Statistics of Scalar Fields in the Atmospheric Boundary Layer Based on Large-Eddy Simulations. Part II: Forced Convection

Forced convection in a quasi-steady atmospheric boundary layer is investigated based on a large-eddy simulation (LES) model. The performed simulations show that in the upper portion of the mixed layer the dimensionless (in terms of mixed layer scales) vertical gradients of temperature, humidity, and wind velocity depend on the dimensionless height z/z _i and the Reech number Rn. The peak values of variances and covariances at the top of the mixed layer, scaled in terms of the interfacial scales, are functions of the interfacial Richardson number Ri. As a result expressions for the entrainment rates, in the case when the interfacial layer has a finite depth, and a condition for the presence of moistening or drying regimes in the mixed layer, are derived. Profiles of dimensionless scalar moments in the mixed layer are proposed to be expressed in terms of two empirical similarity functions F _m and F _i , dependent on dimensionless height z/z _i , and the interfacial Richardson number Ri. The obtained similarity expressions adequately approximate the LES profiles of scalar statistics, and properly represent the impact of stability, shear, and entrainment. They are also consistent with the parameterization proposed for free convection in the first part of this paper.     

Statistics of Scalar Fields in the Atmospheric Boundary Layer Based on Large-eddy Simulations. Part 1: Free Convection

Convection in a quasi-steady, cloud-free, shear-free atmospheric boundary layer is investigated based on a large-eddy simulation model. The performed tests indicate that the characteristic (peak) values of statistical moments at the top of the mixed layer are proportional to the interfacial scales (from gradients of scalars in the interfacial layer). Based on this finding a parameterization is proposed for profiles of scalar variances. The parameterization employs two, semi-empirical similarity functions F_m(z/z_i) andF_i(z/z_i), multiplied by a combination of the mixed-layer scales and the interfacial scales.     

An Evaluation Of Local Similarity At The Top Of The Mixed Layer Based On Large-Eddy Simulations

Local similarity, referred to as type II similarity,in the interfacial, stably-stratified layer at thetop of the atmospheric (or oceanic) mixed layer isdiscussed. Type II scales for scalars are based onthe local values of scalar gradients. Similaritypredictions are derived from the second-orderclosure model of Yamada and Mellor, and also fromsimilarity arguments. The obtainedformulation is verified for active and passive scalarsbased on the large-eddy simulation model.     

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.     

Parameterization of sheared entrainment in a well-developed CBL. Part I: Evaluation of the scheme through large-eddy simulations

The entrainment flux ratio A _e and the inversion layer (IL) thickness are two key parameters in a mixed layer model. A _e is defined as the ratio of the entrainment heat flux at the mixed layer top to the surface heat flux. The IL is the layer between the mixed layer and the free atmosphere. In this study, a parameterization of A _e is derived from the TKE budget in the firstorder model for a well-developed CBL under the condition of linearly sheared geostrophic velocity with a zero value at the surface. It is also appropriate for a CBL under the condition of geostrophic velocity remaining constant with height. LESs are conducted under the above two conditions to determine the coefficients in the parameterization scheme. Results suggest that about 43% of the shear-produced TKE in the IL is available for entrainment, while the shear-produced TKE in the mixed layer and surface layer have little effect on entrainment. Based on this scheme, a new scale of convective turbulence velocity is proposed and applied to parameterize the IL thickness. The LES outputs for the CBLs under the condition of linearly sheared geostrophic velocity with a non-zero surface value are used to verify the performance of the parameterization scheme. It is found that the parameterized A _e and IL thickness agree well with the LES outputs.     

