Velocity profiles,the resistance law and the dissipation rate of mean flow kinetic energy in a neutrally and stably stratified planetary boundary layer

The logarithmic + polynomial approximation is suggested for vertical profiles of velocity components in a planetary boundary layer (PBL) at neutral and stable stratification. The resistance law functions A and B are determined on the basis of this approximation, using integral relations derived from the momentum equations, the Monin-Obukhov asymptotic formula for the wind profile in a stably stratified near-surface layer and the known expressions for the PBL depth. This result gives a realistic and convenient method for calculating the surface friction velocity and direction and the total dissipation rate of mean flow kinetic energy in terms of geostrophic velocity, buoyancy flux at the surface, the roughness parameter and the Coriolis parameter. In the course of these derivations a review is given of current views on the main problems of the neutral and stable PBL.     

The temperature structure in a stably stratified internal boundary layer over a cold sea

Data from the Öresund experiment are used to investigate the structure of the stably stratified internal boundary layer (SIBL) which develops when warm air is advected from a heated land surface over a cooler sea. The present study is based on a theory developed by Stull (1983a, b, c). He proposed that the turbulence and the mean structure of the nocturnal boundary layer is controlled by the time-integrated value of surface heat flux and that the instantaneous heat flux is of less importance.Dimensional arguments are used to define simple, physically consistent, temperature, velocity and length scales. The dimensionless surface heat flux has a high value immediately downwind of the shoreline and it decreases rapidly in magnitude with increasing distance from the coast. Farther away, it is essentially constant. The dimensionless potential temperature change exhibits an exponential profile. It is estimated that turbulence accounts for 71% of boundary-layer cooling while clear-air radiational cooling is responsible for the remaining 29%.Finally it is found that theoretical predictions for the height of the SIBL are in a good agreement with observations.     

Internal gravity waves in a stably stratified boundary layer

Often, a combination of waves and turbulence is present in the stably stratified atmospheric boundary layer. The presence of waves manifest itself in the vertical profiles of variances of fluctuations and in low-frequency contributions to the power spectra. In this paper we study internal waves by means of a linear stability analysis of the mean profiles in a stably stratified boundary layer and compare the results with observed vertical variance profiles of fluctuating wind and temperature along a 200 m mast. The linear stability analysis shows that the observed mean flow is unstable for disturbances in a certain frequency and wavenumber domain. These disturbances are expected to the detectable in the measurements. It is shown that indeed the calculated unstable frequencies are present in the observed spectra. Furthermore, the shape of the measured vertical variance profiles, which increase with height, is explained well by the calculated vertical structure of the amplitude of unstable Kelvin-Helmholtz waves, confirming the contribution of waves to the variances. Because turbulence and waves have quite distinct transport properties, estimates of diffusion from measurements of variances would strongly overestimate this diffusion. Therefore it is important to distinguish between them.     

The stably stratified boundary layer over the great plains

Airplane measurements of the stably stratified boundary layer obtained during the Severe Environmental Storms and Mesoscale Experiment (SESAME) over rolling terrain in south-central Oklahoma indicate that considerable horizontal variability exists in the flow on scales of several kilometers. Much of this wave-like structure appears to be tied to the terrain. The criteria for existence of stationary gravity waves indicate that these waves can exist under the observed conditions. The spectrum of terrain variations also supports the existence of these waves. Observed spectra of the vertical velocity have two peaks: one at wavelengths of several kilometers, which is due to waves and the other at wavelengths of about 100 m, which is due to turbulence. The variance at several kilometers wavelength increases somewhat with height at least up to about 800 m, but the variance contributed by turbulence decreases rapidly with height.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Drag and heat transfer relations for the planetary boundary layer

