具有凝结加热反馈的对称不稳定的解析研究

本文采用非地转非静力条件下存在对流凝结加热反馈的Boussinesq方程组,借用Emanuel(1982)的Wave-CISK方案来考虑凝结反馈作用,并应用Green函数方法和Fourier方法,求得了任意加热廓线时对称不稳定的流函数的解析表达式及其频散关系。本文还对取某些特定的加热廓线时的情况进行了讨论。      

一种地学要素场透视方位投影图的原理及应用

给出了一种地学要素场透视方位投影图的原理,它是将地球球面上任意点O（称投影中心）正上方h高度处A点（称视点）看到的球冠区要素场透视投影在相应球缺的底面（即投影面）上。借助球面三角计算公式,导出了球冠区任意点q与其在投影面上投影点q′的坐标转换关系;给出了绘图步骤,利用MATLAB设计了绘图程序。实际绘图效果表明,所绘图形具有球面立体感和直观性,该透视方位投影图可广泛用于绘制地学要素场图像。     

高阶精度有限差分方案下的非跳点网格试验:基于浅水波方程

非跳点网格在模式动力—物理过程的耦合方面具有独特的优势,但是由于二阶精度差分方案下非跳点网格频散误差较大而很少被使用于数值天气预报模式。随着近年来数值模式计算精度的不断提高,非跳点网格在频散关系方面的计算误差是否会发生变化还有待研究。本文在高阶精度差分格式下通过浅水波方程对跳点网格和非跳点网格的频散关系进行理论分析和数值试验,主要得到以下结论:（1）在低波数区跳点网格的频散关系基本不随计算精度的提高而变化,但是非跳点网格下的频散关系则随着计算精度的提高而更加接近真实解。在四阶精度下,非跳点网格的频散关系已经非常接近跳点网格。（2）差分精度提高以后,在高波数区非跳点网格仍然存在频率极大值,而且极值中心随着计算精度的提高而逐渐向更高波数区移动。跳点网格在计算精度提高以后高波数区的频率仍然随波数单调增加,且更接近真实解。（3）在高阶精度非跳点网格模拟试验的基础上,结合高阶扩散项对高频短波进行滤除,可以得到与二阶精度跳点网格相接近的模拟结果。总之,在高阶精度有限差分方案下利用非跳点网格构造模式动力框架是一种比较可行的做法。     

坡地上风的讨论

本文求解了孤立斜坡上大气的运动方程和热流量方程，揭示了坡地上风的运动变化规律，着重讨论了科氏力在坡风研究中的作用，计算了不同坡度、稳定度、纬度上坡风的强度。     

不均匀惯性重力内波和雷暴、暴雨的关系

本文考虑了基本气流的作用。用WKBJ法得到了不均匀惯性重力内波的频散关系和能量方程。1981年6月26日例子分析表明:雷暴、暴雨落区和波能量变化正值大区相对应,雨带南界大致和1000—500百帕平均涡度零线相合。     

内蒙古倾斜面上太阳辐射资源的计算与分析

本文就倾斜面上太阳辐射资源的计算作了详细的阐述，给出了全区范围内不同倾斜面的辐射总量。经过不同倾斜面上辐射值的分析，以及与水平面的对比，引出了在不同纬度、不同季节的斜面应保持的最佳倾角。     

有关沿岸山地俘获波的研究

在采用线性化的浅水方程组并假设地形坡度沿山脉走向不变的情况下,本文对具有底面地形坡度的沿岸山地俘获波作了研究,结果表明,当底面地形缓变时,可用摄动法得到沿岸山地俘获波的结构,此时零级近似为经典Kelvin波解,一级近似体现了Rossby变形半径内的底面地形对经典Kelvin波解的修正;直至一级近似,沿岸山地俘获波仍是非频散的。在沿岸处当底面地形坡度平缓时,沿岸山地俘获波表现为Kelvin波结构,此时扰动位势高度最大值出现在沿岸;而当底面地形坡度陡峭时,其表现为修正Kelvin波结构,此时扰动位势高度最大值偏离沿岸,在沿岸则扰动位势高度相对为低值,而在沿岸外侧则有位势高度的高值。在沿岸底面地形高度越高,地形坡度越大,扰动位势高度廓线的变化就越剧烈。     

太阳总辐射最佳倾角的时空分布

本文根据倾斜面上太阳总辐最佳倾角的角析表示式，利用平均太阳总辐射和直接辐月总量以及实际地表面反射率，计算分析了我国各月最佳倾角和最佳总辐射比的时空变化特征。同时对用天空散射辐射各同性模式计算倾斜面上总辐日总量的适用性问题亦作了简要讨论。     

浅析计算避雷针保护范围的一个误区

根据防雷设计中常见的避雷针保护范围计算的问题,详细分析了屋顶、斜坡避雷针的保护范围.     

