黄土高原复杂地形受中尺度运动影响的稳定边界层湍流特征

利用兰州大学半干旱气候与环境观测站(Semi-Arid Climate and Environment Observatory of Lanzhou University,简称SACOL)2008年12月观测资料,研究了稳定边界层湍流特征.使用涡动相关资料研究湍流通量时,定义湍流的平均时间τ内的中尺度运动是造成湍流统计量变化范围大的主要原因,稳定情形? τ取几十秒至几分钟.对梯度理查森数大于0.3的强稳定情形的湍流尺度分解(MRD)谱分析表明,感热通量在112.4～449.9 s存在谱隙,尺度大于谱隙的中尺度运动造成了通量观测资料离散性大,甚至有支配性影响.动量通量的谱隙在112.4～224.9 s之间.弱风时,中尺度运动的影响更大,垂直风速标准差以0.1的比率随中尺度风速变化;垂直风速标准差同广义风速表现出很好的相关性,并随着广义风速消失而消失.三维风速标准差与摩擦速度呈很好的线性关系,垂直、水平、横风风速的无量纲标准差分别为1.35、2.54、2.21.对湍流动能的研究发现,在梯度理查森数大于0.3的条件下,仍然存在连续的湍流.以湍动能为依据,分析了湍流的平稳时间长度,其长度随稳定度变化而变化,2008年12月7～11日从133.5 s变化到856.2 s,湍流平稳时间长度反映了中尺度运动的发生频率.     

Turbulence in the Stable Boundary Layer at Higher Richardson Numbers

We present some algebraic and numerical simulations of the stable boundary layer. We also discuss the problem of the existence of a critical Richardson number (Ri), beyond which the turbulence is suppressed. We compare the results of a second-order algebraic model with those of a third-order numerical model and, to this purpose, numerical simulations of a wind-tunnel flow, which is characterized by various Richardson numbers, were performed. As far as the second-order model is concerned, solutions, for the Richardson number greater than any critical value, can be obtained by modifying the time scales of the second-order equation pressure correlation terms in order to account for a buoyancy damping factor. We show that using a third-order model allows the same results (no critical Richardson number) to be obtained without modifications to the time scales. It is suggested that the non-locality, accounted for by the third-order moments, could allow the turbulence to persist also for Ri > 1.     

Rapid vertical sampling in stably stratified turbulent shear flows

A new method for obtaining instantaneous vertical profiles of two components of velocity and temperature in thermally stratified turbulent shear flows is presented. In this report, the design and construction of the traversing system will be discussed and results to date will be presented. The method is based on rapid vertical sampling whereby probe sensors are moved vertically at a high speed such that the measurement is approximately instantaneous. The system is designed to collect many measurements for the calculation of statistics such as vertical wave number spectra, mean square vertical gradients, and Thorpe scales. Results are presented for vertical profiles of temperature and compared to vertical profiles measured by single-point Eulerian time averages. The quality of the vertical profiles is found to be good over many profiles. Some comparisons are made between vertical measurements and standard single-point Eulerian measurements for three cases of stably stratified turbulent shear flow in which the initial microscale Reynolds number, Re_λ≈30. In case 1, the mean conditions are characterized by a gradient Richardson number, Ri_g=0.015, for which the flow is “unstable”, meaning the spatially evolving turbulent kinetic energy (E_k) grows. In case 2, Ri_g=0.095, for which the evolving turbulent kinetic energy is almost constant. In case 3, the flow is highly stable, where Ri_g=0.25 and E_k decays with spatial evolution. The measurements indicate anisotropy in the small scales for all cases. In particular, it is found that the ratio grows initially to a maximum and then decays with further evolution. Maximum Thorpe displacements are measured and compared to single-point measures of the vertical scales. It is found that vertical length scales derived from single-point measurements, such as the Ozmidov scale, L_O=(ε/N³)^1/2 and the overturn scale, L_t=θ′/(dT/dz), do not represent well the wide range of overturning scales which are actually present in the turbulence.     

