solitary waves in the original model with the aid of the phase-plane geometric qualitative theory of a dynamic system defined by the differential equation.The explicit solution of the nonlinear waves is found by means of the approximation method and some significant results are achieved.     

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。     

Analysis of the structure and propagation of a simulated squall line on 14 June 2009

A squall line on 14 June 2009 in the provinces of Jiangsu and Anhui was well simulated using the Advanced Regional Prediction System (ARPS) model. Based on high resolution spatial and temporal data, a detailed analysis of the structural features and propagation mechanisms of the squall line was conducted. The dynamic and thermodynamic structural characteristics and their causes were analyzed in detail. Unbalanced flows were found to play a key role in initiating gravity waves during the squall line's development. The spread and development of the gravity waves were sustained by convection in the wave-CISK process. The squall line's propagation and development mainly relied on the combined effect of gravity waves at the midlevel and cold outflow along the gust front. New cells were continuously forced by the cold pool outflow and were enhanced and lifted by the intense upward motion. At a particular phase, the new cells merged with the updraft of the gravity waves, leading to an intense updraft that strengthened the squall line.     

Algebraic rossby solitary wave and blocking in the atmosphere

In this paper, the atmosphere is divided into two regions which are governed by different equations. Furthermore, multiple-scale method is used to obtain the Benjamin-Ono equation satisfied by the nonlinear Rossby wave in weak shear zonal flow. The equation has algebraic solitary wave solution, and the stationary streamfunction fields in-ithe atmosphere are calculated by using numerical method, and the results demonstrate that the stationary solution is antisymmetric dipoles with the anticyclone north of the cyclone, and the structure is similar to the equivalent modon obtained by Mcwilliams (1980). Because the modon obtained here is an algebraic solitary wave, the modon may be called “algebraic modon”, and the stationary algebraic modon is consistent with observations of blocking pattern in the atmosphere.     

一类非线性海气耦合波的研究

建立了一类非线性海气耦合波的模式,并用该模式作了解析研究,讨论了该类海气耦合波的存在条件,发现当海气耦合较强时分别存在以海洋为主导方面及以大气为主导方面的两支海气耦合波,而耦合较弱时则仅有前者存在。还求得了该模式中该类海气耦合波的椭圆余弦波解及孤立波解,并对以海洋为主导的海气耦合波的性质作了讨论,认为海气相互作用耦合也是产生大气季节内振荡的机制之一。     

大气中行星尺度孤立波的动力特征

大气中的非线性波一直是气象学界所关心和重视的问题,Long和Benney等人最早把孤立波理论应用到大气中来,成功地解释了大气中的一些天气现象,后来我国学者巢纪平、刘式达、刘式适等又进行了这方面的研究工作,取得了一些有意义的结果。本文利用行星大气中的相当正压模式和Burger模式,在一定的条件下分别导出了它们所满足的KdV方程,     

The Stability and Existence Condition of Nonlinear Travelling Wave Solution in Basic Uniform Flow

Summary  Nonlinear waves in a stratified atmosphere with basic uniform flow are studied by adopting geostrophic momentum approximation (cf. Hoskins, 1975) and the method of travelling wave solution. A nonlinear equation containing a unique variable of vertical p velocity is derived from a complete system of equations considering frictionless and adiabatic fluid. The stability of the solution for the nonlinear equation is discussed then. Furthermore, the approximate cnoidal wave solution, solitary wave solution and their existence condition are obtained. Received July 8, 1998 Revised December 1, 1998     

Impacts of SST and SST Anomalies on Low-Prequency Oscillation in the Tropical Atmosphere

Considering the multiscale character of LFO (low-frequency oscillation) in the tropical atmosphere, the effects of SST on LFO in the tropical atmosphere are discussed by using an absolute ageostrophic, baroclinic model. Here, SST effects include sea surface heating and forcing of SST anomalies (SSTAs). Studies of the influences of sea surface heating on LFO frequency and stability show that sea surface heating can slow the speed of waves and lower their frequency when SST is comparatively low; while higher SST leads to unstable waves and less periods of LFO. Since the impact of a SSTA on ultra-long waves is more evident than that on kilometer-scale waves, long-wave approximation is used when we continue to study the effect of SSTAs. Results indicate that SSTAs can lead to a longer period of LFO, and make waves unstable. In other words, positive (negative) SSTAs can make waves decay (grow).     

Impacts of SST and SST Anomalies on Low-Frequency Oscillation in the Tropical Atmosphere

Considering the multiscale character of LFO effects of SST on LFO in the tropical atmosphere （low-frequency oscillation） in the tropical atmosphere, the are discussed by using an absolute ageostrophic, baroclinic model. Here, SST effects include sea surface heating and forcing of SST anomalies （SSTAs）. Studies of the influences of sea surface heating on LFO frequency and stability show that sea surface heating can slow the speed of waves and lower their frequency when SST is comparatively low; while higher SST leads to unstable waves and less periods of LFO. Since the impact of a SSTA on ultra-long waves is more evident than that on kilometer-scale waves, long-wave approximation is used when we continue to study the effect of SSTAs. Results indicate that SSTAs can lead to a longer period of LFO, and make waves unstable. In other words, positive （negative） SSTAs can make waves decay （grow）.