Eddy exchange coefficients in numerical models of the planetary boundary layer

Specification of the eddy exchange coefficients is perhaps one of the most difficult problems in the numerical modeling of the planetary boundary layer. These coefficients have been computed from finite-difference analogs to analytical expressions associated with surface boundary-layer similarity theory, which is based on observations in an equilibrium surface layer. This procedure leads to erroneous results in the region above the surface layer and in a non-equilibrium surface layer. In addition, differencing problems arise in regions of small vertical wind shear. A new turbulence transport model has been obtained through the closure procedures for the transport equations of the Reynolds stress and the turbulent length scale. The new approach could be used to calculate Reynolds stresses and eddy exchange coefficients throughout a non-neutral planetary boundary layer under non-equilibrium conditions.     

A model of atmospheric boundary-layer flow above an isolated two-dimensional ‘hill’; an example of flow above ‘gentle topography’

A numerical model is developed for two-dimensional turbulent boundary-layer flow above gentle topography — defined as not giving rise to mean flow separation. Although the model is formulated in a framework of mixing length and turbulent energy equation models for the surface layer of the atmospheric boundary layer, it could be modified to include higher-order closure hypotheses and/or extended to model gentle topography for the planetary boundary layer or on the sea bed. Results are presented for flow above a specific shape of hill and the effects of surface roughness and hill height are investigated.     

黄河源区鄂陵湖湖面和湖边草地对流边界层湍流结构特征的大涡模拟研究

为研究黄河源区边界层湍流特征及其对物质和能量输送的影响,本文首次采用大涡模拟的方法,对比分析了黄河源区两种不同下垫面上（鄂陵湖和湖边草地）对流边界层（CBL）中精细的湍流结构特征。使用资料为2012年夏季黄河源区鄂陵湖流域野外观测实验的GPS探空资料、涡动相关观测资料。分析表明,模拟的黄河源区草地和湖上CBL的平均结构与实测结果吻合较好,但草地和湖上CBL的湍流结构特征差异较明显。模拟结果显示,草地CBL内湍能收支、湍流特征量的时空分布和湍涡结构特征均与陆地上热力驱动CBL的研究结果一致;湖上CBL顶部存在明显的对流卷特征,且夹卷层的湍流强度比草地的强,而草地近地面湍强则更大。通过改变水平分辨率的模拟试验,发现两个不同下垫面上模拟结果对模式分辨率的敏感性不同,湖面CBL的模拟要选择较高的水平分辨率（50～100 m）,以提高近湖面和夹卷层对湍流动能和湍流通量模拟的精度,也充分模拟出各种尺度的波对湍流通量的累积贡献。考虑到计算时间等影响,模拟草地边界层精细的湍流结构时建议选择网格距为100～200 m。     

A numerical study of the influence of an air temperature-inversion layer and a seawater density-jump layer on the structure of interacting boundary layers

The effects of an air-temperature inversion in the atmosphere and a seawater density jump in the ocean on the structure of the atmospheric and oceanic boundary layers are studied by use of a coupled model. The numerical model consists of a closed system of equations for velocities, turbulent kinetic energy, turbulent exchange coefficient, local turbulent length scale, and stratification expressions for both air and sea boundary layers. The effects of the temperature inversion and the density jump are incorporated into the equations of turbulent kinetic energy of the atmosphere and ocean by a parameterization. A series of numerical experiments was conducted to determine the effects of various strengths of the inversion layer and surface heat fluxes in the atmosphere and of the density-jump layer in the ocean on the structure of the interacting boundary layers.The numerical results show that the temperature inversion in the atmosphere and density jump in the ocean have strong influences on turbulent structure [especially on the turbulent exchange coefficient (TEC) and turbulent kinetic energy (TKE)] and on air-sea interaction characteristics. Maxima of TKE and TEC strongly decrease with increasing strength of the inversion layer, and they disappear for strong inversions in the atmosphere. Certain strengths (density differences between the upper and the lower layers) of the density-jump layer in the ocean (₂ 0.1 g/cm³) produce double maxima in TEC-profiles and TKE-profiles in the ocean. The magnitudes of air-sea interaction characteristics such as geostrophic drag coefficient, and surface drift current increase with increasing strength of the density-jump layer in the ocean. The density-jump layer plays the role of a barrier that limits vertical mixing in the ocean. The numerical results agree well with available observed data and accepted quantitive understanding of the influences of a temperature inversion layer and a density-jump layer on the interacting atmospheric and oceanic boundary layers.     