Classification of Vertical Wind Speed Profiles Observed Above a Sloping Forest at Nighttime Using the Bulk Richardson Number

Wind speed profiles above a forest canopy relate to scalar exchange between the forest canopy and the atmosphere. Many studies have reported that vertical wind speed profiles above a relatively flat forest can be classified by a stability index developed assuming wind flow above a flat plane. However, can such a stability index be used to classify vertical wind speed profiles observed above a sloping forest at nighttime, where drainage flow often occurs? This paper examines the use of the bulk Richardson number to classify wind speed profiles observed above a sloping forest at nighttime. Wind speed profiles above a sloping forest were classified by the bulk Richardson number Ri _B . Use of Ri _B distinguished between drainage flow, shear flow, and transitional flow from drainage flow to shear flow. These results suggest that Ri _B is useful to interpret nighttime CO₂ and energy fluxes above a sloping forest. Through clear observational evidence, we also show that the reference height should be high enough to avoid drainage-flow effects when calculating Ri _B .     

Local Scales of Turbulence in the Stable Boundary Layer

Local, gradient-based scales, which contain the vertical velocity and temperature variances, as well as the potential temperature gradient, but do not include fluxes, are tested using data collected during the CASES-99 experiment. The observations show that the scaling based on the temperature variance produces relatively smaller scatter of empirical points. The resulting dimensionless statistical moments approach constant values for sufficiently large values of the Richardson number Ri. This allows one to derive predictions for the Monin–Obukhov similarity functions φ _m and φ _h , the Prandtl number Pr and the flux Richardson number Rf in weak turbulence regime.     

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.     

The Critical Richardson Number and Limits of Applicability of Local Similarity Theory in the Stable Boundary Layer

Measurements of atmospheric turbulence made over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are used to determine the limits of applicability of Monin–Obukhov similarity theory (in the local scaling formulation) in the stable atmospheric boundary layer. Based on the spectral analysis of wind velocity and air temperature fluctuations, it is shown that, when both the gradient Richardson number, Ri, and the flux Richardson number, Rf, exceed a ‘critical value’ of about 0.20–0.25, the inertial subrange associated with the Richardson–Kolmogorov cascade dies out and vertical turbulent fluxes become small. Some small-scale turbulence survives even in this supercritical regime, but this is non-Kolmogorov turbulence, and it decays rapidly with further increasing stability. Similarity theory is based on the turbulent fluxes in the high-frequency part of the spectra that are associated with energy-containing/flux-carrying eddies. Spectral densities in this high-frequency band diminish as the Richardson–Kolmogorov energy cascade weakens; therefore, the applicability of local Monin–Obukhov similarity theory in stable conditions is limited by the inequalities Ri < Ri _cr and Rf < Rf _cr. However, it is found that Rf _cr  =  0.20–0.25 is a primary threshold for applicability. Applying this prerequisite shows that the data follow classical Monin–Obukhov local z-less predictions after the irrelevant cases (turbulence without the Richardson–Kolmogorov cascade) have been filtered out.     

The role of molecular diffusion in the deepening of the mixed layer

Turbulent mixing across heat-stratified density interfaces was studied in the laboratory using oscillating-grid generated turbulence. The aim was to study the transition between the entrainment regimes dominated by interfacial wave-breaking and molecular diffusion, and to study the characteristics of the latter. It was observed that, above a critical Richardson number Ri_c, which depends on the Peclet number Pe, the mixing due to wave breaking disappears and that Ri_c Pe⁻ⁿ, where the mean value of the exponent n is approximately . Above Ri_c, the entrainment is molecular-diffusion dominated and takes place through a sequence of events: the buoyancy gradient of the initially sharp density interface is weakened by molecular diffusion until the mixed-layer eddies can engulf a portion of the interfacial layer wherefore the interface sharpens again. Thus, the entrainment events are recurrent with a rate-controlling diffusion stage between them. An entrainment law of the form E Ri⁻²Pe⁻², where E is the entrainment coefficient and Ri is the Richardson number, is suggested for the diffusion-dominated entrainment regime.     

