圆形涡旋中的惯性重力内波不稳定和对称不稳定

用Boussinesq近似下的轴对称径向二维柱坐标系中的线性扰动方程组，讨论了圆形大气涡旋系统中扰动的惯性重力不稳定和对称不稳定。在环境为正压情形时，惯性重力内波不稳定的条件为#A(μj/R0)2N2+n2F2<0；当环境为斜压时，具有平行型扰动特征的惯性重力波发展的条件为Ri＊<1-[(3/2)+m]2，此时表现为对称不稳定。可见，惯性重力内波不稳定和对称不稳定都可作为台风、气旋一类圆形涡旋中扰动形成和发展的机制。     

风速垂直切变下非均匀层结大气中重力惯性内波的稳定性

本文应用WKB方法研究了在弱非均匀层结大气中,当基本气流具有弱垂直切变时,重力惯性内波的稳定性问题.由导得的波能量方程出发,分析了风速垂直切变及非均匀大气层结对重力惯性内波波能变化率的影响.     

切变基流对赤道大气波动稳定性的作用

在赤道β平面近似条件下，使用纬向切变基流下线性化Boussinesq方程组，分析了在纬向切变基流下几种赤道大气波动的稳定性特征。研究结果表明，基本气流的水平切变对赤道大气波动起到不稳定的作用，但是对赤道大气Kelvin波的频率、稳定性以及传播的相速度并不起作用。基本气流的水平切变使得相对于基本气流向东传播的重力惯性内波相速度减慢，而使得相对于基本气流向西传播的重力惯性内波的相速度加快，却造成相对于基本气流向西传播的Rossby波相速度减慢。基本气流的水平切变对于对赤道混合Rossby-重力惯性内波的影响主要取决于纬向波数k值的范围大小。当纬向波数k值较小时，基流的水平切变使得相对于基本气流向西传播的混合Rossby-重力惯性内波相速度加快；而当纬向波数k值较大时，则使得相对于基本气流向西传播的混合Rossby-重力惯性内波相速度减慢。在半地转近似下，风速水平切变的存在，会使得波长较大（纬向波数k→0）的赤道Rossby波相对于基本气流向西传播的相速度减慢；而风速垂直切变的存在，必然会引起这种波长较大（k→0）的Rossby波出现不稳定增长，同样也会造成赤道Rossby波相对于基本气流向西传播的相速度减慢。最后通过扰动发展能量方程，说明了基本气流的水平切变和垂直切变可以为扰动的发展提供能量来源。     

关于大气中非线性重力内波的调制

本文利用多重尺度方法研究了大气中重力内波的非线性问题,指出,当大气中的Bruntvaisala频率随高度变化时,我们可以得到一个非线性Schrodinger方程,同时还指出,当N~2按N~2=N_0~2+vcosnz(v>o)和N~2=N_0~2+vsinnz(v>0)分布时,可得到如下结论:当大气中的重力内波的波数满足3n~2-k~2<0时,大气中的重力内波可能会出现Benjammin-Feir不稳定,也就是说,大气中垂直方向的波长较长、水平方向的波长较短的重力内波容易出现Bebhanub-Feir不稳     

切变流中的CISK机制与惯性重力波

利用板对称，有切变的大气动力学方程组，由行波法导出非线性微分方程，通过非线性稳定性理论讨论方程的稳定性，求解了ＫＤＶ方程，并讨论了线性ＣＩＳＫ，非线性ＣＩＳＫ，惯性稳定度参数和大气风速垂切变对惯性重力孤波强度和宽度的影响，目的早通过了解影响惯性重力孤波发展的因子，更深入地理解低纬中尺度天气系统形成和发展的过程。     

