Ekman动量近似下中间边界层模式中的风场结构

发展了一个准三维的、中等复杂的边界层动力学模式，该模式包含了EKman动量近似下的惯性加速度和Blackadar的非线性湍流粘性系数，它进一步改进了Tan和Wu(1993）提出的边界层理论模型。该模型在数值计算复杂性上与经典Ekman模式相类似，但由于包含了Ekman动量近似下的惯性项，使得该模式比传统Ekman模式更近于实际过程。中详细地比较了该模式与其他简化边界层模式在动力学上的差异，结果表明：在经典的Ekman模式中，由于忽略了流动的惯性项作用，导致在气旋性切变气流（反气旋性切变气流）中风速和边界层顶部的垂直速度的高估（低估），而在半地转边界层模式中，由于高估了流动惯性项的作用，结果与经典Ekman模式相反。同样，该模式可以应用于斜压边界层，对于Ekman动量下的斜压边界层风场同时具有经典斜压边界层和Ekman动量近似边界层的特征。     

The numerical experiments on applicating geostrophic momentum approximation to the baroclinic and non-neutral PBL

In this paper, Wu and Blumen’s boundary layer geostrophic momentum approximation model (Wu and Blumen, 1982) is applied to baroclinic and non-neutral PBL, the motion equations for the PBL under the geostrophic momentum approximation are solved, in which the eddy transfer coefficient is a function of the distributions of the wind and temperature. The results are compared with those in barotropic and neutral conditions with the geostrophic momentum approximation. It is found that in the baroclinic condition, the wind distribution has both the characteristics of a steady, homogeneous and baroclinic PBL and those caused by the geostrophic momentum approximation. Those in non-neutral conditions show that they retain the intrinsic characteristics for the wind in non-neutral PBL, at the same time, the effects of the large-scale advection and local variation are also included. We can predict the wind in the non-neutral and baroclinic PBL by use of the geostrophic mo-mentum approximation when the temporal and spatial distributions of the geostrophic wind, as well as the po-tential temperatures and their variation rates at the upper and lower boundary of the PBL are given by large-scale model. Finally, the model is extended to the case over sea surface.     

The influences of orography upon the flow within Ekman boundary layer under the approximation of geostrophic momentum

In this paper, the influences of orography on the boundary layer flow with the approximation of geostrophic momentum are studied. The wind velocity at the lower boundary will not always be zero when the orography exists. So the structure of the boundary layer flow, as well as the vertical velocity at the top of the boundary layer, is affected. There are three factors affecting the vertical motion at the top of the boundary layer: lifting due to orography; divergence due to Ekman flow, and advection of the geostrophic momentum. These effects and the features of the flow within the boundary layer are discussed in detail.     

斜压性与非线性Ekman抽吸的动力特征

本文利用Ekman动量近似研究了斜压性对Ekman层动力学的影响,得到了一些新的结果。大气斜压性对Ekman层的水平风速分布及近地面的风速矢的水平分量夹角有重要的改变作用。斜压边界层顶部的非线性Ekman抽吸(垂直运动)由三个不同的物理因子决定,第一、正压性的地面地转涡度,第二、斜压性作用产生的热成风涡度,第三、正压性的地面地转涡度与斜压性的热成风涡度的非线性相互作用。这些理论结果为边界层的参数化及数值模拟结果的解释提供物理基础。     