Molecular dissipation of turbulent fluctuations in the convective mixed layer part I: Height variations of dissipation rates

During the Limagne and Beauce experiments, the INAG-IGN Aerocommander FL 280 aircraft made extensive ‘in situ’ measurements of turbulent fluctuations in diurnally evolving convective boundary layers. In this paper, these measurements were used to investigate characteristics of the molecular dissipation of turbulent fluctuations through the mixed layer and well into the overlying stable layer. The dimensionless dissipation rates of turbulent kinetic energy, temperature and humidity variances, and temperature-humidity covariance (ψ, ψ_θ, ψ _qand ψ _θq) were computed and their height variations analysed. The behaviour of the dissipation rate ψ was found to differ significantly from those observed for the other rates. In the lowest region of the mixed layer, ψ does not obey the local free convection prediction. Instead, it follows practically a relationship similar to the one established in the surface layer by Wyngaard et al. (1971). The dissipation rate ψ remains fairly constant in the bulk of the mixed layer (0.3 ≤ z/Z _i≤ 0.8) and shows a very rapid decrease above the inversion. These results confirm those reported previously from the Minnesota and Ashchurch data by Kaimal et al. (1976), Caughey and Palmer (1979), etc. The height variations for the other dissipation rates were found to obey, as expected, the (z/Z _i)^-4/3 decrease predicted under the local free convection similarity hypothesis in the lowest region of the mixed layer. This region extends to the height z/Z _i- 0.4, 0.1, and 0.3, respectively, for ψ_θ, ψ_q, and ψ_θq. Above these levels, the dissipation rates ψ_θ and ψ_q show, on average, a slight increase to reach peak-values near the mixed-layer top, while the ‘dissipation’ rate ψ _θqchanges sign from positive to negative around the height z/Z _i, - 0.7. These characteristics confirm the fact that the structures of temperature and humidity fluctuations are considerably affected by their entrainment-induced fluctuations. Therefore, an attempt has been made to non-dimensionalize the dissipation rates near the mixed-layer top with the interfacial scaling factors.     

An upper ocean general circulation model for climate studies: global simulation with seasonal cycle

The global ocean circulation with a seasonal cycle has been simulated with a two-and-a-half layer upper-ocean model. This model was developed for the purpose of coupling to an atmospheric general circulation model for climate studies on decadal time scales. The horizontal resolution is 4° latitude by 5° longitude and is thus not eddy-resolving. Effects of bottom topography are neglected. In the vertical, the model resolves the oceanic mixed layer and the thermocline. A thermodynamic sea-ice model is coupled to the mixed layer. The model is forced at the surface with seasonally varying (a) observed wind stress, (b) heat fluxes, as defined by an atmospheric equilibrium temperature, and (c) Newtonian-type surface salt fluxes. The second layer is coupled to the underlying deep ocean through Newtonian-type diffusive heat and salt fluxes, convective overturning, and mass entrainment in the upwelling regions of the subpolar gyres. The overall global distributions of mixed layer temperature, salinity and thickness are favorably reproduced. Inherent limitations due to coarse horizontal resolution result in large mixed-layer temperature errors near continental boundaries and in weak current systems. Sea ice distributions agree well with observations except in the interiors of the Ross and Weddell Seas. A realistic time rate of change of heat storage is simulated. There is also realistic heat transport from low to high latitudes.     

Radiative Effects on Temperature in the Stable Surface Layer

The interaction between longwave radiation and temperature fluctuations plays a role in the dissipation of temperature variance. This interaction is most easily described by spectral models of atmospheric turbulence and a spectral radiative dissipation function which gives the intensity of the damping at each radiative wavelength and wavenumber k. We have used a Corrsin–Pao closure for the spectral budgets of turbulent kinetic energy and temperature to study the coupling of radiation to turbulence. The spectral radiative dissipation function and a related integral have been fitted by analytical approximations with the correct asymptotic behavior. This resulted in a simple analytical formula for the dimensionless temperature spectrum as a function of Monin-Obukhov stability, and a new dimensionless parameter describing the relative importance of radiation in the temperature spectral budget. The radiative effects both on the temperature spectrum and on the dimensionless temperature variance can then be calculated. Based on typical values of the radiative dimensionless parameters for the surface layer, we conclude that radiative dissipation is probably negligible there.     

