EKMAN PUMPING OVER MOUNTAINS

The analytical results of the previous paper(Wu,1989)are used to study the properties of vertical veloc-ity distribution at the top of the boundary layer.The relative position of a jet like geostrophic flow and el-lipse-shaped orography will affect the characteristic feature of vertical motion at the top of the boundary layerwhen the contributions of friction and orography are taken into consideration simultaneously.     

EKMAN PUMPING OVER MOUNTAINS

The analytical results of the previous paper(Wu,1989)are used to study the properties of vertical veloc-ity distribution at the top of the boundary layer.The relative position of a jet like geostrophic flow and el-lipse-shaped orography will affect the characteristic feature of vertical motion at the top of the boundary layerwhen the contributions of friction and orography are taken into consideration simultaneously.     

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。     

EFFECTS OF OROGRAPHY AND AIR FLOW IN EKMAN BOUNDARY LAYER

It is convenient to use σ-coordinates to discuss the dynamic effect of orography and the flow inEkman boundary layer.In this paper,the theory of mixing length is generalized to the σ-coordinate system.Then the governing equations,describing the motion in the boundary layer over the mountain regions arederived.The features of flow in the boundary layer,especially the effects of Ekman pumping,are discussed indetails.It is pointed out that there are three factors affecting the vertical motion at the top of the boun-dary layer:(1)vorticity distribution in the boundary layer,which is directly related to the divergence andconvergence of air flow caused by friction,(2)the upslope or downslope motion of flow over the mountainslopes,and(3)the mutual effect of orography and friction induced by the ageostrophic component climbing up-ward or downward in the boundary layer over mountain regions.     

EFFECTS OF OROGRAPHY AND AIR FLOW IN EKMAN BOUNDARY LAYER*

It is convenient to use σ-coordinates to discuss the dynamic effect of orography and the flow in Ekman boundary layer.In this paper,the theory of mixing length is generalized to the σ-coordinate system.Then the governing equations,describing the motion in the boundary layer over the mountain regions are derived.The features of flow in the boundary layer,especially the effects of Ekman pumping,are discussed indetails.It is pointed out that there are three factors affecting the vertical motion at the top of the boundary layer:(1) vorticity distribution in the boundary layer,which is directly related to the divergence and convergence of air flow caused by friction,(2) the upslope or downslope motion of flow over the mountain slopes,and(3) the mutual effect of orography and friction induced by the ageostrophic component climbing upward or downward in the boundary layer over mountain regions.     

Ekman边界层动力学的理论研究

大气边界层及其与自由大气之间的相互作用具有明显的非线性特征,而这些特征是经典Ekman理论所不能描述的,因此,发展中等复杂程度(介于完全模式与经典Ekman模型之间)的大气边界层动力学模式,简称中间模式,对人们从理论上认识大气边界层动力学过程的非线性特征具有重要意义。本文对目前最具代表性的几个中间边界层模型:地转动量近似边界层模型、Ekman动量近似边界层模型以及弱非线性边界层模型进行了总结和分析,阐述了Ekman层主要动力学特征。通过分析上述各模型的理论框架,揭示了各模型的物理意义及其在描述Ekman边界层基本动力特征上的优点和局限性,并指出尽管在细节定量描述上有差异,但各中间模型对Ekman层动力学特征的定性描述具有很好的一致性。对于这些Ekman边界层近似理论模型的进一步应用问题,主要回顾和总结了利用上述模型探讨地形边界层结构、大气锋生过程、低层锋面结构和环流以及边界层日变化、低空急流形成等动力学问题的研究,并对这些研究所揭示的Ekman层动力学特征及其对自由大气低层运动的影响进行了分析,结果表明,这些Ekman边界层近似模型可以较好地揭示大气边界层动力学特征,在大气边界层动力学及其与自由大气相互作用的研究上具有重要价值。另外,还对目前Ekman边界层理论研究中存在的问题进行了一些分析,提出了有待进一步研究的科学问题。     

