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1.
In this paper, we lay the foundations of a systematic mathematical formulation for the governing equations for flow through an urban canopy (e.g., coarse-scaled building array) where the effects of the unresolved obstacles on the flow are represented through a distributed mean-momentum sink. This, in turn, implies additional corresponding terms in the transport equations for the turbulence quantities. More specifically, a modified k-- model is derived for the simulation of the mean wind speed and turbulence for a neutrally stratified flow through and over a building array, where groups of buildings in the array are aggregated and treated as a porous medium. This model is based on time averaging the spatially averaged Navier--Stokes equations, in which the effects of the obstacle--atmosphere interaction are included through the introduction of a volumetric momentum sink (representing drag on the unresolved buildings in the array).The k-- turbulence closure model requires two additional prognostic equations, namely one for the time-averaged resolved-scale kinetic energy of turbulence,, and another for the dissipation rate, , of . The transport equation for is derived directly from the transport equation for the spatially averaged velocity, and explicitly includes additional sources and sinks that arise from time averaging the product of the spatially averaged velocity fluctuations and the distributed drag force fluctuations. We show how these additional source/sink terms in the transport equation for can be obtained in a self-consistent manner from a parameterization of the sink term in the spatially averaged momentum equation. Towards this objective, the time-averaged product of the spatially averaged velocity fluctuations and the distributed drag force fluctuations can be approximated systematically using a Taylor series expansion. A high-order approximation is derived to represent this source/sink term in the transport equation for . The dissipation rate () equation is simply obtained as a dimensionally consistent analogue of the equation. The relationship between the proposed mathematical formulation of the equations for turbulent flow within an urban canopy (where the latter is treated as a porous medium) and an earlier heuristic two-band spectral decomposition for parameterizing turbulence in a plant canopy is explored in detail.  相似文献   

2.
The standard E – model generates aplanetary boundary layerthat appears to be much too deep. The cause of theproblem is traced to the equation for the dissipationrate () of turbulent kinetic energy (E), specifically theparameterization of dissipation production anddestruction. In the context of atmosphericboundary-layer modelling, we argue that a part of thedissipation production should be modelled as the inputto the spectral cascade from the energy-containingpart of the spectrum, with a characteristic length , while the equilibrium imbalancebetween local production and destruction ofdissipation is modelled as proportional toE2/E, as in the standard model. Wepropose an E – – turbulence closurescheme, in which both the mixing length, m, and are prescribed. The importance ofthe equation is diminished, though itstill determines the dissipation rate in the Eequation.  相似文献   

3.
Analytical and numerical models of the neutral and stably-stratifiedatmospheric boundary layer are reviewed. Theoretical arguments andcomputational models suggest that a quasi-steady state is attainable in aboundary layer cooled from below and it is shown how this may be incorporatedwithin a time-steady, one-dimensional model. A new length-scale-limitedk- model is proposed for flows where a global maximum mixing length isimposed by the finite boundary-layer depth or, in stably-stratifiedconditions, by the Obukhov length, whilst still reducing to a form consistentwith the logarithmic law in the surface layer. Simulations compare favourablywith data from the Leipzig experiment and from Cardington airfield inEngland.  相似文献   

4.
The k - turbulence model is a standard of computational software packages for engineering, yet its application to canopy turbulence has not received comparable attention. This is probably due to the additional source (and/or sink) terms, whose parameterization remained uncertain. This model must include source terms for both turbulent kinetic energy (k) and the viscous dissipation rate (), to account for vegetation wake turbulence budget. In this note, we show how Kolmogorov's relation allows for an analytical solution to be calculated within the portion of a dense and homogeneous canopy where the mixing length does not vary. By substitution within model equations, this solution allows for a set of constraints on source term model coefficients to be derived.Those constraints should meet both Reynolds averaged Navier–Stokes equationsand large-eddy simulation sub-grid scale turbulence modelling requirements.Although originating from within a limited portion of the canopy, the predictedcoefficients values must be valid elsewhere in order to make the model capable of predicting the whole canopy-layer flow with a single set of constants.  相似文献   