中尺度斜交不稳定的波动性质及其数值模拟

使用三维中小尺度扰动动力学方程组,讨论了一类与基本气流方向成任意夹角的纬向线状扰动的斜交不稳定问题,其主要分析结论如下:(1)在基本气流的切变为线性切变的情况下,可以发生斜交不稳定。但是发生斜交不稳定必须要求沿着线状扰动方向的基本气流存在切变或者垂直于线状扰动方向的基本气流存在切变。此时,斜交不稳定的波动性质是重力惯性内波,而不存在涡旋Rossby波。(2)对于基本气流具有非线性二阶切变的情形,此时斜交型不稳定中的扰动除了包含重力惯性内波之外,还包含了涡旋Rossby波。对于本文所讨论的纬向线状扰动来说,涡旋Rossby波产生的物理根源是基本流场的经向风速V二次切变(β*=Vzz≠0),该涡旋Rossby波相对于基本气流V0是单向传播的。在中尺度斜交不稳定中,涡旋Rossby波的产生主要是由于在与线状扰动相垂直的方向上存在基本气流的二阶切变,而与线状扰动相平行的方向上基本气流是否存在二阶切变无关。(3)对于通常讨论的纬向线状扰动的情况,在基本流场的南北风速V存在二次切变(β*=Vzz≠0)时,即与线状扰动相垂直的方向上存在基本气流的二阶切变,则斜交不稳定有可能是混合的涡旋Rossby—重力惯性内波的不稳定。最后采用WRF模式,对2006年6月的一次福建闽江暴雨过程进行了数值模拟,部分验证了上述结论。通过分析6月6日13时降水区域平均的东西方向风速U随高度变化的曲线,发现在950—100 hPa的大气中,纬向风速U随高度的变化具有二次切变,在对流层低层以及高层附近纬向风速较小,而在对流层中层400 hPa附近的纬向风速则较大。在这种情况下,平均纬向风速随高度变化的二阶导数不为零,因此激发产生沿着纬向传播的涡旋Rossby波,这对于暴雨区域中β中尺度雨团的移动起到比较重要的作用。再分析6月5日23时和6月6日13时的850 hPa以及500hPa降水区域平均纬向风随南北方向的变化,发现在6月5日23时和6月6日13时的850 hPa层次上,都显示出平均纬向风速在南北方向具有二次切变;而在这两个时次的500 hPa层次上,平均纬向风速在南北方向不具有二次切变,只具有线性切变。说明在垂直方向上,对流层低层涡旋Rossby波容易被激发产生;而在对流层中层以上,由于不具备产生涡旋Rossby波的条件,因此不容易激发产生涡旋Rossby波,波动只是具有重力惯性内波的特征。     

重力惯性波及其不稳定——急流附近飞机颠簸产生的可能机制

基于不可压缩流体运动方程组研究了急流附近重力惯性波及其不稳定,结合飞机风速变化方程,分析指出重力波失稳破碎为湍流是飞机颠簸产生的可能机制。斜压大气在急流轴北侧气旋切变区是惯性稳定的,当满足条件σ=f[f-/y] N2m2/n2<0时,由于天气尺度对流不稳定发展而引起重力惯性波不稳定破碎为湍流,可能是急流北侧气旋切变区对流性天气引起飞机颠簸产生的一种机制。但是在急流轴南侧反气旋切变区是惯性不稳定的,当满足条件σ=f[f-/y] N2m2/n2<0时,可能由于惯性不稳定的作用,急流重力波不稳定发展破碎为湍流,可能是急流南侧反气旋气流中晴空湍流和飞机颠簸产生和发展的一种机制。揭示了急流附近晴空湍流和飞机颠簸产生的物理本质,有利于增强航空飞行颠簸的预测能力。     

旋转地球大气中的非线性惯性重力内波

一、引言刘式达等利用非线性常微分方程中关于平衡点和相图分析的慨念,在力学的平衡点附近,设计了将非线性项作Taylor展开的方法,求得旋转地球大气中的非线性惯性波、重力波及Rossby波的椭圆余弦波解和弧立波解。本文将进一步地对旋转地球大气电的非线性惯性重力内波求解。     

