Test Of Turbulence Models For Wind Flow Over Terrain With Separation And Recirculation

Several two-equation turbulence models using isotropic eddy viscosity and wall functions are assessed by solution of the neutral atmospheric boundary layer over a flat surface and wind flow over two- and three-dimensional models and real terrain. Calculations are presented for wind flow over the Sirhowy Valley in Wales, an embankment along the Rhine in Germany and the Askervein Hill in Scotland. Comparisons of predictions with previous work, and laboratory and field data, show that the RNG-based k– model gives the best agreement with respect to the flow profiles and length of the separated flow region. The results of this model are analyzed with a non-linear stress-strain relation to gauge the potential effect of turbulence anisotropy.     

The Adaptation of the Atmospheric Boundary Layer to a Change in Surface Roughness

The adaptation of the atmospheric boundary layer to a change in the underlying surface roughness is an interesting problem and hence much research, theoretical, experimental, and numerical, has been undertaken. Within the atmospheric boundary layer an accurate numerical model for the turbulent properties of the atmospheric boundary layer needs to be implemented if physically realistic results are to be obtained. Here, the adaptation of the atmospheric boundary layer to a change in surface roughness is investigated using a first-order turbulence closure model, a one-and-a-half-order turbulence closure model and a second-order turbulence closure model. Perturbations to the geostrophic wind and the pressure gradients are included and it is shown that the second-order turbulence closure model, namely the standard k - model, is inferior to a lower-order closure model if a modification to limit the turbulent eddy size within the atmospheric boundary layer is not included within the model.     

The effect of orchard crop structure on the integral length-scale of turbulence

The integral length-scalesL for the three orthogonal components of diffusivityK=L are derived from spectral analysis of velocity time series measurements. A 3-D sonic anemometer was used to make these velocity measurements at heights in the range 0.7–7.0 m in and above a 2 m orchard canopy with near-neutral atmospheric boundary-layer stability conditions. The integral length-scale is compared with another length-scale of diffusionL obtained by fitting an exponential model to the auto-correlation spectrumR _E (t) in the region 0.95<R _E (t)<0.5 for smallt. This length-scale is appropriate to a high frequency region of the energy spectrum where turbulent momentum transport becomes diffusion-like and the turbulent energy varies with the inverse square of frequence. This region has been shown by others to determine the magnitude of the dissipation rate of turbulent energy by the action of viscosity even though the dominant dynamics are inviscid. Within the crop, the ratio of the length-scalesL/L were found to be smaller than the values measured above the crop for vertical turbulence. This was attributed to the enhanced decay rate of turbulent energy due to the effect of the airflow interaction with the crop. It is unclear whether similar effects are present in the horizontal plane because of greater scatter in the data, resulting from the more variable nature of the wind direction in the horizontal plane.     

Turbulence Characteristics Over Complex Terrain In West China

Meteorological data of velocity components and temperature have been measured on a mast of height 4.9 m at one site in the Heihe River Basin Field Experiment (HEIFE) conducted in west China. Mean and individual turbulence parameters, power spectra/cospectra, phase angles and their changes withfetch downwind of a change in surface roughness were analyzed. The turbulence characteristics depend strongly on the prevailing wind direction, which in turn is associated with changes in the upwind surface roughness pattern. The results show that values of horizontal velocity standard deviations sigma;_u,v scaled with local friction velocity u under different stratifications are larger than those over flat terrain, while the values of _w/u have the same values as over flat terrain. The differences between variance values of the horizontal velocity components, u and v, over inhomogeneous terrain were found to be significantly smaller than those over flat terrain. Since energy densities of the w spectra, uw and wT cospectra at low frequencies are relatively lower than those of longitudinal velocity spectra, total energies of w spectra, uw and wT cospectra tend to be in equilibrium with the local terrain. The values of phase angles at the low frequency end of the frequency showed obvious differences associated with changes of roughness.     

Transport-Dissipation Analytical Solutions to the E-∈Turbulence Model and their Role in Predictions of the Neutral ABL

E- turbulence model predictions of the neutralatmospheric boundary layer (NABL) are reinvestigated to determine thecause for turbulence overpredictions found in previous applications. Analytical solutions to the coupled E and equations for the case of steady balance between transport and dissipation terms, the dominant balance just below the NABL top, are derived. It is found that analytical turbulence profiles laminarizeat a finite height only for values of closure parameter ratio c ₂ /_e equal toor slightly greater than one, with laminarization as z for greater . The point = 2 is additionally foundthat where analytical turbulent length scale (l) profilesmade a transition from ones ofdecreasing ( < 2) to increasing ( > 2)values with height. Numerically predicted profiles near the NABL topare consistent with analytical findings. The height-increasingvalues of l predicted throughout the NABL with standard values ofclosure parameters thus appear a consequence of 2.5(> 2), implied by these values (c ₂ = 1.92, _{= 1.3}, _{e = 1}). Comparison of numericalpredictions with DNS data shows that turbulence overpredictions obtained with standard-valued parameters are rectifiedby resetting and _e to 1.1 and 1.6, respectively, giving, with c ₂ = 1.92, 1.3, and laminarization of the NABL's cappingtransport-dissipation region at a finite height.     