The perturbed structure of the neutral atmospheric boundary layer over irregular terrain

The differential equations for first-order (linear) response of the planetary boundary layer are formulated for flow over periodic terrain, for variations in both surface roughness and terrain elevation. A simple second-order closure model of the turbulence is used, and Coriolis forces are neglected. Flow over a periodic terrain produces corresponding periodic structure in all meteorological fields above the surface. The periodic structure consists of two components. The first is very nearly evanescent with height. It corresponds to the motion that would be observed were the atmosphere inviscid. The second component, introduced by turbulent viscosity, exhibits a phase variation with height in addition to a decay in amplitude. W.K.B. [Wentzel-Kramers-Brillouin] approximations for the two components are developed, and the coupling between the components is discussed. The formulation for calculating solutions by numerical integration is developed, including specification of appropriate boundary conditions. Calculations are presented in a companion paper.Wave Propagation Laboratory.Environmental Science Group.     

Stratified flow over non-uniform surfaces: Turbulent energy model

A turbulent energy model is developed to simulate the response of a neutrally stratified atmospheric boundary layer to sudden changes in surface roughness. A mechanism of turbulent energy transfer is proposed, based upon the results of numerical experiments, that explains the distribution of shear stress and hence the distribution of velocity profiles in the atmospheric surface layer. Two length scales associated with the turbulent energy equation are obtained from experimental data and the law of the wall. Turbulent energy is also predicted.The predicted growth of the internal boundary layer is slower than that obtained from mixing-length models. Also, the predicted surface shear stress obtained from the turbulent energy model is in better agreement with field data than that obtained from mixing-length models.     

利用TWP-ICE试验资料对比两种边界层参数化方案

利用高分辨率WRF单气柱模式,选取了两种边界层参数化方案(YSU,MYJ),对TWP-ICE(Tropical Warm Pool International Cloud Experiment)试验期间的个例进行数值模拟,比较了两种方案对边界层结构、云和降水模拟的影响。结果表明:季风活跃期,YSU方案模拟的湍流交换系数较小,湍流混合偏弱,边界层内热通量偏小,使地表热量和水汽不易向上输送,水汽含量在近地表明显偏多,而在边界层及其以上大气层具有显著的干偏差,因此该方案模拟的云中液态水和固态水含量偏低,云量偏少,降水率偏小;MYJ方案对于季风活跃期的边界层结构具有较好的模拟能力,其模拟的云和降水更为准确。季风抑制期,MYJ方案模拟的夜间边界层结构存在较大误差,这是因为该方案模拟的夜间湍流交换系数较大,湍流混合偏强,边界层内热通量偏大,模拟的位温和水汽混合比在边界层内随高度变化较小,而观测廓线在边界层内存在较大梯度。季风抑制期两种方案模拟的云和降水均比观测值偏多,方案之间的差异较小。     

层积云覆盖的边界层数值模拟研究(Ⅰ):数值模式的建立

层积云是一种在湍流作用下形成的边界层云,在这种边界层中,层积云顶即边界层顶,云层和非云层耦合在一起,为了加深对这种层积云覆盖的边界层的理解,许多作者已经做了大量的野外观测和数值试验研究,然而在数值模拟研究中存在湍流和云物理模式相互脱节的现象,针对这种缺陷,本文在湍流控制方程组中引入云滴控制方程,发展了一个新的用于研究海区层积云覆盖的边界层的数值模式,所建模式具有如下特点：（1）实现了云物理模式与湍流模式的相互耦合;（2）实现了云滴分档凝结模式和三阶湍流闭合边界层模式相互耦合,利用所建模式对大涡模拟对比试验所采用的个例进行了数值模拟,数值模拟结果表明,该边界层模式能较合理地模拟海区层积云覆盖的边界层微湍流结构和云微物理过程。     

Numerical simulation of the anthropogenic heat effect on urban boundary layer structure

In this paper, several methods of incorporating anthropogenic heat release into the boundary layer are compared. The best scheme was one that included anthropogenic heat release in both the surface energy balance equation and the thermodynamic equations. In addition, it included diurnal variations and a distribution of heat based on building concentrations. We further investigated the influence of anthropogenic heat release on urban boundary layer structure and the urban heat island, and found that the contribution of anthropogenic heat release to the urban heat island is greatest in the evening and at night, and least at noon. The daily average contribution ratio of anthropogenic heat to urban heat island intensity in the winter is 54.5%, compared with just 43.6% in the summer. Anthropogenic heat strengthens the vertical movement of urban surface air flow, changing the urban heat island circulation. It also makes the urban boundary layer more turbulent and unstable, especially in the morning and evening. The degree of influence of anthropogenic heat release on local boundary layer structure depends on its importance to the surface energy budget.     