中尺度对称不稳定和横波不稳定的波动性质

使用纬向线性以及非线性切变基流下中尺度扰动的Boussinesq近似方程组，讨论了两种典型的中尺度扰动发生对称不稳定或者横波不稳定时，其不稳定的一些特征以及扰动的波动性质。研究结果表明：（1）对于扰动的等位相面平行于基本气流方向的对称性扰动来说，对称不稳定的波动实质是沿着与基本气流方向相垂直的方向传播的重力惯性内波的不稳定。基流二次切变对于中尺度对称扰动来说是一个不稳定因子，并且驱动不稳定的中尺度对称扰动在南北方向传播；（2）对于扰动的等位相面垂直于基本气流方向的横波性扰动来说，在基本气流为常数或者只具有线性切变的情况下，此时根本不存在涡旋Rossby波，横波不稳定的波动实质则是沿着基本气流方向双向传播的重力惯性内波的不稳定。如果考虑基本流场的风速存在二次切变或者非线性切变时，此时就会产生一支新的波动（涡旋Rossby波），涡旋Rossby波相对于基本气流^-U0是单向传播的，涡旋Rossby波产生的物理根源是基本流场的风速^-U二次切变（β＊=^-Uzz≠0），此时横波型不稳定可能是混合的涡旋Rossby——重力波的不稳定。实际大气中，涡旋Rossby波对于中够尺度对流云核、暴雨团等天气系统的发生、发展和演变的物理机制具有极其重要的意义。     

热带大气运动的长波和超长波(一)

对热带干大气运动的长波、纬向超长波(纬向扰动尺度L_1～10~4公里,经向扰动尺度L_2～10~3公里)和经向超长波(L_1～10~3公里,L_2～10~4公里)进行了尺度分析,得到了适合这些运动的近似方程。对于纬向超长波,与长波的情况一样为正压无辐散运动;但在经向超长波时,则涡度方程中存在辐散项,这一结果与Matsuno得到的在热带存在Rossby波和惯性-重力波混合的情况是一致的。同时,在存在基本气流切变的情况下,对线性化扰动方程进行了频率分析,结果指出,当n≥1时,Rossby波和惯性-重力波是可分的;当n=0,而纬向尺度L_1～1000公里时,存在混合Rossby-重力波,这就证实了上述尺度分析的结果是正确的。于是,把尺度分析的结果与热带波动运动中Rossby波和惯性-重力波是可分的或混合的特性统一了起来。     

THE EFFECTS OF VERTICAL VARIATION OF BASIC FLOW AND HORIZONTAL GRADIENT OF TEMPERATURE ON LINEAR AND NONLINEAR GRAVITY WAVES

By using two-dimensional dynamical equations in x-z plane with Boussinesq approximation,the effects of the second-order vertical shear of the basic flow u_zz and the horizontal gradient of temperature (M) on the gravity wave and the isolated gravity wave are discussed.The magnitudes of u_zz and M corresponding to the linear and nonlinear stabilities of the gravity waves are worked out,respectively.The results show that amplitude and width of the isolate dgravity wave are closely related to u_zz and M.It is indicated that the isolated gravity wave with a width of about 10 km can be motivated by the disturbance of sub-synoptic scale in the certain ranges of flow field shear and temperature gradient,while the motivated waves may be associated with the cold surge ahead of a cold front and the other mesoscale synoptic systems.     

瞬时经圈环流与西风带环流变化的关系

用一九七六年冬半年八个个例,对纬圈平均非热成风,瞬时经圈环流和西风带环流变化的关系进行了个例分析和统计分析。指出。当纬圈平均非热成风产生率为较大的负值时,出现逆瞬时经圈环流,并有利于长波的阻尼和纬向环流的维持或加强;反之,当为正值时,出现正瞬时经圈环流,并有利于长波的发展和纬向环流的减弱或崩溃。对于上述关系,本文还从物理上进行了初步的讨论。     

台风的螺旋结构

本文从描写台风运动的动力方程组出发,讨论了台风的螺旋结构,给出了这种螺旋结构的图样,指出:(1)台风螺旋结构的形成是台风中重力惯性内波,特别是重力内波的作用所致,(2)台风螺旋结构的形式与波位相速紧密相关,北半球的曳式螺旋结构要求螺旋图样环绕台风眼逆时针且由中心向外运动,其向外运动的速度近于重力内波的传播速度,(3)台风的曳式螺旋倾角一般小于45°,而在台风边缘,倾角约为10°,螺旋臂间距在二旋臂结构中平均为220公里,而在四旋臂结构中平均为110公里,(4)台风螺旋波也有频散作用,在曳式螺旋中c_(gr)与c_r皆为正,且c_(gr)相似文献   