Modification Of The Standard ∈-Equation For The Stable Abl Through Enforced Consistency With Monin–Obukhov Similarity Theory

A condition is derived for consistency of the standard-equation with Monin–Obukhov (MO) similarity theory of thestably-stratified surface layer. The condition is derivedby extending the procedure used to derive the analogous condition forneutral theory to stable stratification. It is shown that consistencywith MO theory requires a function of flux Richardson number, Ri_f, to be absorbed into either of two closure parameters, c ₁ or c ₂.Inconsistency, on the other hand, results if constant values of these are maintained for all Ri_f, as is done in standardapplication of the equation, and the large overpredictions ofturbulence found in such application to the one-dimensionalstable atmospheric boundary layer (1D-SBL) are traced to thisinconsistency. Guided by this, we formulate a MO-consistent-equation by absorbing the aforementioned function intoc ₁, and combine this with a Level-2.5 second-orderclosure model for vertical eddy viscosity and diffusivities.Numerical predictions of the 1D-SBL by the modified model converge to a quasi-steady state, rectifying the predictive failure of the standard -equation for the case.Quasi-steady predictions of non-dimensional variables agree stronglywith Nieuwstadt's theory. Qualitative accuracy of predictionsis inferred from comparisons to field data, large-eddy simulationresults and Rossby-number similarity relationships.     

Study On Development And Application Of A Regional Pbl Numerical Model

A regional scale (a few km to a few hundred km, minutes to days)planetary boundary layer (PBL) numerical model (RPBLM) has been successfully developed to simulateprecisely the boundary-layer three-dimensional characteristics. The RPBLM model with a high-resolutionnon-hydrostatic E - turbulence closure scheme has been applied to diagnose and prognosticate the PBL characteristicsover a complex underlying surface in the Hong Kong area of 60 km × 48 km. It is shown that the RPBLMmodel can be used to simulate the PBL characteristics including wind, temperature, water vapour andturbulence over such a complex underlying surface and that the simulated result is reasonably in agreementwith observations.     

Evaluating Models Of The Neutral, Barotropic Planetary Boundary Layer Using Integral Measures: Part Ii. Modelling Observed Conditions

The steady-state, horizontally homogeneous, neutral, barotropiccase forms the foundation of our theoretical understanding of the planetary boundary layer (PBL).While simple analytical models and first-order closure models simulate atmospheric observationsof this case well, more sophisticated models, in general, do not. In this paperwe examine how well three higher-order closure models, E - - l, E - l, and LRR - l,which have been especially modified for PBL applications, perform in predicting the behaviour of thecross-isobaric angle ₀, the geostrophic drag coefficient C_g, and the integral of the dissipationrate over the boundary layer, as a function of the surface Rossby number Ro. For comparison we alsoexamine the performance of three first-order closure mixing-length models, two proposed byA. K. Blackadar and one by H. H. Lettau, and the performance of the standard model forsecond-order closure and a modification of it designed to reduce the overprediction of turbulence inthe upper part of the boundary layer.     

Turbulent exchange over a surface with chessboard-type inhomogeneities

The results of an experiment carried out in the summer of 1988 in the forest-steppe region of the USSR are given. The aim of the experiment was to study turbulent exchange between the atmosphere and a non-homogeneous underlying surface consisting of a patchwork quilt of agricultural lands sown with different crops (hereafter called chessboard-type inhomogeneities). Simultaneous measurements of turbulent fluxes of heat, momentum and humidity by the eddy-correlation methods and also the measurements of the mean wind velocity and temperature are described. The values of turbulent fluxes calculated from the profile measurements are in good agreement with those obtained from the eddy-correlation measurements. Thus it may be concluded that the universal functions of Monin-Obukhov similarity theory (determined from measurements over a flat and homogeneous underlying surface) pertain also to a non-homogeneous (chessboard-type) underlying surface.     