Models of the wave boundary layer

A general approach to model the structure of the wave boundary layer, based on the nonlinear Reynolds equations in a curvilinear system of coordinates, is described. Both spectral and numerical grid models are used. The energetic interactions between wind and wave in terms of Miles' parameter are studied. For waves outrunning or running against the wind, the range of the inverse flux of energy is found. For waves running slower than the wind, quadratic growth of is established. Vertical profiles of the wave momentum flux for different fetches are given. Following P. Janssen, a one-dimensional analytical model of the wave boundary layer is suggested. The effect of waves on the drag coefficient is analyzed.     

Local advection of momentum,heat, and moisture in micrometeorology

The local advection of momentum, heat and moisture in micrometeorology due to a horizontal inhomogeneity in surface conditions is numerically investigated by a higher-order turbulence closure model which includes equations for the mean quantities, turbulent fluxes, and the viscous dissipation rate. The application of the two-dimensional model in this paper deals with the simulation of the flow from an extensive smooth dry area to a grassy wet terrain. The mean wind speed, temperature, and humidity distributions in the resulting internal boundary layer downstream of the surface discontinuity are determined such that the energy and moisture balances at the Earth's surface are satisfied.Numerical calculations of the mean temperature and humidity profiles are compared with available observed ones. The results include the advective effects on turbulent flux distributions, surface energy balance, evaporation rate, and Bowen ratio. The sensitivity of the predicted mean profiles and turbulent flux distributions to the surface relative humidity, thermal stratification, and the roughness change is discussed.NRC-NAS Resident Research Associate at AFCRL.     

The effect of idealized water waves on the turbulence structure and kinetic energy budgets in the overlying airflow

The influence of an idealized moving wavy surface on the overlying airflow is investigated using direct numerical simulations (DNS). In the present simulations, the bulk Reynolds number is Re = 8000 (; where U₀ is the forcing velocity of the flow, h the height of the domain and v the kinematic viscosity) and the phase speed of the imposed waves relative to the friction velocity, i.e., the wave age varies from very slow to fast waves. The wave signal is clearly present in the airflow up to at least 0.15λ (where λ is the wave length) and is present up to higher levels for faster waves. In the kinetic energy budgets, pressure transport is mainly of importance for slow waves. For fast waves, viscous transport and turbulent transport dominate near the surface. Kinetic energy budgets for the wave and turbulent perturbations show a non-negligible transport of turbulent kinetic energy directed from turbulence to the wave perturbation in the airflow. The wave-turbulent energy transport depends on the size, tilt, and phase of the wave-induced part of the turbulent Reynolds stresses.According to the DNS data, slow waves are more efficient in generating isotropic turbulence than fast waves.Despite the differences in wave-shape as well as in Reynolds number between the idealized direct numerical simulations and the atmosphere, there are intriguing similarities in the turbulence structure. Important information about the turbulence above waves in the atmosphere can be obtained from DNS—the data must, however, be interpreted with care.     

农林复合带一维非静力大气边界层模式及其模拟分析

建立了一个农林复合带地区一维非静力大气边界层能量闭合模式，对1000m以下的大气边界层内的风、温、湿作了24h的预报，并对下垫面3种不同参数化方案(农作物、森林、无植被)的输出结果与实测值进行了分析和比较；同时通过敏感性试验，突出比较了农作物和森林下垫面对大气边界层垂直流场，湍流垂直交换和湍能的影响。结果表明，本模式能改善边界层风速、位温和湿度预报的模拟效果，下垫面植被对边界层气象要素大小和分布有显著的作用，对湍能垂直分布有一定影响。     

A multi-limit formulation for the equilibrium depth of a stably stratified boundary layer

Currently no expression for the equilibrium depth of the turbulent stably-stratified boundary layer is available that accounts for the combined effects of rotation, surface buoyancy flux and static stability in the free flow. Various expressions proposed to date are reviewed in the light of what is meant by the stable boundary layer. Two major definitions are thoroughly discussed. The first emphasises turbulence and specifies the boundary layer as a continuously and vigorously turbulent layer adjacent to the surface. The second specifies the boundary layer in terms of the mean velocity profile, e.g. by the proximity of the actual velocity to the geostrophic velocity. It is shown that the expressions based on the second definition are relevant to the Ekman layer and portray the depth of the turbulence in the intermediate regimes, when the effects of static stability and rotation essentially interfere. Limiting asymptotic regimes dominated by either stratification or rotation are examined using the energy considerations. As a result, a simple equation for the depth of the equilibrium stable boundary layer is developed. It is valid throughout the range of stability conditions and remains in force in the limits of a perfectly neutral layer subjected to rotation and a rotation-free boundary layer dominated by surface buoyancy flux or stable density stratification at its outer edge. Dimensionless coefficients are estimated using data from observations and large-eddy simulations. Well-known and widely used formulae proposed earlier by Zilitinkevich and by Pollard, Rhines and Thompson are shown to be characteristic of the above interference regimes, when the effects of rotation and static stability (due to either surface buoyancy flux, or stratification at the outer edge of the boundary layer) are roughly equally important.     