涡旋发展和移动的动力和热力问题Ⅱ:广义倾斜涡度发展

从位涡-位温（PV-θ）以及拉格朗日观点,引入广义倾斜涡度发展的概念研究绝热条件下的垂直涡度发展。广义倾斜涡度发展是一个与涡度发展的坐标无关的概念框架,该框架包括倾斜涡度发展。倾斜涡度发展研究当大气处于稳定或不稳定层结情形,空气质点沿着向上凸的陡峭等熵面下滑或沿着向下凹的陡峭等熵面上滑过程垂直涡度激烈发展。因此,倾斜涡度发展是研究强烈天气过程的涡度发展非常强的情形。此外,广义倾斜涡度发展概念澄清了涡度发展和倾斜涡度发展的区别,涡度发展和倾斜涡度发展的判别标准表明,倾斜涡度发展的要求比涡度发展的要求严格很多。在空气质点沿着向上凸的陡峭等熵面下滑或沿着向下凹的陡峭等熵面上滑过程,当在稳定大气中静力稳定度（θ_z）迅速减小或在不稳定大气中静力稳定度（θ_z）迅速增大,即静力稳定度（θ_z）趋于0时,如果C_D<0,那么垂直涡度将急速发展。应用得到的理论结果分析了2008年7月下旬的一次青藏高原低涡过程,该低涡形成于青藏高原中西部,东移滑出青藏高原然后继续东移,给四川盆地和长江中下游带来强降水。诊断表明,2008年7月22日00—06时（世界时）青藏高原低涡沿着四川盆地东北边的斜坡爬升时低涡加强发展,PV₂变化对低涡加强发展有贡献,因为此时的水平涡度（η_s）变化和斜压度（θ_s）变化都对垂直涡度发展起正贡献。而且,22日06时,330 K等熵面的倾斜涡度发展判据满足,表明倾斜涡度发展并对垂直涡度发展起重要贡献。围绕着低涡中心较强的涡度发展和倾斜涡度发展信号表明,广义倾斜涡度发展概念框架可以作为诊断天气过程的一个有用工具。     

Coastal trapped waves,with application to the northeast pacific ocean

The dispersion relation is derived for long coastal trapped waves of sub‐inertial frequency that propagate along a single‐step continental shelf in a two‐layer fluid. When the internal (Rossby) deformation radius is smaller than the shelf width, we show that the dispersion relation can be factored exactly, giving two possible modes: i. an internal Kelvin wave modified by topography;

ii. a continental shelf wave modified by the stratification.

A detailed discussion of the eigen‐functions associated with each of these modes is presented. Then the shelf wave dispersion relation is plotted for parameters applicable to the Oregon‐Washington coast. Theoretical values for the periods and wavelengths predicted from these plots are shown to agree favorably with observed values for this region.     

A unified linear theory of wavelike perturbations under general ocean conditions

A linearized instability analysis model with five unknowns was proposed to describe disturbance motions under general oceanic background conditions, including large-scale current shear, density stratification, frontal zone, and arbitrary topography. A unified linear theory of wavelike perturbations for surface gravity waves, internal gravity waves and inertial gravity waves was derived for the adiabatic case, and the solution was then found using Fourier integrals. In this theory, we discarded the assumptions widely accepted in the literature concerning derivations of wave motions such as the irrotationality assumption for surface gravity waves, the rigid-lid approximation for internal gravity waves, and the long-wave approximation for inertial gravity waves. Analytical solutions based on this theory indicate that the complex dispersion relationships between frequency and wave-number describing the propagation and development of the three types of wavelike perturbation motions include three components: complex dispersion relationships at the sea surface; vertical invariance of the complex frequency; and expressions of the vertical wave-number (phase). Classical results of both surface waves and internal waves were reproduced from the unified theory under idealized conditions. The unified wave theory can be applied in the dynamical explanation of the generation and propagation properties of internal waves that are visible in the satellite SAR images in the southern part of the China Seas. It can also serve as the theoretical basis for both a numerical internal-wave model and analytical estimation of the ocean fluxes transported by wavelike perturbations.     

On leaky modes on a buoyancy interface

When the fluid below a buoyancy interface such as the seasonal thermocline in the ocean is stably stratified as it is often, energy radiation by internal waves into regions deep below is possible. In this paper, the dispersion relation for a sharp thermocline separating a well-mixed layer from a weakly but stably stratified fluid below is derived and examined for such energy leakage into the fluid below. It is found that the interfacial waves running along such a buoyancy interface leak their energy to radiating internal waves and are rapidly attenuated, if their frequency is less than the buoyancy frequency of the fluid below. The implications the leaky nature of the modes have on resonant excitation of internal waves in the ocean by atmospheric pressure fluctuations and turbulence in the mixed layer are also examined. It is found that efficient resonant build up of interfacial waves is possible only for nonleaky modes and even then their growth rate is modified slightly by the presence of stratified fluid below the interface.     

Oscillatory Rossby Solitary Waves in the Atmosphere

The linear Rossby wave frequency expression is expanded at higher accuracy based on the scale difference char?acteristics of atmospheric long waves in the and directions. That the nature of the waves represented by the expan?sion is identical to that of the original ones is demonstrated both in phase velocity and wave energy dispersion speed , followed by the derivation of the nonlinear expression describing atmospheric long wave behaviors with the associated approximate analytic solution obtained. Then, for the first time atmospheric’ oscillatory Rossby solitary wave’ with its dispersion relation is obtained by numerical calculation with the aid of physical parameters of the real atmosphere. The solitary wave is found to be very close to such longwave systems as blocking highs and cut-off de?pressions in the actual atmosphere.     

