Stable Boundary-Layer Scaling Regimes: The Sheba Data

Turbulent and mean meteorological data collected at five levels on a 20-m tower over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are analyzed to examine different regimes of the stable boundary layer (SBL). Eleven months of measurements during SHEBA cover a wide range of stability conditions, from the weakly unstable regime to very stable stratification. Scaling arguments and our analysis show that the SBL can be classified into four major regimes: (i) surface-layer scaling regime (weakly stable case), (ii) transition regime, (iii) turbulent Ekman layer, and (iv) intermittently turbulent Ekman layer (supercritical stable regime). These four regimes may be considered as the basic states of the traditional SBL. Sometimes these regimes, especially the last two, can be markedly perturbed by gravity waves, detached elevated turbulence (‘upside down SBL’), and inertial oscillations. Traditional Monin–Obukhov similarity theory works well in the weakly stable regime. In the transition regime, Businger–Dyer formulations work if scaling variables are re-defined in terms of local fluxes, although stability function estimates expressed in these terms include more scatter compared to the surface-layer scaling. As stability increases, the near-surface turbulence is affected by the turning effects of the Coriolis force (the turbulent Ekman layer). In this regime, the surface layer, where the turbulence is continuous, may be very shallow (< 5 m). Turbulent transfer near the critical Richardson number is characterized by small but still significant heat flux and negligible stress. The supercritical stable regime, where the Richardson number exceeds a critical value, is associated with collapsed turbulence and the strong influence of the earth’s rotation even near the surface. In the limit of very strong stability, the stress is no longer a primary scaling parameter.     

Spatial and Temporal Occurrences of Intermittent Turbulence During CASES-99

Occurrences of intermittent turbulence in very stable conditions during theCASES-99 field study near Leon, Kansas were detected at several sites separatedby horizontal distances from 1 km to 25 km using sonic anemometers, minisodarsand a laser scintillometer. Periods with significant turbulent heat fluxes wereseparated by extended quiescent periods with little or no flux, and most of theflux during a night was realized in relatively small fractions (<20%) of thetotal time. There appeared to be no relationship between this intermittencyfraction and the median z/L (z being height and L the Obukhov length)value for the night, although overall sensible heat flux values on very stablenights were significantly less than those on less stable nights. The intermittencyfraction at 7 m was found to increase with mean wind speed at 20 m and, to alesser extent, with wind shear between 20 m and 30 m. While correspondenceof turbulent episodes at two sites separated by 1 km was common, it was less common at separations on the order of 20 km. There were time periods, however, during which enhanced turbulence levels were seen nearly simultaneously at large separation distances. Turbulence episodes were found to propagate upward or downward at different times with no readily defined large-scale controlling mechanism.     

Turbulence Characteristics of the Stable Boundary Layer Over a Mid-Latitude Glacier. Part I: A Combination of Katabatic and Large-Scale Forcing

Profile and eddy-correlation (heights of 4 and 10 m) measurements performed on the Pasterze glacier (Austria) are used to study the characteristics of the stable boundary layer under conditions of katabatic and large-scale forcing. We consider cases where large-scale forcing results in a downslope (or following) ambient wind. The analysis of averaged spectra and cospectra reveals low frequency perturbations that have a large influence on the variances of temperature and horizontal wind components and also alter the cospectra of momentum and sensible heat flux. Only the spectrum of the vertical wind speed is comparable to universal spectra. The low frequency perturbations occur as brief intermittent events and result in downward entrainment of ambient air thereby producing enhanced downward sensible heat fluxes and downward as well as upward momentum fluxes with various magnitudes and timescales. After the variances were high pass filtered, the normalised standard deviations of wind speed and temperature compare favourably to findings in the literature within the range 0>z/L>0.5. For larger z/L they deviate as a result of an increased influence from low frequency perturbations and thus non-stationarity. In line with this, the turbulent kinetic energy budget (at 4 m height) indicates that production (shear) is in balance with destruction (buoyancy and dissipation) within the range 0>z/L>0.3. Non-dimensional gradients of wind speed within the range 0>z/L>0.3 have a slope of about 3.5. The scatter for the dimensionless temperature gradient is quite large, and the slope is comparable to that for wind speed gradients. For z/L>0.3 the imbalance in the turbulent kinetic energy budget grows and non-dimensional gradients for wind speed and temperature deviate considerably from accepted values as a result of increased non-stationarity. Average roughness lengths for momentum and sensible heat flux derived from wind speed and temperature profiles are respectively 1 × 10^-3 m and 6 × 10^-5 m, consistent with the literature. The ratio (z_0h/z_0m) compares to those predicted by surface renewal models. A variation of this ratio with the roughness Reynolds number is not indicated by our data.     