5.
A modified k- model is used for the simulation of the mean wind speed and turbulence for a neutrally-stratified flow through and over a building array, where the array is treated as a porous medium with the drag on the unresolved buildings in the array represented by a distributed momentum sink. More specifically, this model is based on time averaging the spatially averaged Navier–Stokes equation, in which the effects of the obstacle-atmosphere interaction are included through the introduction of a distributed mean-momentum sink (representing drag on the unresolved buildings in the array). In addition, closure of the time-averaged, spatially averaged Navier–Stokes equation requires two additional prognostic equations, namely one for the time-averaged resolved-scale kinetic energy of turbulence,, and another for its dissipation rate, . The performance of the proposed model and some simplified versions derived from it is compared with the spatially averaged, time-mean velocity and various spatially averaged Reynolds stresses diagnosed from a high-resolution computational fluid dynamics (CFD) simulation of the flow within and over an aligned array of sharp-edged cubes with a plan area density of 0.25. Four different methods for diagnosis of the drag coefficient CDfor the aligned cube array, required for the volumetric drag force representation of the cubes, are investigated here. We found that the model predictions for mean wind speed and turbulence in the building array were not sensitive to the differing treatments of the source and sink terms in the and equations (e.g., inclusion of only the `zeroth-order' approximation for the source/sink terms compared with inclusion of a higher-order approximation for the source/sink terms in the and equations), implying that the higher-order approximations of these source/sink terms did not offer any predictive advantage. A possible explanation for this is the utilization of the Boussinesq linear stress–strain constitutive relation within the k– modelling framework, whose implicit omission of any anisotropic eddy-viscosity effects renders it incapable of predicting any strong anisotropy of the turbulence field that might exist in the building array.  相似文献   

6.
应用城市冠层模式研究建筑物形态对城市边界层的影响   总被引：5，自引：1，他引：4  
文中将城市冠层模式耦合到南京大学城市尺度边界层模式中,通过模拟对比发现,耦合模式对城市地区气温模拟结果更接近于观测值,尤其是对城市地区夜间气温模拟的改进.运用改进耦合模式通过多个敏感性试验的模拟,从城市面积扩张、建筑物高度增加、建筑物分布密度变化等角度研究城市建筑物三维几何形态变化对城市边界层及城市气象环境的影响,试验结果表明:(1)城市面积扩张使得城市下垫面的热通量增大,热力湍流活动增强,动量通量输送增强,城市湍能增大,湍流扩散系数变大,城市气温升高,且对不同时刻城市区域大气层结稳定度均有不同程度的影响.(2)建筑物高度增加增大了城市下垫面的粗糙度和零平面位移.同时也增大了城市街渠高宽比.城市建筑物越高,白天城市地区地表热通量越小,城市上空大气温度越低,平均风速减小,湍能减小;夜间由于高大建筑物释放储热比低矮建筑物要多,其热力湍流相对活跃,地表热通量增大,使得城市区域气温较高.(3)建筑物密度增大,会减小城市下垫面的粗糙度同时增强街渠对辐射的影响.建筑物密度增大在白天会减小地表热通量和动量通量,使城市气温降低,平均风速增大,城市湍流活动能力减弱;夜间城市释放较多储热使得气温较高.  相似文献   

7.
The paper considers a puff diffusion in its inertial stage when particle separation obeys the laws of the inertial subrange and depends only on eddy energy dissipation rate . The can be determined in the surface layer by the turbulent kinetic energy equation. Similarity equations connect with diffusion measure .A simple analytical model has been deduced to estimate pollutants diffusion during calms.  相似文献   

8.
A mesoscale planetary boundary layer (PBL) numerical model has been developed to study airflow over complex topography. Turbulence closures using the turbulent kinetic energy (TKE) and dissipation () equations are investigated in combination with the level 2.5 scheme of Mellor and Yamada (1982) to determine eddy diffusivities for momentum and heat. This modified E- closure is simpler than the level 3 one which requires more prognostic equations for moist turbulent transport.One-dimensional (1-D) model results show that the PBL mean flows under various stability conditions are not significantly sensitive to the modified Blackadar and Kolmogorov eddy mixing-length formulations used in this E- model, although the latter yields excessively large mixing lengths in the entrainment region of the upper PBL. Eddy mixing lengths in the Kolmogorov-type formulation can be better defined by introducing background dissipation. Using the same prognostic TKE equation, the 1-D model results are not significantly affected by different diagnostic formulations in the closures. The simulated results compare well with large-eddy simulations and those obtained using higher-order closure schemes including the level 3 one. The results are found to be insensitive to eddy Prandtl number, in contrast to the 2-D model results (see Part II).  相似文献   