Transition of two‐layer stratified flow from the slope of bottom topography to a horizontal channel

Abstract

An experimental study was conducted to investigate the transition of two‐layer stratified flow from the slope of bottom topography to a horizontal channel. Three experiments, with a reduced gravity of g’ = 1.64, 6.47 and 18.0 cm s^?2, were performed. Particle image velocimetry and planar laser‐induced fluorescence were used to obtain the measurements of velocity and concentration fields. The flow rate, obtained from the measured velocity field, increases significantly toward the toe of the topography by almost 40% from that at the sill crest due to the interfacial wave activities. In the horizontal channel, however, the flow rate only increases marginally. Estimates of the composite Froude number indicate that the supercritical flow on the slope of the topography goes through the transition to the subcritical flow in the horizontal channel. The transition is mainly due to the increase in the lower‐layer thickness because of increasing interfacial friction caused by the breaking of interfacial waves, and no internal hydraulic jumps are observed. The measured mean concentration field showed the formation of an intermediate layer of medium density, which increased its thickness with g’ and helped to suppress turbulence. Spectral analysis of the density interfacial fluctuations indicated that the interfacial waves that developed on the slope of the topography broke up downstream of the toe into smaller amplitude waves at larger frequencies. The waves at several channel cross‐sections were also examined.     

Statistics of shallow convection on Mars based on large-eddy simulations. Part 1: shearless conditions

Results of large-eddy simulations of shallow, quasi-steady, shear-less convection in the Martian boundary layer are presented and discussed. In the considered three cases, turbulence is forced by the radiative flux divergence, prescribed as given functions of height, and the strength of the surface heat flux. It is constrained by the temperature inversion at the boundary-layer top. The resulting convective boundary layer exhibits horizontal cellular structures. The presence of radiative heating causes dimensionless statistics of turbulence to depend on the parameter F, defined in terms of the integrated radiative and turbulent heating rates in the boundary layer.     

Observations of the barotropic Ekman layer over an urban terrain

Data from low-level soundings over Cambridge, U.S.A. were selected on the basis of an Ekman-like variation of the wind vector with altitude combined with evidence of a barotropic atmosphere. The method of geostrophic departure was used to determine the shear-stress distribution. The analysis yields the dimensionless properties of the barotropic Ekman layer under neutral and stable stratification. Some important results include: the geostrophic drag coefficient displays no dependence on the degree of static stability; the dimensionless height of the boundary layer decreases with increasing stability in agreement with the prediction of Zilitinkevich; the properties of the urban surface layer, where the roughness elements are multistory buildings, show no dependence on atmospheric stability under the moderate wind conditions which display the Ekman-like wind profile; and the directions of the horizontal shear stress and the vertical derivative of the velocity vector usually tend to be parallel only near the surface layer. Values of the two constants of the Rossby number similarity theory are found for the neutral barotropic Ekman layer at a surface Rossby number equal to 2 × 10⁵. The implications of the work with respect to wind-tunnel simulation of the flow over models of urban areas are discussed.     

Ondes de gravite interfaciales marginalement instables dans la couche limite planetaire