Early Warning Signals for Regime Transition in the Stable Boundary Layer: A Model Study

The evening transition is investigated in an idealized model for the nocturnal boundary layer. From earlier studies it is known that the nocturnal boundary layer may manifest itself in two distinct regimes, depending on the ambient synoptic conditions: strong-wind or overcast conditions typically lead to weakly stable, turbulent nights; clear-sky and weak-wind conditions, on the other hand, lead to very stable, weakly turbulent conditions. Previously, the dynamical behaviour near the transition between these regimes was investigated in an idealized setting, relying on Monin–Obukhov (MO) similarity to describe turbulent transport. Here, we investigate a similar set-up, using direct numerical simulation; in contrast to MO-based models, this type of simulation does not need to rely on turbulence closure assumptions. We show that previous predictions are verified, but now independent of turbulence parametrizations. Also, it appears that a regime shift to the very stable state is signaled in advance by specific changes in the dynamics of the turbulent boundary layer. Here, we show how these changes may be used to infer a quantitative estimate of the transition point from the weakly stable boundary layer to the very stable boundary layer. In addition, it is shown that the idealized, nocturnal boundary-layer system shares important similarities with generic non-linear dynamical systems that exhibit critical transitions. Therefore, the presence of other, generic early warning signals is tested as well. Indeed, indications are found that such signals are present in stably stratified turbulent flows.     

Nocturnal stable boundary layer height model and its application

A model of the evolution of the nocturnal stable boundary layer height, based on the heat conservation equation for a turbulent flow, is presented. This model is valid for nights with weak winds and little cloudiness in rural areas. The model includes an expression of vertical profile of potential temperature within the boundary layer, which is obtained using micrometeorological information from Prairie Grass, Wangara and O'Neill Projects. The expression turned out to be a second-grade polynomial of the dimensionless height of the nocturnal stable boundary layer. The resulting model is a function of the Monin–Obukhov length, the surface potential temperature of air and the roughness length. This model was satisfactorily compared with micrometeorological data. It was applied at three stations of Argentina, using surface hourly meteorological information. From the results that were obtained, the monthly average values of the stable boundary layer thickness were analysed. The maximum monthly average values occur during the cold season and the minimum ones take place during the hot season. It was observed that the monthly average thickness increases with latitude.     

Boundary-Layer Adjustment Over Small-Scale Changes of Surface Heat Flux

Four months of eddy correlation data collected over a grass field and a nearby sage brush community are analyzed to examine the adjustment of the boundary-layer structure as it flows from the heated brush to the snow-covered grass. The grass site includes a 34-m tower with seven levels of eddy correlation data. The midday heat flux over the snow-covered grass and bare ground surfaces is often downward particularly with melting conditions, while the corresponding heat flux over the brush is almost always upward. For most of these cases, a stable internal boundary layer over the snow is well defined in terms of vertical profiles of the buoyancy flux over the snow-covered grass. The stable internal boundary layer is generally embedded within a deeper layer of flux divergence corresponding to increasing upward heat flux with height above the internal boundary layer. With thin snow cover, the surface heat flux over the grass is weak upward due to heating of grass protruding above the snow so that the flow adjusts to a decrease of the upward surface heat flux in the downwind direction. This common case of an adjusting boundary layer contrasts with the formation of an internal boundary layer due to a change of sign of the surface heat in flux the downwind direction. The adjustment of the boundary layer to the decrease of the surface heat flux leads to vertical divergence of the upward heat flux in contrast to the usual heated boundary layer over homogeneous surfaces. The consequences of the cooling due to the vertical divergence of the heat flux are discussed in terms of the heat budget of the adjusting and internal boundary layers.     