9.
The study is focused on the retrieval and validation of the turbulent kinetic energy dissipation rate from spectral width measurements made by a UHF wind profiler in the convective atmospheric boundary layer. The possibility to deduce , which is one of the most important parameters for boundary-layer study and monitoring, from Doppler radar spectral width measurements has a firm theoretical basis established by numerous earlier works. However, the major drawback of this approach lies in various meteorological and instrumental sources of non-turbulent spectral width broadening which have to be recognised and accounted for. In the first part of the study, the theoretical background of the retrieval is detailed and all possible causes of spectral broadening are listed and evaluated. In the second part, the method is applied to four days of UHF diurnal boundary-layer observations, collected during the TRAC-98 experiment, for which in situ aircraft measurements were available. Comparison between radar-retrieved and in situ aircraft measurements yields a fairly good agreement with a linear correlation coefficient of about 0.9 and a residual bias less than 2 × 10-4 m2 s-3. The analysis of derived from vertical and off-zenith observation leads to the recommendation, that in the boundary layer, where the wind is usually moderate, data collected by off-zenith beams should be used. Indeed, the measurement of the vertical spectral width, less affected by the large-scale broadening factor, can still be altered by the ground clutter removal.  相似文献   

10.
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.  相似文献   

11.
Local Similarity Relationships In The Urban Boundary Layer   总被引：5，自引：3，他引：2  
To investigate turbulent structures in an urban boundary layer (UBL) with many tallbuildings, a number of non-dimensional variable groups based on turbulent observationsfrom a 325-m meteorological tower in the urban area of Beijing, China, are analyzedin the framework of local similarity. The extension of surface-layer similarity to localsimilarity in the stable and unstable boundary layer is also discussed. According to localsimilarity, dimensionless quantities of variables: e.g., velocity and temperature standarddeviations i/u*l (i=u,v,w) andT/T*l,correlation coefficients of uw and wT covariance, gradients of wind and temperaturem and h, and dissipation rates of turbulent kinetic energy (TKE) andtemperature variance and N can be represented as a functiononly of a local stability parameter z/, where is the local Obukhovlength and z is the height above ground. The average dissipation rates of TKE andtemperature variance are computed by using the u spectrum, and the uw and wTcospectra in the inertial subrange. The functions above were found to be in a goodagreement with observational behaviour of turbulence under unstable conditions, butthere were obvious differences in the stable air.  相似文献   

12.
A mesoscale Planetary Boundary Layer (PBL) model with a simple turbulence closure scheme based on the turbulence kinetic energy (TKE) equation and the dissipation () equation is used to simulate atmospheric flow over mesoscale topography. Comparative studies with different parameterizations suggest that with a proper closure assumption for turbulence dissipation, the E-model can simulate the circulation induced by the mesoscale topography with results similar to those obtained using the E- model. On the other hand, the first-order closure using O'Brien's cubic interpolation for eddy diffusivities (K) generally produces much larger K profiles in the stable and the unstable regions, which is believed to be due to the overprediction of the height of the PBL. All models with the TKE equation yield quite similar ensemble mean fields, which are found to be little sensitive to the closure assumption for turbulence dissipation, though their predicted magnitudes of TKE and K may differ appreciably. A discussion on the diurnal evolution of the mesoscale topography-induced circulation and the spatial variations of the turbulence fluxes in the surface layer is also given based on the E- model results.  相似文献   

13.
A numerical case study with a second-order turbulence closure model is proposed to study the role of urban canopy layer (UCL) for the formation of the nocturnal urban boundary layer (UBL). The turbulent diffusion coefficient was determined from an algebraic stress model. The concept of urban building surface area density is proposed to represent the UCL. Calculated results were also compared with field observation data. The height of the elevated inversion above an urban center was simulated and found to be approximately twice the average building height. The turbulent kinetic energy k, energy dissipation rate , and turbulence intensities u 2 and w 2 increase rapidly at the upwind edge of the urban area. The Reynolds stress uw displayed a nearly uniform profile inside the UBL, and the vertical sensible heat flux w had a negative value at the inversion base height. This indicates that the downward transport of sensible heat from the inversion base may play an important role in the formation of the nocturnal UBL.  相似文献   