Helicity Dynamics of Atmospheric Flow

Helicity is an important physical variable which is similar to the energy and enstrophy in three-dimensional fluid. It can be used to describe the motion in the direction of fluid rotation and also can be regarded as a new physi-cal variable in turbulence theory. In recent years, it has been used in atmospheric dynamics. In this paper, helicity of atmospheric flow, especially helicity in the boundary layer and in the vicinity of front was discussed. These results show that helicity is usually positive in the boundary layer due to the effect of friction. The helicity of boundary layer flow is larger in anticyclone than that in cyclone, resulting from the different wind structures of boundary layers in an-ticyclone and cyclone under the geostrophic momentum approximation. It is possible that the helicity is negative at certain height in the baroclinic boundary layer. The influences of nonlinearity and baroclinity on the helicity are im-portant. The so called “Cloud Street” in the boundary layer is related to the dynamics of helicity. Helicity in the at-mosphere can be expressed as the temperature advection under some conditions, so helicity would be allowed to des-cribe the frontogenesis and development of frontal structure. The amplitude of helicity increases with time in the frontogenesis. A large gradient of helicity is generated in the region located to the northeast of the surface low and in which the front is formed. In warm frontal region, as well as behind the trough of temperature, the helicity is positive, while the helicity is negative in cold frontal sector and in the ahead ridge of temperature. The largest helicity occurs in the boundary.     

A numerical experiment of the PBL with geostrophic momentum approximation

In this paper, a numerical experiment of the motion in the PBL (planetary boundary layer) is perform-ed with geostrophic momentum approximation, in which a nonlinear eddy transfer coefficient is used. Some results are obtained for the boundary layer winds in cyclone-anticyclone and trough-ridge systems. This treat-ment improves W-B’s work. The effects of geostrophic wind tendency and the advection of the geostrophic wind on the winds in the PBL are also discussed.     

Dynamics of nonlinear baroclinic Ekman boundary layer

By the geostrophic momentum approximation, the wind structure and vertical motion within the non-linear baroclinic Ekman layer matching with the surface layer are determined. A comparison of the Ekman solution with the classical one is made. It is demonstrated that the contributions of baroclinity, stratification and nonlinear effects to the wind profile within the layer are all of definite importance.     

The Ekman momentum approximation and its application

In the boundary layer, the flow is basically an equilibrium of three forces: Coriolis, pressure gradient and frictional. This means that it is an Ekman flow while the basic flow in the free atmosphere is an equilibrium of two forces: Coriolis and pressure gradient, and is a geostrophic flow. Therefore, it is natural to try to modify the geostrophic momentum approximation in the free atmosphere to become an Ekman momentum approximation in the boundary layer. The physical explanation and foundation of the Ekman momentum approximation are discussed.     

Some Effects Of An Ekman Boundary-Layer Parameterization On Various Models Of Atmospheric Flow

The traditional Ekman boundary-layer parameterization is introduced into the quasigeostrophic Eady baroclinic instability model and into the deformation flow model, to couple the planetary boundary layer with the inviscid interior flow aloft. An explicit time-dependent version of this parameterization is then introduced into an unbalanced zero potential vorticity model to evaluate the initial transient response. It is noted that the adaptation of the geostrophic flow to the same parameterization is different in each of the balanced models. The characteristic flow response reflects thedifferent constraints imposed by each model. Further, the zero potential vorticity condition constrains the evolution of the baroclinic geostrophic part of the flow, which leads to an unphysical flow response when the Ekman boundary-layer parameterization is employed with this unbalanced model. The barotropic part of the flow does, however, evolve in a physically consistent manner spinning down to reflect the introduction of low momentum air pumped into the interior from the boundary layer. Moreover, the transient spin-up processis shown to have an insignificant effect on this spin-down process.     

斜压性对地转动量Ekman流的影响——理论分析

本文研究了斜压效应对地转动量Ekman流的影响。利用两变量奇异摄动方法求得了边界层中风场及顶部垂直速度的前二级一致有效渐近解析解,解中明显地反映了斜压情形地转风随高度变化(即热成风)的影响,尤其是其中一级近似解完全由热成风影响所致。在边界层顶垂直速度的解中导出了三种由斜压效应引起的Ekmon抽吸新物理因子,即热成风形变、热成风涡度及热成风涡度交叉项等抽吸因子。分析表明,这些因子只在具有水平温度梯度不均匀的系统(譬如锋区)中方能出现。文中还对锋区内上述三种抽吸因子的动力特征作了具体的分析,指出在锋区这样的强斜压系统中,此三种抽吸因子的贡献是显著的。下一文中,我们将利用本文所得理论解对斜压效应进行具体的定量计算。      