Wavelike motions within a strong morning inversion of the planetary boundary layer were investigated experimentally using two atmospheric research aircraft: an Aerocommander 280FL and a Cessna 206. The Aerocommander aircraft, instrumented for the measurement of rapid fluctuations of temperature, water vapour density and air velocities, was flown horizontally at different levels within the inversion layer in order to document adequate data on the wave motion. An example of such motions observed on 8 June, 1974 is described and analyzed in the present paper. The aircraft records obtained within the inversion layer at about 600 m above the ground show large fluctuations of the meteorological variables with well-defined amplitudes and wavelengths.Spectra and cross-spectra of temperature, water vapour density and air velocities were computed and analyzed to determine characteristics of gravity waves according to the method described by Metcalf (1975). These spectra exhibit a sharp maximum associated with high coherences at a particular wavelength. In this narrow spectral band, phase angles ±90 ° are obtained between vertical velocity and temperature as well as between vertical and horizontal velocities. These features suggest that observed motions are horizontally propagating trapped or evanescent waves. They enable us to estimate true wavelengths (500 m), wave vector azimuths, intrinsic frequencies and phase velocities of these waves. These results appear to be mutually consistent. Furthermore, it is possible to confirm these latter with the detailed vertical profiles of the boundary layer provided by the Cessna aircraft making spiral soundings. In this regard, the vertical structure of the Brunt-Väisälä frequency confirms that the waves are everywhere evanescent except within a thin highly stable layer between the diurnal mixed layer and the overlapping inversion. Moreover, examination of the wind profiles reveals that the interfacial vertical wind shear might be a relevant parameter reducing phase velocities. Such a conclusion is also supported by the observed wave vector directions which appear to be closely parallel to the wind shear vectors at the 600-m level. Additional confirmation is found by comparing the observed wavelengths to those predicted by applying the hydrodynamical stability model of Hazel (1972) to the measured profiles. Although the wind shear clearly plays a role in wave development, local heat flux and temperature variance values show that in this case the instability is only a marginal and sporadic event embedded in nearly neutral waves. Accordingly, it is argued that the observed motions are interfacial waves at the inversion base level, the amplitude and wave vector azimuth of which are controlled by the vertical wind shear.

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Ondes de gravite interfaciales marginalement instables dans la couche limite planetaire

Résumé Des ondes de gravité interfaciales progressives sont étudiées à l'aide de deux avions dans la couche limite planétaire. Les spectres des vitesses et de la température fournissent les directions et vitesses de propagation. La comparaison des résultats aux profils verticaux du vent et de la température montre que ces ondes sont marginalement instables sous l'effet du cisaillement vertical du vent.

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混合层深度对热带气旋强度的影响

利用建立的中尺度海气耦合模式进行一组敏感性试验,以考察初始混合层深度对热带气旋(TC)强度的影响。试验结果表明,初始混合层深度对TC最大强度和增强时间影响都较大。一般来说,初始混合层越深,模拟的TC最大强度越大,TC增强时间越长。另外,TC与混合层深度的关系并不是线性的。当混合层较浅时,TC强度对其变化更为敏感。     

A numerical study of daily transitions in the convective boundary layer

We examine daily (morning–afternoon) transitions in the atmospheric boundary layer based on large-eddy simulations. Under consideration are the effects of the stratification at the top of the mixed layer and of the wind shear. The results describe the transitory behaviour of temperature and wind velocity, their second moments, the boundary-layer height Z _m (defined by the maximum of the potential temperature gradient) and its standard deviation σ _m , the mixed-layer height z _i (defined by the minimum of the potential temperature flux), entrainment velocity W _e, and the entrainment flux H _i . The entrainment flux and the entrainment velocity are found to lag slightly in time with respect to the surface temperature flux. The simulations imply that the atmospheric values of velocity variances, measured at various instants during the daytime, and normalized in terms of the actual convective scale w_*, are not expected to collapse to a single curve, but to produce a significant scatter of observational points. The measured values of the temperature variance, normalized in terms of the actual convective scale Θ_*, are expected to form a single curve in the mixed layer, and to exhibit a considerable scatter in the interfacial layer.     

Similarity studies of entrainment in convective mixed layers

A similarity study of entrainment at the top of convectively driven mixed layer is presented. The similarity framework is used for a comparison between various parameterized models of mixed-layer growth rate and between closely related models for the ratio of heat fluxes at ground and inversion levels. These various models are also tested, in dimensionless form, against data from laboratory, field experiments and numerical higher-order-modeling of the convective layer. It is concluded that a rather accurate prediction of mixed-layer growth can be achieved with the simple constant flux ratio model, but that more refined studies of entrainment are required to account for the decrease of the heat flux ratio with increasing convective intensity.List of acronyms CRPE Centre de Recherches en Physique de l'Environnement, Issy-les-Moulineaux, France - EERM Etablissement d'Etudes et de Recherches Météorologiques, Boulogne, France - INRA Institut National de la Recherche Agronomique, Versailles, France - LAMP Laboratoire Associé de Météorologie Physique, Clermont-Ferrand, France - NCAR National Center for Atmospheric Research, Boulder, U.S.A. - NOAA National Oceanic and Atmospheric Administration, Environmental Research Laboratories, Boulder, U.S.A.     