Surface-Layer Fluxes in Stable Conditions

Micrometeorological tower data from the Microfronts experiment are analyzed. Scale-dependencies of the flux and flux sampling error are combined to automatically determine Reynolds turbulence cut-off time scales for computing fluxes from time series. The computed downward heat flux at the 3 m height averaged over nine nights with 7.3 hours each night is 20% greater than the downward heat flux computed at the 10 m height. In contrast, there is only a 1.2% difference between 3 m and 10 m heat fluxes averaged over daytime periods, and there is less than a 2% difference between 3 m and 10 m momentum fluxes whether averaged over nighttime or daytime periods.Stability functions, M(z/L) and H(z/L) are extended to z/L up to 10, where z is the observational height and L is the Obukhov length. For 0.01 < z/L < 1 the estimated functions generally agree with Businger-Dyer formulations, though the H estimates include more scatter compared to the M estimates. For 1 < z/L < 10, the flux intermittency increases, the flux Richardson number exceeds 0.2, and the number of flux samples decreases. Nonetheless the estimates of the stability function M based on 3-m fluxes are closer to the formula proposed by Beljaars and Holtslag in 1991 while the M functions based on 10-m fluxes appears to be closer to the formula proposed by Businger et al. in 1971. The stability function H levels off at z/L = 0.5.     

The Characteristics of Turbulence Structure and Transfer over the Middle Area of the Tibetan Plateau

In this paper, turbulent data obtained from the Damxung site during the Secondary Tibetan Plateau Science Experiment (TIPEX) in 1998 are used to study the characteristics of the turbulent spectra, turbulence transport, and the dissipation rates of turbulent kinetic energy, temperature variance, and humidity variance in the middle area of the Tibetan Plateau. The turbulent spectra of wind velocity, potential temperature, and humidity satisfy the-2/3 power law in the high frequency range. Horizontal transportation of heat and water vapor is negligible compared with vertical transportation under strong unstable conditions, and as the stability parameter z/L increases (where z is the observational height, and L is the Monin Obukhov length), horizontal transportation becomes dominant under near-neutral, neutral, and stable conditions. The non-dimensional temperature and humidity variances are 20% less than the temperature and humidity gradient variances. These deficits appear to increase as the absolute stability parameter increases. Moreover, the effects of turbulence transportation and pressure variance exist throughout the entire stability region.     

Helicopter-Borne Flux Measurements in the Nocturnal Boundary Layer Over Land – a Case Study

This case study introduces measurements of turbulent fluxes in a nocturnal boundary layer in North Germany with the new helicopter-borne turbulence measurement system HELIPOD, a detailed data analysis and examination in regard of systematic errors of the instrument, and some comparison with local similarity theory and experiments of the past, in order to confirm the occurrence of small vertical turbulent fluxes. The examined nocturnal boundary layer offered excellent conditions to analyse the quality of the measurement system. In this connection, a detailed look at a strong ground-based inversion disclosed small turbulent fluxes with a spectral maximum at ten metres wavelength or less, embedded in intermittent turbulence. For verification of these fluxes, the measurements were compared with well established results from past experiments. Local similarity theory was applied to calculate dimensionless variances of the turbulent quantities, which were found in good agreement with other observations. Since shear and stratification varied significantly on the horizontal flight legs due to global intermittency, a method was developed to determine vertical gradients on a horizontal flight pattern, by use of small fluctuations of the measurement height. With these locally determined gradients, gradient transport theory became applicable and the turbulent diffusivities for heat and momentum, the Richardson number, and the flux Richardson number were estimated within isolated strong turbulent outbursts. Within these outbursts the flux Richardson number was found between 0.1 and 0.2. The functional relationship between the gradient Richardson number and the turbulent Prandtl number agreed well with observations in past experiments and large eddy simulation. The impact of the stratification on the vertical turbulent exchange, as already described for the surface layer using Monin–Obukhov similarity, was analogously observed in the very stably stratified bulk flow when local scaling was applied.     