A theory is offered for the drag and heat transfer relations in the statistically steady, horizontally homogeneous, diabatic, barotropic planetary boundary layer. The boundary layer is divided into three regionsR ₁,R ₂, andR ₃, in which the heights are of the order of magnitude ofz ₀,L, andh, respectively, wherez ₀ is the roughness length for either momentum or temperature,L is the Obukhov length, andh is the height of the planetary boundary layer. A matching procedure is used in the overlap zones of regionsR ₁ andR ₂ and of regionsR ₂ andR ₃, assuming thatz ₀ L h. The analysis yields the three similarity functionsA(),B(), andC() of the stability parameter, = u _*/fL, where is von Kármán's constant,u _* is the friction velocity at the ground andf is the Coriolis parameter. The results are in agreement with those previously found by Zilitinkevich (1975) for the unstable case, and differ from his results only by the addition of a universal constant for the stable case. Some recent data from atmospheric measurements lend support to the theory and permit the approximate evaluation of universal constants.     

Similarity of structure-function parameters in the stably stratified boundary layer

The structure-function parametersC _T ² andC _v ² of temperature and velocity, respectively, from the 1973 Minnesota experiments and from large-eddy and direct numerical simulations show a smooth transition from M–O similarity to the local scaling hypothesized by Nieuwstadt for the outer regions of the stable boundary layer. Under that hypothesis, turbulence statistics aloft depend on the local vertical fluxes of momentum and temperature, so these results suggest that remote-sensing measurements ofC _T ² andC _v ² could be used to infer vertical profiles of those fluxes. We argue that the sensitivity of the fluxes to unsteadiness, baroclinity, terrain slope, and breaking gravity waves precludes the universality of the vertical profiles of structure-function parameters in the stable PBL. We find that theC _T ² profile is particularly sensitive to these effects, which is consistent with observations that it varies considerably from case to case.     

Study of near-surface models for large-eddy simulations of a neutrally stratified atmospheric boundary layer

In large-eddy simulations (LES) of the atmospheric boundary layer (ABL), near-surface models are often used to supplement subgrid-scale (SGS) turbulent stresses when a major fraction of the energetic scales within the surface layer cannot be resolved with the temporal and spatial resolution at hand. In this study, we investigate the performance of both dynamic and non-dynamic eddy viscosity models coupled with near-surface models in simulations of a neutrally stratified ABL. Two near-surface models that are commonly used in LES of the atmospheric boundary layer are considered. Additionally, a hybrid Reynolds- averaged/LES eddy viscosity model is presented, which uses Prandtl’s mixing length model in the vicinity of the surface, and blends in with the dynamic Smagorinsky model away from the surface. Present simulations show that significant portions of the modelled turbulent stresses are generated by the near-surface models, and they play a dominant role in capturing the expected logarithmic wind profile. Visualizations of the instantaneous vorticity field reveal that flow structures in the vicinity of the surface depend on the choice of the near-surface model. Among the three near-surface models studied, the hybrid eddy viscosity model gives the closest agreement with the logarithmic wind profile in the surface layer. It is also observed that high levels of resolved turbulence stresses can be maintained with the so-called canopy stress model while producing good agreement with the logarithmic wind profile.     

稳定行星边界层相似性函数A,B,C的实验研究

本文使用位于粗糙和不均匀地形上北京320米气象塔夜间边界层风速、风向和温度资料,用行星边界层u分量第一个极值高度作为行星边界层高度尺度,用边界层内的平均风速和平均位温作为速度和位温特征尺度,分析得到在稳定条件下相似性函数A_m、B_m和C_m以及行星边界层高度的参数化表达式。 分析表明,可以将广义相似性理论推广到粗糙而不均匀地形上的大气边界层中。     

The stably stratified internal boundary layer for steady and diurnally varying offshore flow