经典Ekman流,Ekman层的平衡风场及其扰动稳定性

本文首先利用变分方法,考察了边界层运动能量的变化,指出经典Ekman流是在不可压缩条件下,能量积分达最小值时的一种平衡运动。这对Ekman层运动的物理本质有了进一步的认识。其次,讨论了Ekman动量近似下的Ekman层的平衡风场特征,研究了该平衡风场附近扰动的稳定性问题,结果表明,在自由大气气压场不发生扰动条件下,Ekman层中存在一类新的与惯性不稳定相类似的动力不稳定,且其不稳定性可与Ekman抽吸相联系,还讨论了一般性条件下的扰动不稳定性问题。     

变化涡动沾性系数的Ekman动量近似模式风场结构

在边界层动力学中，涡动粘性系数是影响边界层风场结构的一个重要参数。本文利用边界层动力学中的Ekman动量近似理论，给出了涡动粘性系数随高度缓变条件下的Ekman动量近似边界层模式解，着重讨论了边界层的风场结构、水平散度、垂直涡度以及边界层顶部的垂直速度。结果分析表明：与常值涡动粘性系数情况相比，在边界层低层随高度增加的涡动粘性系数可以导致低层边界层风速随高度迅速增加，即风速垂直切变增加，同时风速矢与地转风之间的夹角减小。惯性项作用可以导致上述作用在气旋性区域减小、而在反气旋性区域增大。随高度增加的涡动粘性系数导致水平散度绝对值、垂直涡度绝对值以及边界层顶部的垂直速度绝对值在气旋性区域减小，而在反气性旋区域增大。涡动粘性系数与惯性之间的非线性相互作用是边界层动力学中重要过程。     

西南低涡Ekman层流场特征分析

本文利用大气边界模式，对1979年7月24－25日的一次西南低涡暴雨进行了Ekman层的流场分析。在理论计算的前提下，通过加入有限的实测风资料进行动力学调整，不仅在Ekman层中能较好地模拟出高层（850，700hPa）气旋环流特征，且发现西南低涡笔星边界层具有中尺度扰动的特征。在整个气旋环流中有局部的反气旋环流出现，这是850，700hPa 天气图上得不到的，且与边界层诊断分析相符合。     

非线性系统在随机力作用下的响应

用矩方程的方法研究了非线性系统在随机激励下的响应，用牛顿迭代法得出该方程解的统计特性，列举了一些数值例子，指出在一定条件下的一些特殊现象。     

强迫耗散非线性临界层动力学的初步研究

研究了强迫耗散非线性临界层动力学，得到了强迫耗散非线性临界层的解析解。解析解表明，在含有强迫耗散的条件下，非线性临界仍有“Ｋｅｌｖｉｎ猫眼”，当时间很大时，“猫眼”趋于定常，强迫耗散因子对非线性临界层激发的“Ｋｅｌｖｉｎ猫眼”的涡度场有重要的调制作用。     