14.
A two-dimensional E- model, which included the effects of plant-atmosphere interaction, was used to simulate air flow downwind of forest edges for the purpose of predicting the microclimate in forest openings. A suitable set of wall functions was selected to consider the aerodynamic effects of the ground in the opening. The model with discretization and parameter schemes was validated using a set of data from a wind-tunnel experiment. The simulated wind speed and turbulence kinetic energy closely agreed with the measured values. After validation, the model was used to predict eddy diffusivity in the lee of the forest edge. The modelled spatial distribution of the eddy diffusivity agreed in general with that calculated using wind-tunnel measurements. The usefulness and limitations of the E- model are discussed.Presently with Intera Information Technologies Corporation, IMS Division, 2 Gurdwara Road, Nepean, Ontario, Canada K2E 1A2.Corresponding author, and presently with Canada Centre for Remote Sensing, 419-588 Booth Street, Ottawa, Ontario, Canada K1A 0Y7.  相似文献   

15.
Cloud water and interstitial aerosol samples collected at Mt. Sonnblick (SBO) were analyzed for sulfate and aerosol carbon to calculate in-cloud scavenging efficiencies. Scavenging efficiencies for sulfate (SO) ranged from 0.52 to 0.99 with an average of 0.80. Aerosol carbon was scavenged less efficiently with an average value (AC) of 0.45 and minimum and maximum values of 0.14 and 0.81, respectively. Both SO and AC showed a marked, but slightly different, dependence on the liquid water content (LWC) of the cloud. At low LWC, SO increased with rising LWC until it reached a relatively constant value of 0.83 above an LWC of 0.3 g/m3. In the case of aerosol carbon, we obtained a more gradual increase of AC up to an LWC of 0.5 g/m3. At higher LWCs, _ remained relatively constant at 0.60. As the differences between SO and A varied across the LWC range observed at SBO, we assume that part of the aerosol carbon was incorporated into the cloud droplets independently from sulfate. This hypothesis is supported by size classified aerosol measurements. The differences in the size distributions of sulfate and total carbon point to a partially external mixture. Thus, the different chemical nature and the differences in the size and mixing state of the aerosol particles are the most likely candidates for the differences in the scavenging behavior.  相似文献   

16.
The dissipation rate of turbulent kinetic energy, , and the temperature structure function parameter, C T 2, have been measured over water from the near surface (Z = 3 m) to the top of the boundary layer. The near surface values of and C T 2 were used to calculate the velocity and temperature Monin-Obukhov scaling parameters u * and T *. The data collected during unstable lapse rates were used to evaluate the feasibility of extrapolating the values of and C T 2 as a function of height with empirical scaling formulae. The dissipation rate scaling formula of Wyngaard et al. (l971 a) gave a good fit to an average of the data for Z < 0.8 Z i. In the surface layer the scaling formula of Wyngaard et al. (1971b) disagreed with the C T 2 values by as much as 50%. This disagreement is due to an unexpected reduction in the measured values of C T 2 forZ < 30 m. At this point it is not clear if the discrepancy is a unique property of the marine boundary layer or if it is simply some unknown instrumental or analytical problem. The mixed layer scaling results were similar to the overland results of Kaimal et al. (1976).  相似文献   

17.
Eulerian turbulence observations, madein the surface layer under unstable conditions (z/L > 0),by a sonic anemometer were used to estimatethe Lagrangian structure function constant O. Twomethods were considered. The first one makes use of arelationship, widely used in the Lagrangian stochasticdispersion models, relating O to the turbulent kineticenergy dissipation rate , wind velocity variance andLagrangian decorrelation time. The second one employsa novel equation, connecting O to the constant of thesecond-order Eulerian structure function. Beforeestimating O, the measurements were processed in orderto discard non-stationary cases at least to a firstapproximation and cases in which local isotropy couldnot be assumed. The dissipation was estimated eitherfrom the best fit of the energy spectrum in theinertial subrange or from the best fit of the third-orderlongitudinal Eulerian structure function. Thefirst method was preferred and applied to the subsequentpart of the analysis. Both methods predict thepartitioning of O in different spatial components as aconsequence of the directional dependence of theEulerian correlation functions due to the isotropy.The O values computed by both methods are presented anddiscussed. In conclusion, both methods providerealistic estimates of O that compare well withprevious estimations reported in the literature, evenif a preference is to be attributed to the second method.  相似文献   