Remote sensing of the dynamic stability of the atmospheric boundary layer

Summary The relative strength of the stabilizing effect of buoyancy and the destabilizing effect of velocity shear in a stratified shear flow, such as a stable atmospheric boundary layer, is measured by the gradient Richardson number, Ri_g. The boundary layer static stability, as described by the buoyancy frequency, N, can be calculated from the virtual potential temperature gradient derived from RASS temperature profiles. The mean wind profiles from a sodar can be used to calculate the mean vertical velocity shear. In combination these profilers are potentially a powerful tool for the remotely sensing the dynamic stability of the boundary layer. However, experience shows that the combinations of two experimentally derived quantities, like N and shear, may give highly variable results. On the other hand, a simple sensitivity analysis shows that reasonable estimates of Ri_g are achievable over a range of conditions in the stable nocturnal boundary layer. To test this conclusion, high spatial and temporal resolution temperature and velocity soundings were obtained above 50m in the stable nocturnal boundary layer using a 920MHz continuous wave Radio Acoustic Sounding System (RASS) and 1.875kHz and 5.00kHz Doppler sodars. Examples of the evolution of Ri_g are presented from 24 hours of observations of the boundary layer in Canberra, on the tablelands in south- eastern Australia. Most of the boundary layer had Ri_g between 0.1 and 1. Thus, it was marginally dynamically stable, even with the gradient Richardson number calculated from finite differences over a vertical interval of 68m. A comparison of the results from the two sodars showed that the velocity shear increased significantly when the vertical differencing interval was decreased from 68m to 20m.     

Coherence and Scale of Vertical Velocity in the Convective Boundary Layer from a Doppler Lidar

We utilized a Doppler lidar to measure integral scale and coherence of vertical velocity w in the daytime convective boundary layer (CBL). The high resolution 2 μm wavelength Doppler lidar developed by the NOAA Environmental Technology Laboratory was used to detect the mean radial velocity of aerosol particles. It operated continuously in the zenith-pointing mode for several days in the summer 1996 during the “Lidars in Flat Terrain” experiment over level farmland in central Illinois. We calculated profiles of w integral scales in both the alongwind and vertical directions from about 390 m height to the CBL top. In the middle of the mixed layer we found, from the ratio of the w integral scale in the vertical to that in the horizontal direction, that the w eddies are squashed by a factor of about 0.65 as compared to what would be the case for isotropic turbulence. Furthermore, there is a significant decrease of the vertical integral scale with height. The integral scale profiles and vertical coherence show that vertical velocity fluctuations in the CBL have a predictable anisotropic structure. We found no significant tilt of the thermal structures with height in the middle part of the CBL.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Turbulence statistics of a Kelvin–Helmholtz billow event observed in the night-time boundary layer during the Cooperative Atmosphere–Surface Exchange Study field program

An apparent shear flow instability occurred in the stably stratified night-time boundary layer on 6 October 1999 over the Cooperative Atmosphere–Surface Exchange Study (CASES-99) site in southeast Kansas. This instability promoted a train of billows which appeared to be in different stages of evolution. Data were collected by sonic anemometers and a high-frequency thermocouple array distributed on a 60 m tower at the site, and a high resolution Doppler lidar (HRDL), situated close to the tower. Data from these instruments were used to analyze the characteristics of the instability and the billow event. The instability occurred in a layer characterized by a minimum Richardson number Ri0.13, and where an inflection in the background wind profile was also documented. The billows, which translated over the site for approximately 30 min, were approximately L320 m in length and, after billow evolution they were contained in a layer depth H30 m. Their maximum amplitude, determined by HRDL data, occurred at a height of 56 m. Billow overturns, responsible for mixing of heat and momentum, and high-frequency intermittent turbulence produce kurtosis values above the Gaussian value of 3, particularly in the lower part of the active layer.     