The effect of orchard crop structure on the integral length-scale of turbulence

The integral length-scalesL for the three orthogonal components of diffusivityK=L are derived from spectral analysis of velocity time series measurements. A 3-D sonic anemometer was used to make these velocity measurements at heights in the range 0.7–7.0 m in and above a 2 m orchard canopy with near-neutral atmospheric boundary-layer stability conditions. The integral length-scale is compared with another length-scale of diffusionL obtained by fitting an exponential model to the auto-correlation spectrumR _E (t) in the region 0.95<R _E (t)<0.5 for smallt. This length-scale is appropriate to a high frequency region of the energy spectrum where turbulent momentum transport becomes diffusion-like and the turbulent energy varies with the inverse square of frequence. This region has been shown by others to determine the magnitude of the dissipation rate of turbulent energy by the action of viscosity even though the dominant dynamics are inviscid. Within the crop, the ratio of the length-scalesL/L were found to be smaller than the values measured above the crop for vertical turbulence. This was attributed to the enhanced decay rate of turbulent energy due to the effect of the airflow interaction with the crop. It is unclear whether similar effects are present in the horizontal plane because of greater scatter in the data, resulting from the more variable nature of the wind direction in the horizontal plane.     

Turbulence decay in stratified and homogeneous marine layers

A spectral approach is applied to shear-induced turbulence in stratified layers. A system of spectral equations for stationary balance of turbulent energy and temperature variances was deduced in the vicinity of the local shear scale L_U = (ε/U_Z³)^1/2. At wavenumbers between the inertial-convective (k^−5/3) and wak turbulence (k⁻³) subranges, additional narrow spectral intervals—‘production’ subranges—may appear (E k⁻¹, E_T k⁻²). The upper boundary of these subranges is determined as L_U, and the lower boundaries as L_R (ε/U_ZN²)^1/2(χ/T_Z²). It is shown that the scale L_U is a unique spectral scale that is uniform up to a constant value for every hydrophysical field. It appears that the spectral scale L_U is equivalent to the Thorpe scale L_Th for the active turbulence model. Therefore, if turbulent patches are generated in a background of permanent mean shear, a linear relation between temperature and mass diffusivities exists. In spectral terms, the fossil turbulence model corresponds to the regime of the Boldgiano-Obukhov buoyancy subrange (E k^−11/5, E_T k^−7/5). During decay the buoyancy subrange is expanded to lower and higher wavenumbers. At lower wavenumbers the buoyancy subrange is bounded by L_** = 3(χ^1/2/N^1/2T_Z), which is equivalent to the Thorpe scale L_Th. In such a transition regime only, when the viscous dissipation rate is removed from the set of main turbulence parameters, the Thorpe scale does not correlate with the buoyancy scale L_N ε^1/2/N^3/2 and fossil turbulence is realized. Oceanic turbulence measurements in the equatorial Pacific near Baker Island confirm the main ideas of the active and fossil turbulence models.     

Topographic generation of intermediate-scale motions by wind-driven currents — A model for the circulation in the vicinity of the Indian-Antarctic ridge

When a broad ocean current encounters a large-scale topographic feature, standing Rossby wave patterns can be generated. Short Rossby waves with a scale L_i = √ Q/β (Q is the speed of the approaching flow; β is the meridional gradient of f) are generated east of the topography. If the zonal scale of the topography, L, is planetary, long standing Rossby waves can be generated west of the topography, when the current has a meridional component. The long waves focus the disturbance zonally and produce alternating regions of intensified or reduced zonal flow. The meridional scale that characterizes these zonal bands is the intermediate scales, L = L_i^2/3L^1/3. When the meridional topographic scale is comparable to L, the amplitude of the long-wave disturbance is dominant. Using multiple-scale methods to exploit the scale gap between the planetary, intermediate and Rossby wave scales, the topographically induced pressure and velocity fields due to a zonal ridge are obtained. When the planetary-scale flow field is directed poleward, a westward counterflow can occur along the poleward flank of the ridge. The meridional scales of these topographically induced flows are comparable to those observed along the Indian-Antarctic Ridge by Callahan (1971).     