A two-dimensional numerical mesoscale model is used to investigate the internal structure and growth of the stably stratified internal boundary layer (IBL) beneath warm, continental air flowing over a cooler sea. Two situations are studied — steady-state and diurnally varying offshore flow. In the steady-state case, vertical profiles of mean quantities and eddy diffusion coefficients (K) within the IBL show small, but significant, changes with increasing distance from the coast. The top of the IBL is well defined, with large vertical gradients within the layer and a maximum in the coast-normal wind component near the top. Well away from the coast, turbulence, identified by non-zero K, decreases to insignificant levels near the top of the IBL; the IBL itself is characterised by a critical value of the layer-flux Richardson number equal to 0.18. The overall behaviour of the mean profiles is similar to that found in the horizontally homogeneous stable boundary layer over land.A simple physical model is used to relate the depth of the layer h to several relevant physical parameters viz., x, the distance from the coast and U, the large-scale wind (both normal to the coastline) and g/, being the temperature difference between continental mixed-layer air and sea surface, is the mean potential temperature and g is the acceleration due to gravity. Excellent agreement with the numerical results is found, with h = 0.014x ^1/2 U (g/)^–1/2.In the diurnally varying case, the mean profiles within the IBL show only small differences from the steady-state case, although diurnal variations, particularly in the wind maximum, are evident within a few hundred kilometres of the coast. A mesoscale circulation normal to the coast, and superimposed upon the mean offshore flow, develops seawards of the coastline with maximum vertical velocities about sunset, of depth about 2 km and horizontal scale 500 km. The circulation is related to the advection, and subsequent decay, of daytime convective turbulence over the sea.     

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.     

An examination of local similarity theory in the stably stratified boundary layer

A stable boundary layer is investigated in terms of local similarity theory. A study is based on a set of seven runs from the BAO tower (Colorado, U.S.A.). It is shown that a theoretical prediction of constant-with-height similarity functions applies only to ensemble-averaged quantities. Scatter of observational data is analysed.On leave from: Institute of Environmental Engineering, Warsaw Technical University, 00653, Warsaw, Poland.     

The structure of the stably stratified internal boundary layer in offshore flow over the sea

Observations obtained mainly from a research aircraft are presented of the mean and turbulent structure of the stably stratified internal boundary layer (IBL) over the sea formed by warm air advection from land to sea. The potential temperature and humidity fields reveal the vertical extent of the IBL, for fetches out to several hundred of kilometres, geostrophic winds of 20–25 m s^–1, and potential temperature differences between undisturbed continental air and the sea surface of 7 to 17 K. The dependence of IBL depth on these external parameters is discussed in the context of the numerical results of Garratt (1987), and some discrepancies are noted.Wind observations show the development of a low-level wind maximum (wind component normal to the coast) and rotation of the wind to smaller cross-isobar flow angles. Potential temperature () profiles within the IBL reveal quite a different structure to that found in the nocturnal boundary layer (NBL) over land. Over the sea, profiles have large positive curvature with vertical gradients increasing monotonically with height; this reflects the dominance of turbulent cooling within the layer. The behaviour is consistent with known behaviour in the NBL over land where curvature becomes negative (vertical gradients of decreasing with height) as radiative cooling becomes dominant.Turbulent properties are discussed in terms of non-dimensional quantities, normalised by the surface friction velocity, as functions of normalised height using the IBL depth. Vertical profiles of these and the normalised wavelength of the spectral maximum agree well with known results for the stable boundary layer over land (Caughey et al., 1979).     

Some aspects of the structure of the stably stratified atmospheric boundary layer

Results of an analysis based on the Leipzig wind data are presented. The computed stress profiles and the proportionality constant in the inverse relationship between the non-dimensionalized stable boundary-layer height and the square root of the stability parameter seem to agree well with the model results of Businger and Arya (1974).     

A similarity model for maximum ground-level concentration in a height-invariant,stably stratified atmospheric boundary layer

A model is presented for determining the location and magnitude of the maximum ground-level concentration arising from an elevated buoyant source in a very stable atmospheric boundary layer. The development combines the turbulent structure of such a boundary layer, Lagrangian similarity of the diffusion process, and similarity solutions of the conservation equations of the buoyant plume with mass conservation to produce a simple, experimentally verifiable formulation. Functional analogy with previous results for the constant flux layer and a deep convectively unstable layer suggest a heuristic model by which to visualize the process.     