Aircraft Observations Of The Mean And Turbulent Structure Of A Shallow Boundary Layer Over The Persian Gulf

Stable internal boundary layers form when warm air isadvected over a cooler surface, a common occurrence incoastal areas. The internal boundary layer deepenswith distance along-wind, eventually reachingequilibrium with the surface and becoming a fullydeveloped marine boundary layer. We presentobservations of the late stages of internalboundary-layer evolution made bythe U.K. Meteorological Office'sC-130 Hercules research aircraft over the Persian Gulfin April 1996. Northwesterly winds brought warm dryair from the surrounding desert landmass across thecooler waters of the Gulf. Loss of heat to the surfaceresulted in the formation of a shallow, stableinternal boundary layer downwind of the coast. The aircraftmeasurements were made several hundred kilometresdownwind, by which point the original deep convectiveboundary layer had been eroded away and the internalboundary layer was well developed, effectively a newmarine atmospheric boundary layer. Throughout most ofits depth the boundary layer was statically stable anda downward heat flux of approximately 15 W m^-2was observed; however, an exceptionally strong latentheat flux, in excess of 250 W m^-2 near thesurface, was sufficient to overcome the downwards heatflux and maintain weak buoyant convection in the lower30–50% of the boundary layer.Scaling of boundary-layer turbulence statistics usinglocal similarity theory produces results in agreementwith previous studies. Because of the strong humiditycontribution to the buoyancy flux, however, care isrequired with the definition of the similarity scales.It is usual for either the sensible heat or buoyancyflux to be used in the definitions of both thetemperature and length scales; the latter being usedover water where humidity plays a significant role indetermining stability. In the present case we findthat while the buoyancy flux is appropriate in thedefinition of the length scale, the temperature scalemust be defined in terms of the sensible heat flux.     

Reynolds-Number Dependence of Gas Dispersion Over a Wavy Wall

Direct numerical simulations of an Ekman layer are performed to study flow evolution during the response of an initially neutral boundary layer to stable stratification. The Obukhov length, L, is varied among cases by imposing a range of stable buoyancy fluxes at the surface to mimic ground cooling. The imposition of constant surface buoyancy flux , i.e. constant-flux stability, leads to a buoyancy difference between the ground and background that tends to increase with time, unlike the constant-temperature stability case where a constant surface temperature is imposed. The initial collapse of turbulence in the surface layer owing to surface cooling that occurs over a time scale proportional to \(L/u_*\), where \(u_*\) is the friction velocity, is followed by turbulence recovery. The flow accelerates, and a “low-level jet” (LLJ) with inertial oscillations forms during the turbulence collapse. Turbulence statistics and budgets are examined to understand the recovery of turbulence. Vertical turbulence exchange, primarily by pressure transport, is found to initiate fluctuations in the surface layer and there is rebirth of turbulence through enhanced turbulence production as the LLJ shear increases. The turbulence recovery is not monotonic and exhibits temporal intermittency with several collapse/rebirth episodes. The boundary layer adjusts to an increase in the surface buoyancy flux by increased super-geostrophic velocity and surface stress such that the Obukhov length becomes similar among the cases and sufficiently large to allow fluctuations with sustained momentum and heat fluxes. The eventual state of fluctuations, achieved after about two inertial periods (\(ft \approx 4\pi \)), corresponds to global intermittency with turbulent patches in an otherwise quiescent background. Our simplified configuration is sufficient to identify turbulence collapse and rebirth, global and temporal intermittency, as well as formation of low-level jets, as in observations of the stratified atmospheric boundary layer.     

Variability Of The Stable And Unstable Atmospheric Boundary-Layer Height And Its Scales Over A Boreal Forest

Radiosondes releases during the NOPEX-WINTEX experiment carried out in late winter in Northern Finland were analysed for the determination of the height h of the atmospheric boundary layer. We investigate various possible scaling approaches, based on length scales using micrometeorological turbulence surface measurements and the background atmospheric stratification above h. Under stable conditions, the three previously observed turbulence regimes delineated by values of z/L (L is the Obukhov length) appears as a blueprint for understanding the departures found for the suitability of the Ekman scaling based on L_E = u_/f (u is the friction velocity and f the Coriolis parameter). The length scale L_N = u_/N (where N is the Brunt–Väisälä frequency) appears to be a useful scale under most stable conditions, especially in association with L. Under unstable conditions, shear production of turbulence is still significant, so that the three scales L, L_N and L_E are again relevant and the dimensionless ratios _N = L_N/L and L_N/L_E = N/f describe well the WINTEX data. Furthermore, in the classical scaling framework, the unstable domain may also be divided into three regimes as reflected by the dependence ofu_/f on instability (z/L).     