The temporal evolution of a geostrophic flow in a rotating stratified basin

A laboratory study in a rotating stratified basin examines the instability and long time evolution of the geostrophic double gyre introduced by the baroclinic adjustment to an initial basin-scale step height discontinuity in the density interface of a two-layer fluid. The dimensionless parameters that are important in determining the observed response are the Burger number S=R/R₀ (where R is the baroclinic Rossby radius of deformation and R₀ is the basin radius) and the initial forcing amplitude (H₁ is the upper layer depth). Experimental observations and a numerical approach, using contour dynamics, are used to identify the mechanisms that result in the dominance of nonlinear behaviour in the long time evolution, τ>2⁻¹ (where τ is time scaled by the inertial period T_I=2π/f). When the influence of rotation is moderate (0.25≤S≤1), the instability mechanism is associated with the finite amplitude potential vorticity (PV) perturbation introduced when the double gyre is established. On the other hand, when the influence of rotation is strong (S≤0.1), baroclinic instability contributes to the nonlinear behaviour. Regardless of the mechanism, nonlinearity acts to transfer energy from the geostrophic double gyre to smaller scales associated with an eddy field. In the lower layer, Ekman damping is pronounced, resulting in the dissipation of the eddy field after only 40T_I. In the upper layer, where dissipative effects are weak, the eddy field evolves until it reaches a symmetric distribution of potential vorticity within the domain consisting of cyclonic and anticyclonic eddy pairs, after approximately 100T_I. The functional dependence of the characteristic eddy lengthscale L_E on S is consistent with previous laboratory studies on continuously forced geostrophic turbulence. The cyclonic and anticyclonic eddy pairs are maintained until viscous effects eventually dissipate all motion in the upper layer after approximately 800T_I. The outcomes of this study are considered in terms of their contribution to the understanding of the energy pathways and transport processes associated with basin-scale motions in large stratified lakes.     

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.     

气候系统的非线性特征及其预测理论

本文针对气候问题的特殊性,对气候的定义、气候系统的非线性特征、演变机制、可预报性问题以及气候状态的预报方法等做了较全面的研究,这些内容初步形成了气候系统的准动力—准随机理论,是气候动力学的新发展。     

The influence of the geostrophic wind advection approximation on a well-mixed layer

Numerical results indicate that advection of momentum in the boundary layer may significantly alter both the structure of the planetary boundary layer and its influence on the overlying free atmosphere. However, due to the nonlinearity of the inertial terms, it is always difficult to obtain the analytical solution of the boundary-layer model that retains the flow acceleration. In order to overcome this difficulty, the geostrophic momentum (hereafter GM) approximation has been introduced into boundary-layer models. By replacing the advected momentum with the geostrophic wind, the effect of the flow acceleration is partially considered and the original nonlinear partial differential equation set is converted to ordinary differential equations, the solutions of which can be obtained easily with standard techniques. However, the model employing GM fails to capture the features of the boundary layer when the spatio-temporal variation of the boundary-layer flow cannot be properly approximated by the geostrophic wind. In the present work, a modified boundary-layer model with the inertial acceleration in a different approximate form is proposed, in which the advecting wind instead of the advected momentum is approximated by the geostrophic wind (hereafter GAM).Comparing the horizontal velocity and boundary-layer pumping obtained from the classical Ekman theory, and the model incorporating (i) GM and (ii) GAM, it is found that the model with GAM describes most facets of the steady well-mixed layer beneath a north-westerly flow with embedded mesoscale perturbations that is considered in the present work. Inspection of the solution of the model with GAM shows that, within the limit of the validation of the model (i.e., the Rossby number R_O is not very large and the drag coefficient C_D is not too small), the horizontal convergence (divergence) is strengthened by the effect of the inertial acceleration in the region of maximum positive (negative) geostrophic vorticity. Consequently, the boundary-layer pumping there is intensified. It is found that the intensification is firstly strengthened and then weakened as R_O or C_D increases.     

The Distribution and Uncertainty Quantification of Wind Profile in the Stochastic General Ekman Momentum Approximation Model

The general Ekman momentum approximation boundary-layer model(GEM) can be effectively used to describe the physical processes of the boundary layer. However, eddy viscosity, which is an approximated value, can lead to uncertainty in the solutions. In this paper, stochastic eddy viscosity is taken into consideration in the GEM, and generalized polynomial chaos is used to quantify the uncertainty. The goal of uncertainty quantification is to investigate the effects of uncertainty in the eddy viscosity on the model and to subsequently provide reliable distribution of simulation results. The performances of the stochastic eddy viscosity and generalized polynomial chaos method are validated based on three different types of eddy viscosities, and the results are compared based on the Monte Carlo method. The results indicate that the generalized polynomial chaos method can be accurately and efficiently used in uncertainty quantification for the GEM with stochastic eddy viscosity.