18.
A simple energy balance model which simulates the thermal regime of urban and rural surfaces under calm, cloudless conditions at night is used to assess the relative importance of the commonly stated causes of urban heat islands. Results show that the effects of street canyon geometry on radiation and of thermal properties on heat storage release, are the primary and almost equal causes on most occasions. In very cold conditions, space heating of buildings can become a dominant cause but this depends on wall insulation. The effects of the urban greenhouse and surface emissivity are relatively minor. The model confirms the importance of local control especially the relation between street geometry and the heat island and highlights the importance of rural thermal properties and their ability to produce seasonal variation in the heat island. A possible explanation for the small heat  相似文献   

19.
Summary A radiative transfer model has been used to determine the large scale effective 6.6 GHz and 37 GHz optical depths of the vegetation cover. Knowledge of the vegetation optical depth is important for satellite-based large scale soil moisture monitoring using microwave radiometry. The study is based on actual observed large scale surface soil moisture data and observed dual polarization 6.6 and 37 GHz Nimbus/SMMR brightness temperatures over a 3-year period. The derived optical depths have been compared with microwave polarization differences and polarization ratios in both frequencies and with Normalized Difference Vegetation Index (NDVI) values from NOAA/AVHRR. A synergistic approach to derive surface soil emissivity from satellite observed brightness temperatures by inverse modelling is described. This approach improves the relationship between satellite derived surface emissivity and large scale top soil moisture fromR 2=0.45 (no correction for vegetation) toR 2=0.72 (after correction for vegetation). This study also confirms the relationship between the microwave-based MPDI and NDVI earlier described and explained in the literature.List of Symbols f frequency [Hz] - f i(p) fractional absorption at polarizationp - h surface roughness - h h cos2 - H horizontal polarization - n i complex index of refraction - p polarization (H orV) - R s microwave surface reflectivity - T B(p) brightness temperature at polarizationp - T * normalized brightness temperature - T polarization difference (T v-T H) - T s temperature of soil surface - T c temperature of canopy - T max daily maximum air temperature - T min daily minimum air temperature - V vertical polarization - soil moisture distribution factor; also used for the constant to partition the influence of bound and free water components to the dielectric constant of the mixture - empirical complex constant related to soil texture - microwave transmissivity of vegetation (=e –) - * effective transmissivity of vegetation (assuming =0) - microwave emissivity - s emissivity of smooth soil surface - rs emissivity of rough soil surface - vs emissivity of vegetated surface - soil moisture content (% vol.) - K dielectric constant [F·m–1] - K fw dielectric constant of free water [F·m–1] - K ss dielectric constant of soil solids [F·m–1] - K m dielectric constant of mixture [F·m–1] - K o permittivity of free space [8.854·10–12 F·m–1] - high frequency limit ofK wf [F·m–1] - wavelength [m] - incidence angle [degrees from nadir] - polarization ratio (T H/T V) - b soil bulk density [gr·cm–3] - s soil particle density [gr·cm–3] - R surface reflectivity in red portion of spectrum - NIR surface reflectivity in near infrared portion of spectrum - eff effective conductivity of soil extract [mS·cm–1] - vegetation optical depth - 6.6 vegetation optical depth at 6.6 GHz - 37 vegetation optical depth at 37 GHz - * effective vegetation optical depth (assuming =0) - single scattering albedo of vegetation With 12 Figures  相似文献   

20.
A modified three-parameter model of turbulence for a thermally stratified atmospheric boundary layer (ABL) is presented. The model is based on tensor-invariant parameterizations for the pressure–strain and pressure–temperature correlations that are more complete than the parameterizations used in the Mellor–Yamada model of level 3.0. The turbulent momentum and heat fluxes are calculated with explicit algebraic models obtained with the aid of symbol algebra from the transport equations for momentum and heat fluxes in the approximation of weakly equilibrium turbulence. The turbulent transport of heat and momentum fluxes is assumed to be negligibly small in this approximation. The three-parameter $E - \varepsilon - {\left\langle {\theta ^{2} } \right\rangle }$ model of thermally stratified turbulence is employed to obtain closed-form algebraic expressions for the fluxes. A computational test of a 24-h ABL evolution is implemented for an idealized two-dimensional region. Comparison of the computed results with the available observational data and other numerical models shows that the proposed model is able to reproduce both the most important structural features of the turbulence in an urban canopy layer near the urbanized ABL surface and the effect of urban roughness on a global structure of the fields of wind and temperature over a city. The results of the computational test for the new model indicate that the motion of air in the urban canopy layer is strongly influenced by mechanical factors (buildings) and thermal stratification.  相似文献   

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