Steadily translating anticyclones on the beta plane

Approximately stationary anticyclones in shallow water on a rotating planet are studied both analytically and numerically. They consist of a monopolar part with large amplitude and a dipolar part with small amplitude, proportional to the beta parameter. An explicit solution for the dipolar part is o obtained with an arbitrary radial profile of the monopolar part. Numerical experiments show that this dipolar part accelerates or decelerates an initially circular vortex depending on the vortex size. The propagation speed is determined by a general integral relation. It is found that for the vortices to be stationary, this speed should not be close to the phase velocity of linear Rossby waves. This requires a strongly elevated surface (large amplitude). The vortices contain a core region with trapped fluid, unlike one-dimensional KdV solitons. Applications of the solution to long-lived geophysical eddies are discussed.     

一个简单的准地转海气耦合模式

文章采用准地转带耗散因子的大气和海洋的动量、热力学方程,建立了一个简单的描写大尺度运动的准地转海气耦台浅水模式,分别在中高纬和低纬地区讨论了海气的耦合效应,分析了耦合低频模(海洋模)的振荡周期随耦合频率和经向波数的变化转征,并由此而说明低频振荡与海气相互作用有关。然后从海洋和大气的频散曲线中揭示出耦合强度对Rossby波传播的影响,还从缓变波列的观点,讨论了两种模之间的转换机制。 结果表明:Newton冷却Rayleigh摩擦对海洋Rossby波起稳定作用。随着耦合频率的增加,耦合低频模的周期也相应增加;经向波数越大,这种增加就越迅速。当耦合频率趋近于临界值时,海洋Rossby波趋于静止。当海气耦合强度增加到一定程度时,海洋Rossby波的传播方向变成与原来相反。通过海气相互作用,海洋Rossby波的一部分将转换成大气Rossby波,本文求解了其能量转换系数。      

Some effects of truncation on topographic instability

Abstract

The topographic stability of forced planetary waves in α β‐channel is investigated using a barotropic model. The equilibrium forced waves are the result of the interaction of a constant mean zonal wind over finite‐amplitude surface orography. Small‐amplitude perturbations of the equilibrium flows are considered that have a wavy part with the same zonal wavenumber as the forcing but an arbitrary meridional structure. The mean zonal part of the perturbations is also taken to be arbitrary. This configuration allows us to (1) isolate those instabilities that depend crucially on topography through form drag and (2) investigate non‐topographic effects on topographic instability that arise from the convergence of Reynolds stresses. A numerical stability analysis is then performed wherein the effects of truncation are emphasized.

This numerical approach casts doubts about the results obtained from some earlier studies involving various ad hoc assumptions. We find, in particular, that unstable long waves (i.e. waves with the zonal wavelength greater than the meridional wavelength) exist under superresonant conditions. This contradicts some previous results that suggest long waves are unstable only when the flow is subresonant. Further, our model reveals the existence of some interesting travelling instabilities. The latter are shown to depend on both form drag and Reynolds stresses in that these two mechanisms alternate in time in supplying the perturbation with the required energy to maintain the exponential growth.     

Rossby waves in a rotating fluid of spheroidal configuration

The ray method is used to study quasi-geostrophic waves in a thin layer of incompressible, inviscid fluid of constant density both in a rotating spheroidal shell and on a rotating spheroid bounded above by a free surface. Asymptotic approximations to solutions of both the time-dependent and time-reduced problems are found; the dispersion relation obtained has the form of the Rossby-Haurwitz formula when the shell is spherical, and is asymptotically equivalent to that found by Longuet-Higgins (1965) for the free surface problem on a sphere. The approximation is first applied to free oscillations in a rotating spherical shell and Longuet-Higgins' (1964) results are rederived. Spheroidal shells in which the shell thickness depends only upon the latitude are studied next and a necessary and sufficient condition for oscillations to occur is obtained.     

北半球冬季准定常行星波的三维传播及其年际变化

作者回顾了应用叶笃正先生所创立的Rossby波频散理论,来研究准定常行星波在三维大气的能量频散以及在北半球冬季三维大气中的传播规律,并应用NCEP/NCAR再分析资料和由大气环流数值模拟所得的模式资料的40年风场、温度场资料计算了冬季北半球准定常行星波的E-P通量.计算结果表明了北半球冬季准定常行星波在三维大气传播具有沿两支波导的传播特征,这与从理论分析所得的结果相吻合.作者还分析了冬季准定常行星波的E-P通量分布的年际变化,分析结果表明了准定常行星波在北半球冬季三维大气中传播的这两支波导有明显的年际振荡;并且,从冬季准定常行星波的E-P通量辐散辐合的年际变化与北极涛动的年际变化相比较,发现准定常行星波两支波导的年际振荡直接影响着北极涛动(AO),因而说明了准定常行星波活动的年际变化可以影响对流层的气候变化.     

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.