Heat Flux in the Coastal Zone

Various difficulties with application of Monin–Obukhov similarity theory are surveyed including the influence of growing waves, advection and internal boundary-layer development. These complications are normally important with offshore flow. The transfer coefficient for heat is computed from eddy correlation data taken at a mast two kilometres off the Danish coast in RASEX. For these coastal zone data, the thermal roughness length shows no well-defined relation to the momentum roughness length or roughness Reynolds number, in contrast to previous theories. The variation of the momentum roughness length is dominated by wave state. In contrast, the thermal roughness length shows significant dependence on wave state only for small values of wave age where the mixing is apparently enhanced by wave breaking. The development of thin internal boundary layers with offshore flow substantially reduces the heat transfer and thermal roughness length but has no obvious influence on momentum roughness length. A new formulation of the thermal roughness length based on the internal boundary-layer depth is calibrated to the RASEX data. For the very stable case, the turbulence is mainly detached from the surface and existing formulations do not apply.As an alternative to adjusting the thermal roughness length, the transfer coefficient is related directly to the stability and the internal boundary-layer depth. This avoids specification of roughness lengths resulting from the usual integration of the non-dimensional temperature function. The resulting stability function is simpler than previous ones and satisfies free convection similarity theory without introduction of the gustiness factor. The internal boundary layer also influences the moisture transfer coefficient.     

On the turbulence structure in the stable boundary layer over the Greenland ice sheet

Turbulence measurements from a 30 m tower in the stably stratifiedboundary layer over the Greenland ice sheet are analyzed. The observationsinclude profile and eddy-correlation measurements at various levels. Atfirst, the analysis of the turbulence data from the lowest level (2 m aboveground) shows that the linear form of the non-dimensional wind profile(m) is in good agreement with the observations for z/L <0.4, whereL represents the Obukhov length. A linear regression yieldsm=1+5.8z/L. The non-dimensional temperature profile (h) at the2m level shows no tendency to increase with increasing stability. The datafrom the upper levels of the tower are analyzed in terms of both localscaling and surface-layer scaling. The m and the h values show atendency to level off at large stability (z/>0.4) where represents the local Obukhov length. Hence, the linear form of the functions is no longer appropriate under such conditions. The bestcorrespondence to the data can be achieved when using the expression ofBeljaars and Holtslag for m and h. The vertical profiles of theturbulent fluxes, the wind velocity variances and temperature variance arealso determined. The momentum flux profile and the profiles of wind speedvariances are in general agreement with other observations if a welldeveloped low-level wind maximum occurs, and the height of this maximum isused as a height scale.     

Estimation Of Atmospheric Water Vapour Flux Profiles In The Nocturnal Unstable Urban Boundary Layer With Doppler Sodar And Raman Lidar

The vertical wind profiles determined by Doppler sodar and the water vapourmixing ratio profiles obtained by Raman lidar are used to estimate the atmosphericwater vapour flux profiles in the nocturnal urban boundary layer under unstableconditions. The experiment was conducted for several nights in the central areaof Rome under a variety of moisture conditions and different urban boundary-layerflow regimes. Despite some scatter in the profiles, the latent heat flux is found tobe positive throughout the depth of the nocturnal urban boundary-layer. Thelayer-averaged flux shows a variation between -4 to +40 W m^-2, whileindividual values of flux in excess of +150 W m^-2 pertain to a case offree convection during cold air advection caused by the sea breeze. The qualityof flux estimates is found to be highly limited by the low sampling rates employedin the experiment resulting in errors to the order of 60%. Therefore, the results mustbe viewed as estimates rather than precise measurements. The skewness profiles ofthe turbulent fluctuations of vertical velocity and water vapour mixing ratio are alsopositive.     