Boundary-layer effects on mountain waves: a new look at some historical studies

Early studies of mountain waves reported various results that have rarely been investigated since. These include: large-amplitude mountain waves above an unstable boundary layer much higher than the mountains; a repeated downwind drift and upwind jump of mountain waves; and larger vertical wind magnitude near sunrise and/or sunset. These are investigated using over 3,000 radiosondes and meso-strato-troposphere (MST) radar. Superadiabatic temperature gradients are found beneath mountain waves, explainable by convection which appears to raise the mountain-wave launching height. Movement of mountain-wave patterns is studied by a new method using height–time vertical wind data. A swaying motion of mountain waves, with period of a few minutes, appears to be equally upwind and downwind, rather than asymmetric at the heights measurable. Also, vertical wind shows no change in mean, variance or extreme values near sunrise and sunset, despite the expected diurnal changes of boundary-layer structure. An explanation for differences between MST radar and other measurements and models of mountain waves is suggested in terms of more than one variety of mountain wave. Type 1 has stable air near the ground; type 2 is above a convective/turbulent boundary layer of significant height as compared to the mountains.     

人为热源和城市绿化对冬季山谷城市边界层结构影响的数值模拟

为了探讨人为热源和城市绿化对城市边界层的影响,本文在RAMS模式中引入周期性日变化的人为热源和人工改变下垫面状况,初步模拟分析了人为热源和城市绿化对城市边界层结构的影响.结果表明:人为热源具有明显的增温效应,增强了城市的湍流交换,白天增加了大气不稳定度,促进了混合层的发展,夜间降低了大气稳定度,减弱了城市夜间逆温.城市绿化减小了地表反照率,增加了到达地面的净辐射,模拟期间土壤冻结,增加的净辐射其中一部分以感热的形式来加热大气;绿化后地气之间的湍流交换增强,增加了大气不稳定度,减弱了白天高空逆温;本文还讨论了不同绿化布局对白天高空逆温的影响以及人为热源和城市绿化之间的非线性相互作用.     

Mean Flow and Turbulence Statistics Over Groups of Urban-like Cubical Obstacles

Direct numerical simulations of turbulent flow over regular arrays of urban-like, cubical obstacles are reported. Results are analysed in terms of a formal spatial averaging procedure to enable interpretation of the flow within the arrays as a canopy flow, and of the flow above as a rough wall boundary layer. Spatial averages of the mean velocity, turbulent stresses and pressure drag are computed. The statistics compare very well with data from wind-tunnel experiments. Within the arrays the time-averaged flow structure gives rise to significant ‘dispersive stress’ whereas above the Reynolds stress dominates. The mean flow structure and turbulence statistics depend significantly on the layout of the cubes. Unsteady effects are important, especially in the lower canopy layer where turbulent fluctuations dominate over the mean flow.     

Interaction of internal waves and turbulence in the ocean

Within the framework of the semiempirical theory of turbulence for stratified fluids some aspects of the problem of internal wave-turbulence interaction in the upper layer of the ocean are discussed. The conditions of amplification and sustaining of turbulence by internal waves are investigated. Stationary distributions of turbulent energy are found for a stratified fluid with a shear flow produced, for example, by a low-frequency internal wave. The internal wave damping due to both turbulent viscosity and turbulent diffusion in the thermocline is studied. For a two-layer model damping constant is determined as a function of the wave number. The variation of surface turbulence by internal waves is estimated and the role of this process in slick formation is considered.     

The influence of convergence movement on turbulent transportation in the atmospheric boundary layer

Classical turbulent K closure theory of the atmospheric boundary layer assumes that the vertical turbulent transport flux of any macroscopic quantity is equivalent to that quantity‘s vertical gradient transport flux. But a cross coupling between the thermodynamic processes and the dynamic processes in the atmospheric system is demonstrated based on the Curier-Prigogine principle of cross coupling of linear thermodynamics. The vertical turbulent transportation of energy and substance in the atmospheric boundary layer is related not only to their macroscopic gradient but also to the convergence and the di-vergence movement. The transportation of the convergence or divergence movement is important for the atmospheric boundary layer of the heterogeneous underlying surface and the convection boundary layer.Based on this, the turbulent transportation in the atmospheric boundary layer, the energy budget of the heterogeneous underlying surface and the convection boundary layer, and the boundary layer parameteri-zation of land surface processes over the heterogeneous underlying surface are studied. This research offers clues not only for establishing the atmospheric boundary layer theory about the heterogeneous underlying surface, but also for overcoming the difficulties encountered recently in the application of the atmospheric boundary layer theory.