A numerical study of second-order turbulent moments in the stably stratified nocturnal boundary layer

The structures and the vertical profiles of turbulent variance and covariance of the stably stratified boundary layer (SBL) are simulated with a second-order closure turbulence model. The results confirm that the vertical profiles of the dimensionless turbulence variance and covariance can be well represented by the form F = A(1 - Z / h)x. Here h is the height of SBL. and both exponent a and coefficient A are the functions of terrain, baroclinicity, radiation cooling and the state of temporal development of SBL. Comparing with Minnesota and Cabauw experiment data, we have analysed the value of a and expounded the main reasons that great difference in a exists among different literatures.     

Experimental study of heat and water vapor transfer processes in the planetary boundary layer (PBL)

The turbulent structure of the planetary boundary layer (PBL) is investigated based on measurements from a 213 m meteorological tower. It is found that the sensible heat flux decreases with height, resulting in a temperature increase during the daytime. On the other hand, the water vapor flux is almost constant with height and the diurnal variation of specific humidity is not so clear. Time variations of sensible heat flux and water vapor flux are closely correlated to the variation of net radiation and some differences are seen in their response times. Transient processes in the mixed layer including those related to the moisture structure are also investigated during periods of development and disappearance of the layer.     

The wind structure in planetary boundary layer

The investigations on the dynamics of the PBL have been developed in recent years. Some authors emphasized macro-dynamics and others emphasized micro-structure of the PBL. In this paper, we study and review some main characteristics of the wind field in the PBL from the view point connecting the macro-dynamics and micro-structure of the PBL, thus providing the physical basis for the further research of the dynamics and the parameterization of the PBL.     

行星边界层中多极值风速廓线的研究

本文利用325米气象塔及声雷达探测资料分析了夜间平稳天气条件下行星边界层中风速出现多极值的现象。分析指出,多极值风速与边界层中多层逆温有密切的联系,当温度场出现多层逆温并维持一定的强度和时间后,便相应地出现了多层风速极大,风速极大值出现的高度在逆温顶附近或稍高。 文内还用一维非定常模式模拟了多极值风速廓线的形成。     

Minimum friction velocity and heat transfer in the rough surface layer of a convective boundary layer

A simple model is deduced for the surface layer of a convective boundary layer for zero mean wind velocity over homogeneous rough ground. The model assumes large-scale convective circulation driven by surface heat flux with a flow pattern as it would be obtained by conditional ensemble averages. The surface layer is defined here such that in this layer horizontal motions dominate relative to vertical components. The model is derived from momentum and heat balances for the surface layer together with closures based on the Monin-Obukhov theory. The motion in the surface layer is driven by horizontal gradients of hydrostatic pressure. The balances account for turbulent fluxes at the surface and fluxes by convective motions to the mixed layer. The latter are the dominant ones. The model contains effectively two empirical coefficients which are determined such that the model's predictions agree with previous experimental results for the horizontal turbulent velocity fluctuations and the temperature fluctuations. The model quantitatively predicts the decrease of the minimum friction velocity and the increase of the temperature difference between the mixed layer and the ground with increasing values of the boundary layer/roughness height ratio. The heat transfer relationship can be expressed in terms of the common Nusselt and Rayleigh numbers, Nu and Ra, as Nu ~ Ra^{% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSGbaeaaca% aIXaaabaGaaGOmaaaaaaa!3779!\[{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}\]}. Previous results of the form Nu ~ Ra^{% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSGbaeaaca% aIXaaabaGaaG4maaaaaaa!377A!\[{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}\]} are shown to be restricted to Rayleigh-numbers less than a certain value which depends on the boundary layer/roughness height ratio.     

Similarity theory and calculation of turbulent fluxes at the surface for the stably stratified atmospheric boundary layer

In this paper we revise the similarity theory for the stably stratified atmospheric boundary layer (ABL), formulate analytical approximations for the wind velocity and potential temperature profiles over the entire ABL, validate them against large-eddy simulation and observational data, and develop an improved surface flux calculation technique for use in operational models.