1998年夏季风爆发前后南海上混合层的特征及成因

利用1998年“南海季风实验（SCSMEX）”南北部两个点的资料,采用J.Launianen和T.Vihma提出的方法,计算了潜热通量、感热通量和风应力,分析了南海上混合层动力、热力特征及其与南海夏季风爆发之间的关系。发现在西南季风爆发前后,南海北部、南部的两个观测点的海洋上混合层温度和深度随时间的变化具有不同的特点：北部混合层温度经历由高到低再变高,混合层深度经历由浅变深再变浅的3个时段;南部混合层温度经历由低到高再变低,混合层深度经历由深变浅再变深的3个时段。这与南海南、北部海面的风和海面热通量具备不同的特征有关。在5～6月南海上混合层动力、热力特征基本受局地风与短波辐射控制,海面潜热和感热的作用较小。在5月份,南海南部观测点海面附近存在浅薄的高盐高密度层,在60m以上的上层海洋内存在着许多高盐高密度核。在1998年“南海季风实验”期间南海南、北部两个观测点都存在较浅薄的障碍层,在西南季风爆发期间,南海北部观测点的障碍层较厚达到20m以上。     

An efficient PBL model for global circulation models-design and validation

An efficient, pianetary boundary layer (PBL) model is developed and validated with empirical data for applications in general circulation models (GCMs). The purpose of this PBL model is to establish the turbulent surface fluxes as a function of the principal external PBL parameters in a numerically efficient way. It consists of a surface layer and a mixed layer matched together with the conditions of constant momentum and heat flux at the interface. An algebraic solution to the mean momentum equations describes the mixed-layer velocity profile and thus determines the surface wind vector. The velocity profile is globally valid by incorporating the effect of variable Coriolis force without becoming singular at the equator. Turbulent diffusion depends on atmospheric stability and is modeled in the surface layer by a drag law and with first-order closure in the mixed layer. Radiative cooling in the stably stratified PBL is considered in a simple manner. The coupled system is solved by an iterative method. In order to preserve the computational efficiency of the large-scale model, the PBL model is implemented into the GISS GCM by means of look-up tables with the bulk PBL Richardson number, PBL depth, neutral drag coefficient, and latitude as independent variables.A validation of the PBL model with observed data in the form of Rossby number similarity theory shows that the internal feedback mechanisms are represented correctly. The model, however, underpredicted the sensible heat-flux. A subsequent correction in the turbulence parameterization yields better agreement with the empirical data. The behavior of the principal internal PBL quantities is presented for a range of thermal stabilities and latitudes.     

GRAPES变分同化系统中动力平衡约束的统计求解

该文在GRAPES (Global/Regional Assimilation and PrEdiction System) 模式面三维变分 (3D_Var) 框架中引入了一种描述不同控制变量之间动力平衡约束的新方案。新方案采用统计得到的流函数和模式气压变量 ( π ) 之间的回归系数代替原方案中的线性平衡方程,来表达旋转风和质量场之间的平衡关系;采用流函数和势函数之间的回归系数,补充表达了原方案中所没有的旋转风和散度风之间的平衡关系。与原方案相比,新方案算法简单,避免了垂直方向的反复插值,减少了插值误差的引入。通过随机扰动试验和单点试验可以发现,在地转关系成立较好的区域,新方案中旋转风和质量场的耦合程度与原方案接近一致;而在地转关系不适用区域,新方案可以有效减小两者的耦合程度。此外,由于新方案中添加了旋转风和散度风之间的动力平衡约束,边界层的风场分析也更加接近大气真实状况。