TURBULENCE STRUCTURE IN A STRATIFIED BOUNDARY LAYER UNDER STABLE CONDITIONS

Turbulence structure in stably stratified boundary layers isexperimentally investigated by using a thermally stratified wind tunnel. Astably stratified flow is created by heating the wind tunnel airflow to atemperature of about 50 °C and by cooling the test-section floor to asurface temperature of about 3 °C. In order to study the effect ofbuoyancy on turbulent boundary layers for a wide range of stability, thevelocity and temperature fluctuations are measured simultaneously at adownwind position of 23.5 m from the tunnel entrance, where the boundarylayer is fully developed. The Reynolds number, Re, ranges from 3.14× 104 to 1.27 × 105, and the bulk Richardson number, Ri,ranges from 0 to 1.33. Stable stratification rapidly suppresses thefluctuations of streamwise velocity and temperature as well as the verticalvelocity fluctuation. Momentum and heat fluxes are also significantlydecreased with increasing stability and become nearly zero in the lowest partof the boundary layer with strong stability. The vertical profiles ofturbulence quantities exhibit different behaviour in three distinct stabilityregimes, the neutral flows, the stratified flows with weak stability(Ri = 0.12, 0.20) and those with strong stability (Ri= 0.39,0.47, 1.33). Of these, the two regimes of stratified flows clearly showdifferent vertical profiles of the local gradient Richardson number Ri,separated by the critical Richardson number Ri cr of about 0.25. Moreover,turbulence quantities in stable conditions are well correlated with Ri.     

Measurement of Prandtl Number as a Function of Richardson Number Avoiding Self-Correlation

The empirical dependence of turbulence Prandtl number (Pr) on gradient Richardson number (Ri) is presented, derived so as to avoid the effects of self-correlation from common variables. Linear power relationships between the underlying variables that constitute both Pr and Ri are derived empirically from flux and profile observations. Pr and Ri are then reconstructed from these power laws, to indicate their interdependence whilst avoiding self-correlation. Data are selected according to the stability range prior to regression, and the process is iterated from neutral to higher stability until error analysis indicates the method is no longer valid. A Butterworth function is fitted to the resulting Pr ⁻¹(Ri) regression to give an empirical summary of the analysis. The form suggests that asymptotically Pr ⁻¹ decreases as Ri ^3/2. Scatter in the data increases above Ri ~ 1, however, indicating additional constraints to Pr are not captured by Ri alone in this high stability regime. The Butterworth function is analytic for all Ri > 0, and may be included in suitable boundary-layer parameterisation schemes where the turbulent diffusivity for heat is derived from the turbulent diffusivity for momentum.     

On the Velocity Gradient in Stably Stratified Sheared Flows. Part 1: Asymptotic Analysis and Applications

We give a new derivation of the familiar linear relation for the dimensionless velocity gradient in the stably stratified surface layer and provide physical and empirical grounds for its universal applicability in stationary homogeneous turbulence over the whole range of static stabilities from Ri =  0 to very large Ri. Combining this relation with the budget equation for the turbulent kinetic energy we obtain the “equilibrium formulation” of the turbulent dissipation length scale, and recommend it for use in turbulence closure models.     

Application of a Large-Eddy Simulation Database to Optimisation of First-Order Closures for Neutral and Stably Stratified Boundary Layers

Large-eddy simulation (LES) is a well-established numerical technique, resolving the most energetic turbulent fluctuations in the planetary boundary layer. By averaging these fluctuations, high-quality profiles of mean quantities and turbulence statistics can be obtained in experiments with well-defined initial and boundary conditions. Hence, LES data can be beneficial for assessment and optimisation of turbulence closure schemes. A database of 80 LES runs (DATABASE64) for neutral and stably stratified planetary boundary layers (PBLs) is applied in this study to optimize first-order turbulence closure (FOC). Approximations for the mixing length scale and stability correction functions have been made to minimise a relative root-mean-square error over the entire database. New stability functions have correct asymptotes describing regimes of strong and weak mixing found in theoretical approaches, atmospheric observations and LES. The correct asymptotes exclude the need for a critical Richardson number in the FOC formulation. Further, we analysed the FOC quality as functions of the integral PBL stability and the vertical model resolution. We show that the FOC is never perfect because the turbulence in the upper half of the PBL is not generated by the local vertical gradients. Accordingly, the parameterised and LES-based fluxes decorrelate in the upper PBL. With this imperfection in mind, we show that there is no systematic quality deterioration of the FOC in the strongly stable PBL provided that the vertical model resolution is better than 10 levels within the PBL. In agreement with previous studies, we found that the quality improves slowly with the vertical resolution refinement, though it is generally wise not to overstretch the mesh in the lowest 500 m of the atmosphere where the observed, simulated and theoretically predicted stably stratified PBL is mostly located. The submission to a special issue of the “Boundary-Layer Meteorology” devoted to the NATO advanced research workshop “Atmospheric Boundary Layers: Modelling and Applications for Environmental Security”.     