BAROCLINITY AND NONLINEAR EKMAN PUMPING DYNAMICS

With the Ekman momentum approximation,the influence of atmospheric baroclinity on the dynamics of boundarylayer is studied.Some new results are obtained.These results show that the atmospheric baroclinity plays an importantrole in altering the horizontal velocity of Ekman boundary layer and its angle with the horizontal wind velocity compo-nent near the surface.There are three different physical factors affecting the nonlinear Ekman suction,the vertical mo-tion at the top of boundary layer:first,barotropic geostrophic relative vorticity at the ground;second,the thermal windvorticity induced by the baroclinity;and third,the nonlinear interaction between the barotropic geostrophic relativevorticity and the baroclinic thermal wind vorticity.These results may provide a better physical basis for theparameterization of boundary layer and the interpretation of the numerical modeling results.     

大气边界层强风的阵性和相干结构

我国北方春季冷锋过境后,常骤发强风,甚至起沙扬尘,持续数小时甚至一二天,通过对边界层超声风温仪的资料分析,可知大风常叠加有周期为3～6 min的阵风,较有规律,且有明显的相干结构:阵风风速峰期有下沉运动,谷期有上升运动;阵风扰动以沿平均流的顺风方向分量为主,横向和垂直方向的分量都较小,其本质是低频次声波和重力波的混合;阵风沿顺风向且向下传播.周期小于1 min的脉动在水平面上基本是各向同性的不规则的湍涡.大风期间,无论是平均流、阵风和湍流脉动,至少在120 m高度以下,主要都有西风和北风动量下传,感热上传.平均流的动量下传强于由脉动下传的量,与一般天气情况不同,而且阵风与湍流的动量下传的量值差不多.平均流和阵风在动量传送上起相当大的作用.     

The effect of barotropic shear on baroclinic instability Part I: Normal mode problem

The effect of barotropic shear in the basic flow on baroclinic instability is investigated using a linear multilevel quasi-geostrophic β-plane channel model and a nonlinear spherical primitive equation model. Barotropic shear has a profound effect on baroclinic instability. It reduces the growth rates of normal modes by severely restricting their structure, confirming earlier results with a two-layer model. Dissipation, in the form of Ekman pumping and Newtonian cooling, does not change the main characteristics of the effect of the shear on normal mode instability.Barotropic shear in the basic state, characterized by large shear vorticity with small horizontal curvature, also effects the nonlinear development of baroclinic waves. The shear limits the energy conversion from the zonal available potential energy to eddy energy, reducing the maximum eddy kinetic energy level reached by baroclinic waves. Barotropic shear, which controls the level of eddy activity, is a major factor which should be considered when parameterizing the eddy temperature and momentum fluxes induced by baroclinic waves in a climate model.     

边界层动力学中的Ekman动量近似

自由大气中,大气运动的基本状态是地转风,近年来发展的地转动量近似,是为了进一步研究非均匀地转流的动力学问题,然而,在边界层大气中,运动的基本状态是经典的Ekman流,所以对边界层运动来说,地转动量近似是不合适的,需作一推广。本文提出了一种所谓Ekman动量近似,它相似于自由大气中的地转动量近似,并讨论了Ekman动量近似的物理基础,对边界层的风场结构及边界屋顶部的垂直速度也作了详细分析。     

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.     

A diagnostic study of the southern hemisphere summer circulation of the CCC general circulation model

Abstract

The medium‐scale wave regime, consisting largely of zonal wavenumbers 5–7, frequently dominates the summer Southern Hemisphere tropospheric circulation. We perform a diagnostic study of this circulation as simulated by the Canadian Climate Centre (CCC) general circulation model (GCM). The analysis of Hövmöller diagrams, space‐time and zonal wavenumber spectra shows that the CCC GCM is able to simulate the observed medium‐scale wave regime.

The zonally averaged meridional eddy heat and momentum transports and the associated baroclinic and barotropic energy conversions are also examined. The distributions of the transports on the vertical plane agree well with the observations. After comparison with the observed December‐January‐February 1979 distributions, some quantitative differences remain: the heat transport is too weak aloft and too large near the surface, whereas the momentum transport tends to be too weak. The baroclinic and barotropic conversions show a maximum in the medium‐scale waves. The time evolution of the Richardson number of the mean flow suggests that the medium‐scale wave is due to a baroclinic instability.     