夜间稳定边界层中间歇性湍流热通量的 提取及其谱特征

在夜间稳定边界层中, 湍流热通量往往具有间歇性特征。在一阵阵出现的强度较大的湍流热通量之间, 混杂着弱噪声或其他微弱的难以辨识的高频脉动信号。为了研究间歇性湍流热通量的特征, 必须将这些无关信 号剔除, 以提取出干净的湍流热通量。本文提出了一种新的提取间歇性湍流热通量的方法, 该方法通过分析 湍流热通量的概率密度函数, 并与稳定分布进行比较, 湍流热通量的概率密度函数开始偏离稳定分布的位置, 即是间歇性湍流热通量开始出现的阈值。本文通过夜间稳定边界层外场试验数据的验证, 发现利用稳定分布确定 的阈值可有效地提取出间歇性湍流热通量。在此基础之上, 本文对比了提取前后湍流热通量的功率谱, 发现 提取后低频信号的方差所占比重下降, 而高频信号略有上升。此外, 间歇性湍流热通量在高频区的功率谱满足“-7/6”律。     

夜间近地面稳定边界层湍流间歇与增温

在夜间晴空条件下，近地面大气湍流表现出很强的间歇性，这种间歇现象导致夜间气温短时的急剧下降，随后大幅度增温。近地面大幅度增温表明此时存在着很大的湍流热通量散度，常通量层的概念这时不存在。从各高度层温度和风速变化的曲线上分析，我们发现湍流大多在距离地面较高一点的高度上发生发展，然后向下层传递，尽管上层的湍流可能是由于下层的某一触发机制向上传递而引起的。湍流偶尔也出现自下向上传递的过程，但这一过程较少发生。湍流的这种上下传递说明稳定边界层大气经常处于非平衡状态，在运用相似理论研究稳定边界层大气结构时要特别注意这一情形。     

Wind-Tunnel Simulation of Weakly and Moderately Stable Atmospheric Boundary Layers

The simulation of horizontally homogeneous boundary layers that have characteristics of weakly and moderately stable atmospheric flow is investigated, where the well-established wind engineering practice of using ‘flow generators’ to provide a deep boundary layer is employed. Primary attention is given to the flow above the surface layer, in the absence of an overlying inversion, as assessed from first- and second-order moments of velocity and temperature. A uniform inlet temperature profile ahead of a deep layer, allowing initially neutral flow, results in the upper part of the boundary layer remaining neutral. A non-uniform inlet temperature profile is required but needs careful specification if odd characteristics are to be avoided, attributed to long-lasting effects inherent of stability, and to a reduced level of turbulent mixing. The first part of the wind-tunnel floor must not be cooled if turbulence quantities are to vary smoothly with height. Closely horizontally homogeneous flow is demonstrated, where profiles are comparable or closely comparable with atmospheric data in terms of local similarity and functions of normalized height. The ratio of boundary-layer height to surface Obukhov length, and the surface heat flux, are functions of the bulk Richardson number, independent of horizontal homogeneity. Surface heat flux rises to a maximum and then decreases.     

Nonuniform Distribution Of High-Frequency Turbulence In The Unstable Boundary Layer

Turbulent flow data of wind velocity and temperature in the unstably stratifiedatmospheric boundary layer, derived from steel tower observations in the field and wind-tunnel experiments were used to study the relationship between the plumes and the small-scale eddies in the inertial subrange. Flow visualisation experiments in the wind tunnel were also conducted to observe the structure of the flow in the plumes, and time series data were analysed by using wavelet transforms. The results show that variances of velocity and temperature due to the small-scale eddies are large in the plumes and small outside of the plumes, and that the momentum and heat fluxes due to the small-scale eddies follow the same tendency as found in the variances. The ratios of the variances caused by the small-scale eddies in the plumes to the whole of the variances caused by the small-scale eddies in and out the plumes increase with non-dimensional height -z/L in which L is the local Obukhov length. Similar ratios of the fluxes caused by the small-scale eddies also show the same tendency. These ratios can be expressed as functions of -z/L for results based on field observationand the wind tunnel experiments. This relation hardly changes even if the wavelet function is changed. The flow visualisation experiments show that the plumes have a complicated structure in which mushroom type flows are stacked on top of each other. This characteristic structure seems to increase the energy of the small-scale eddies in the plumes.