An experimental study of nonlinear baroclinic instability and mode selection in a large basin

This paper reports on two-layer rotating liquid experiments designed to study the behavior of non-linear baroclinic waves under conditions where the Rossby radius of deformation R_d is much smaller than the geometric length scale L imposed by the size of the laboratory apparatus. The apparatus is constructed to consistently simulate f-plane dynamics. When F = L²/R_d² > > 1, it is found that the unstable waves first encountered as friction is decreased have high frequencies, in accord with linear theory. As the friction parameter $\text{Q = 0.7 E}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{/R}{}_0$ (where E is the Ekman number and R₀ the Rossby number) is further decreased into the non-linear region, singlewave amplitude vacillation is observed. Generally, as Q decreases lower frequencies (and low wavenumbers) dominate the response, which ultimately becomes turbulent at values of Q of the order 0.1. This is contrary to the result expected from an extrapolation of linear theory. Further observations show that the finite-amplitude state is not unique: multi-equilibria are possible depending on the initial conditions.     

大气中臭氧9.6μ带辐射收支的计算

计算大气中的长波辐射时,吸收气体的光学厚度要作气压订正,一般取气压订正后的光学厚度u′=(p/p_0)~K,对于O_3的9.6μ带,理论分析和实验都表明K是u和p的函数,气压订正可取 u′=(p/p_0)~(K(u,p))=uf(u,p). 我们以Walshaw的实验为基础,求出f(u,p)的囹形,并求出辐射通量及辐射通量散度的计算表。 当u很小时,弱线近似成立。漫射辐射的吸收率A_f=1-exp(-2su/d),K→0。在u→0时,dA_f/du=s2/d为一常量。     

The Control Of Coherent Eddies In Vegetation Canopies: Streamwise Structure Spacing, Canopy Shear Scale And Atmospheric Stability

An analogy has been established between a plane mixing layer and the atmospheric flow near the top of a vegetation canopy. It is based on a common feature, a strong inflection in the mean velocity profile, responsible for hydrodynamical instabilities that set the pattern for the coherent eddies and determine the turbulence length scales. In an earlier study, this analogy was tested using a small data set from thirteen experiments, all in near-neutral conditions. It provided a good prediction of the streamwise spacing _w of the dominant canopy eddies (evaluated from time series of vertical velocity) that appears to depend on a shear length scale L_s = U(h)/U'(h), where h is canopy height, U is mean velocity and U' the vertical gradient dU/dz. The present analysis utilizes an extensive data set of approximately 700 thirty-minute runs, from six experiments on two forest sites and a maize crop, with a large range of stability conditions. _w was estimated for each run using the wavelet transform as an objective, automated detection method. First, the variations of _w and L_s with atmospheric stability are discussed. Neutral and unstable values exhibit a large scatter whereas in stable conditions both variables decrease with increasing stability. It is subsequently found that _w is directly related to L_s, in a way close to the neutral prediction _w /h = 8.1L_s/h.The Strouhal number S_tr = L_s /_w is then shown to vary with atmospheric stability, weakly in unstable conditions, more significantly in stable conditions. Altogether these results suggest that, to some extent, the plane mixing-layer analogy can be extended to non-neutral conditions. It is argued that the primary effect of atmospheric stability, at least in stable conditions, is to modify the shear length scale L_s through changes in U(h) and U'(h), which in turn determines the streamwise spacing of the active, coherent motions.     

Effect of atmospheric stability on the growth of surface gravity waves

In this paper we study the effect of atmospheric stability on the growth of surface gravity waves. To that end we numerically solved the Taylor-Goldstein equation for wind profiles which deviate from a logarithmic form because stratification affects the turbulent momentum transport. Using Charnock's relation for the roughness height z ₀ of the wind profile, it is argued that the growth rate of the wave depends on the dimensionless phase velocity c/u _* (where u _* is the friction velocity) and a measure of the effect of atmospheric stability, namely the dimensionless Obukhov length gL/u _* ², whereas it only depends weakly on gz _t /u _* ² (where z _t is the roughness height of the temperature profile). Remarkably for a given value of u _* /c, the growth rate is larger for a stable stratification (L > 0) than for an unstable one (L < 0). We explain why this is the case. If, on the other hand, one considers the growth rate as a function of c/U ₁₀ (where U ₁₀ is the windspeed at 10 m), the situation reverses for c/U ₁₀ < 1. For practical application in wave prediction models, we propose a new parameterization of the growth rate of the waves which is an improvement of the Snyder et al. (1981) proposal because the effect of stability is taken into account.