日间对流边界层中的非局地动量混合

日间对流边界层最显著的结构特征是在热力作用下所形成的组织化对流。与小尺度湍涡不同的是，组织化对流具有边界层尺度的垂直相干性，可实现垂直贯穿边界层的非局地物质和能量传输。本文针对对流边界层中的动量混合，探究组织化对流对动量输送的贡献。以高精度大涡模拟数据为研究资料，通过傅里叶变换、本征正交分解和经验模态分解3种滤波方法，分离组织化对流和背景湍涡，计算与两者相关的非局地和局地动量通量，发现与组织化对流相关的非局地动量通量是总通量的重要组成部分，并主导混合层中的垂直动量输送。而后，基于协谱和相位谱分析，探究组织化对流的空间结构对动量传输的影响，发现在热力主导的不稳定环境中，单体型环流结构对动量的传输效率较低。而在风切较强的近中性环境中，滚涡型组织化结构可使垂直和水平流向扰动速度的相位差减小，从而提升动量传输效率。研究结果表明，边界层方案需要包含非局地动量通量项，其参数化应考虑整体稳定度对传输效率的影响。     

非均匀风场与急流强迫的水体涡旋动力特征模拟

通过数值模拟有限区域水气界面由强迫作用驱动形成的水体涡旋及环流动力结构特征,分析非均匀风场、水体急流、两者叠加以及环境边界和地转偏向力等因子的综合影响,探讨此类水体涡旋结构和动力特征。风应力驱动的水体涡旋尺度大,相对深厚,正涡旋具有下凹表面,负涡旋具有上凸表面。水体急流驱动的涡旋形成在急流两侧,对应急流所在深度及厚度尺度相对较小,也较浅,但流速与强度均大于风场驱动的涡旋环流。地形阻挡起着引导涡旋环流走向的作用;同时在北半球地转偏向力对急流侧向负涡旋形成和强度增强更为有利。此外正涡旋对应的辐合辐散势函数强于负涡旋,有利于正涡旋区垂直上升运动强于负涡旋中垂直下沉运动。非均匀风场及水体急流两种强迫叠加作用下,涡旋数量增加、尺度减小,底层的流场形态及强度与表层差异增大。形成的水体涡旋结构呈现多种形态：深厚的整层一致;浅薄的仅维持在上层,或上下层环流相反等。风应力驱动的涡旋以正压性为主,水体急流驱动的涡旋因急流的垂直强切变而具有强的斜压性,在正斜压动能的转换中,正压性涡旋区有斜压动能向正压动能转换,斜压性涡旋区有正压动能向斜压动能转换,均有利于这两个区域正负涡旋的维持。     

The Ekman boundary layer over orography: An analysis of vertical motion

A model of the planetary boundary layer is used to determine the field of vertical motion over large-scale orography. This model represents Ekman boundary-layer dynamics modified by the inclusion of accelerations of the geostrophic wind under the geostrophic momentum approximation. The orography is represented by a circular mountain. The inviscid solution is provided by the sum of a constant translation and a steady, uniform potential vorticity, anticyclonic vortex. The boundary-layer solution vanishes on the mountain, but is matched to the inviscid solution as the top of the boundary layer is approached. The vertical velocity field at the top of the boundary layer is determined by integration of the continuity equation. The field of motion is largely determined by descent from above into the anticyclonic circulation, as in the classical Ekman model. Contributions that arise from the inclusion of accelerations are associated with boundary-layer advection and ageostrophic divergence that produce vorticity tendencies. Finally, the boundary-layer vertical motion is shown to be comparable in magnitude to the vertical motion forced by inviscid flow over the orography, although the distributions of each are significantly different. Effects of mountain asymmetry and a changing pressure field, that can be treated more fully by numerical model simulations, are not considered in the present study.On leave at the University of Colorado, 1990.