Estimation of the Monin-Obukhov similarity functions from a spectral model

From measured one-dimensional spectra of velocity and temperature variance, the universal functions of the Monin-Obukhov similarity theory are calculated for the range –2 z/L + 2. The calculations show good agreement with observations with the exception of a range –1 z/L 0 in which the function _m , i.e., the nondimensional mean shear, is overestimated. This overestimation is shown to be caused by neglecting the spectral divergence of a vertical transport of turbulent kinetic energy. The integral of the spectral divergence over the entire wave number space is suggested to be negligibly small in comparison with production and dissipation of turbulent kinetic energy.Notation a,b,c contants (see Equations (–4)) - C_i constants i=u, v, w, (see Equation (5) - k_me,k_mT peak wave numbers of 3-d moel spectra of turbulent kinetic energy and of temperature variance, respectively - k_mi peak wave numbers of 1-d spectra of velocity components i=u, v, w and of temperature fluctuations i= - k_sb, k_c characteristics wave numbers of energy-feeding by mechanical effects being modified by mean buoyancy, and of convective energy feeding, respectively - L Monin-Obukhov length - % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Gabeivayaaraaaaa!3C5B!\[{\rm{\bar T}}\] difference of mean temperature and mean potential temperature - T* Monin-Obukhov temperature scale - velocity of mean flow in positive x-direction - u* friction velocity - u, v, w components of velocity fluctuations - z height above ground - von Kármanán constant - temperature fluctuation - _m nondimensional mean shear - _H nondimensional mean temperature gradient - nondimensional rate of lolecular dissipation of turbulent kinetic energy - _D nondimensional divergence of vertical transports of turbulent linetic energy     

Review of non-local mixing in turbulent atmospheres: Transilient turbulence theory

Some of the larger eddies in a turbulent region can be coherent structures that turbulently advect air parcels across large vertical distances before smaller eddies mix the parcels with the environment. Such a process is nonlocal rather than diffusive. Transilient turbulence theory, named after a Latin word maaning jump over, provides a framework for considering the ensemble-averaged effect of many eddies of different sizes on the net nonlocal mixing in the vertical. Nonlocal turbulence statistics can then be examinated, and nonlocal first-order closure can be formulated.     

A three-dimensional model for calculating the concentration distribution in inhomogeneous turbulence

A new approach for calculating the concentration distribution in inhomogeneous turbulence is suggested. The model is a 3-D model, constrained to describe incompressible flow. The model requires a knowledge of the covariance matrix of the Eulerian velocities and the two-point third moments. The model is applied for three types of turbulent field: homogeneous isotropic turbulence, constant flux neutral boundary layer and free convective turbulence. The required Eulerian moments are calculated using the eddy model of the turbulent field. Concentration moments are calculated and results are compared to experimental data. Other model predictions which have no experimental support can be compared to measurements when available.     

Flow and transport modeling in the sea-breeze. Part I: A modifiedE — ∈ model with a non-equilibrium level 2.5 closure

In order to overcome shortcomings of the conventionalE — model and to develop a more general model applicable to the variety of atmospheric conditions observed, for example, during a land-sea breeze cycle, a modifiedE — model is proposed. The model is a simplified form of an algebraic stress model including wall proximity effects of Gibson and Launder (1978). The proposed model is similar to the popular Mellor and Yamada (1982) level 2.5 model but does not employ a local equilibrium assumption in the algebraic equations for Reynolds stresses. The resulting model shows a wider realization region under unstable conditions than the Mellor and Yamada model.The modified model is compared herein to observations, higher order closure simulations and large eddy simulations under neutral, stable and convective conditions. Various dissipation rate equations were employed and compared to understand their performance with the modified model. The modifiedE — model reproduced the observed behavior well under all conditions except near the base of an elevated inversion layer under convective conditions. The ability of the model to describe flow dynamics under a wide range of atmospheric stabilities suggests that the model can be used to describe the complicated diurnal behavior of the land-sea breeze circulation.     

Turbulent flows over mountainous terrain modelled by the Reynolds equations

A numerical model based upon fundamental principles, a standard (k, ) turbulence closure and a finite element integration technique, is applied to separated flows over hills. Predictions are compared to experimental data from a wind tunnel. Although few-equation turbulence closures have been shown to have obvious deficiencies with respect to comparable flows, the model predicts remarkably accurately, without coefficient adjustments of any kind. Even the turbulent intensity is predicted quite realistically.     