Comments on the Numerical Simulation of Homogeneous Stably-Stratified Turbulence

The standard design for the direct numerical simulation of homogeneous stably-stratified turbulence assumes that the simulated turbulence is fully characterised by the gradient Richardson number. This assumption is justified only in sufficiently strong stratification when the Obukhov turbulent length scale, L, is essentially smaller than the depth of the computational domain, H. Otherwise simulations are not quite realistic because they cut off the large-scale part of the turbulence spectrum, namely, the scales comparable with or larger than H but smaller than L, that is just the eddies most sensitive to the stratification.     

Outlier Problem in Evaluating Similarity Functions in the Stable Atmospheric Boundary Layer

The gradient-based similarity approach removes turbulent fluxes as governing parameters and replaces them with vertical gradients of mean wind speed and potential temperature. As a result, the gradient Richardson number, Ri, appears as a stability parameter instead of the Monin–Obukhov stability parameter z/L (L is the Obukhov length). The gradient-based scaling is more appropriate for moderate and very stable conditions when the gradients are large and their errors are relatively small whereas z/L becomes ambiguous in these conditions because turbulent fluxes are small. However, the gradient-based formulation is faced with a problem related to the influence of Ri outliers: outliers with high values of Ri can exist in conditions that are really near-neutral. These outliers are mapped into the very stable range in plots in which Ri is the independent variable and may lead to spurious dependencies for bin-averaged data (spurious bin-averaging). This effect is quite large for functions that are steep for the gradient-based scaling. The present study uses the Surface Heat Budget of the Arctic Ocean (SHEBA) data to examine the problem and proposes two methods, conditional analysis and independent binning, to limit the influence of outliers on bin-averaging. A disadvantage of the conditional analysis is associated with eliminating outliers based on criteria that could be considered as subjective. The independent bin-averaging method does not have this disadvantage, but the scatter of the bin-averaged points is higher than for the conditional analysis, rendering data analysis and interpretation difficult.     

Intermittent Bursting of Turbulence in a Stable Boundary Layer with Low-level Jet

The atmospheric stable boundary layer (SBL) with a low-level jet is simulated experimentally using a thermally stratified wind tunnel. The turbulence structure and flow characteristics are investigated by simultaneous measurements of velocity and temperature fluctuations and by flow visualization. Attention is focused on the effect of strong wind shear due to a low-level jet on stratified boundary layers with strong stability. Occasional bursting of turbulence in the lower portion of the boundary layer can be found in the SBL with strong stability. This bursting originates aloft away from the surface and transports fluid with relatively low velocity and temperature upward and fluid with relatively high velocity and temperature downward. Furthermore, the relationship between the occurrence of turbulence bursting and the local gradient Richardson number (Ri) is investigated. The Ri becomes larger than the critical Ri, Ri_cr = 0.25, in quiescent periods. On the other hand, the Ri number becomes smaller than Ri_cr during bursting events.     

A Hierarchy of Energy- and Flux-Budget (EFB) Turbulence Closure Models for Stably-Stratified Geophysical Flows

Here we advance the physical background of the energy- and flux-budget turbulence closures based on the budget equations for the turbulent kinetic and potential energies and turbulent fluxes of momentum and buoyancy, and a new relaxation equation for the turbulent dissipation time scale. The closure is designed for stratified geophysical flows from neutral to very stable and accounts for the Earth’s rotation. In accordance with modern experimental evidence, the closure implies the maintaining of turbulence by the velocity shear at any gradient Richardson number Ri, and distinguishes between the two principally different regimes: “strong turbulence” at ${Ri \ll 1}$ typical of boundary-layer flows and characterized by the practically constant turbulent Prandtl number Pr _T; and “weak turbulence” at Ri > 1 typical of the free atmosphere or deep ocean, where Pr _T asymptotically linearly increases with increasing Ri (which implies very strong suppression of the heat transfer compared to the momentum transfer). For use in different applications, the closure is formulated at different levels of complexity, from the local algebraic model relevant to the steady-state regime of turbulence to a hierarchy of non-local closures including simpler down-gradient models, presented in terms of the eddy viscosity and eddy conductivity, and a general non-gradient model based on prognostic equations for all the basic parameters of turbulence including turbulent fluxes.