An application of the E-ε turbulence model for studying coupled air-sea boundary-layer structure

An E- turbulence model is used to study air-sea interaction characteristics and turbulence structure using a coupled model for air-sea boundary layers. The E- turbulence model consists of equations for the turbulent kinetic energy, the energy-dissipation, and for the turbulent exchange coefficient expressed in terms of turbulent kinetic energy and energy-dissipation. The energy-dissipation equations for the air-sea interface are solved analytically to obtain boundary conditions for energy-dissipation at the interface. The air-sea interaction and turbulence characteristics of the E- model are compared with those of the mixing-length model and with available observations.The simulations demonstrate that the air-sea interaction parameters obtained by the E- model agree well with observations. The numerical studies also show that the E- turbulence model with appropriate constants can give good results in modeling coupled air-sea boundary-layer flows.     

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.     

Nitrate in the atmospheric boundary layer of the tropical South Pacific: Implications regarding sources and transport

Weekly bulk aerosol samples collected at Funafuti, Tuvalu (8°30S, 179°12E), American Samoa (14°15S, 170°35W), and Rarotonga (21°15S, 159°45W), from 1983 through most of 1987 have been analyzed for nitrate and other constituents. The mean nitrate concentration is about 0.11 g m^–3 at each of these stations: 0.107±0.011 g m^–3 at Funafuti; 0.116±0.008 at American Samoa; and 0.117±0.010 at Rarotonga. Previous measurements of mineral aerosol and trace metal concentrations at American Samoa are among the lowest ever recorded for the near-surface troposphere and indicate that this region is minimally affected by transport of soil material and pollutants from the continents. Consequently, the nitrate concentration of 0.11 g m^–3 can be regarded as the natural level for the remote marine boundary layer of the tropical South Pacific Ocean. In contrast, over the tropical North Pacific which is significantly impacted by the transport of material from Asia and North America, the mean nitrate concentrations are about three times higher, 0.29 and 0.36 g m^–3 at Midway and Oahu, respectively. The major sources of the nitrate over the tropical South Pacific are still very uncertain. A very significant correlation between the nitrate concentrations at American Samoa and the concentrations of ²¹⁰Pb suggests that transport from continental sources might be important. This continental source could be lightning, which occurs most frequently over the tropical continents. A near-zero correlation with ⁷Be indicates that the stratosphere and upper troposphere are probably not the major sources. A significant biogenic source would be consistent with the higher mean nitrate concentrations, 0.16 to 0.17 g m^–3, found over the equatorial Pacific at Fanning Island (3°55N, 159°20W) and Nauru (0°32S, 166°57E). The lack of correlation between nitrate and nss sulfate at American Samoa does not necessarily preclude an important role for marine biogenic sources.     

étude expérimentale de la couche limite au-dessus d'un relief modéré proche d'une chaîne de montagne

For the heterogeneous site described in the first part, some aspects of the turbulent structure of the planetary boundary layer are studied. Using mixed-layer scaling, the normalized profiles are compared with those obtained over flat terrain during convective conditions. The measurements were made with the same instrumented aircraft at both sites. The dissipative and spectral length scales are smaller over complex terrain within the whole boundary layer. This is due to the shifting of the wavelength peak toward the high frequencies by dynamic turbulence.This last effect can also explain the increase of the dissipation rate over the heterogeneous site during strong wind conditions. The vertical profiles of sensible heat flux and temperature-water vapor correlation show a lack of entrainment process at the top of the boundary layer. This fact suggests that the investigated boundary layer is advected from the neighbouring plain over the complex site (plateau de Lannemezan).     

Pollutant dispersion close to an urban surface – the BUBBLE tracer experiment

Summary In this publication first results of an urban tracer experiment are reported. This experiment was realized in the framework of the Basel UrBan Boundary-Layer Experiment (BUBBLE) in an area with abundant information on turbulence and flow conditions available. Release height was close to roof level and so was the height of the concentration samplers. The meteorological conditions during the experiments were mainly convective, but due to the rough character of the underlying surface also the mechanical turbulence was substantial.The concentration distribution is found to be essentially Gaussian in the horizontal plane and some commonly used methods to estimate the plume widths in applied dispersion models are compared to the observations. From measurements at one site downwind of the source it is found that for a near-roof level source, only an insignificant vertical gradient in tracer concentration is present within a street canyon. Using a Lagrangian Particle Dispersion Model the tracer experiments are simulated. It is shown that the exact form of the parameterization for the flow and turbulence structure within the urban roughness sublayer is of great importance for the simulation results. Also the numerical simulation results underline the necessity (and difficulty) to describe the vertical profile of the dissipation rate of turbulent kinetic energy close to an urban surface.