Meteorol Atmos Phys 87, 3–21 (2004)DOI 10.1007/s00703-003-0058-3

School of Meteorology, University of Oklahoma, Norman, USA

Dispersion of passive tracer in the atmosphericconvective boundary layer with wind shears: a reviewof laboratory and numerical model studies

E. Fedorovich

With 9 Figures

Received July 5, 2003; revised August 9, 2003; accepted September 21, 2003Published online: June 2, 2004 # Springer-Verlag 2004

Summary

Paper reviews recent laboratory and numerical model stud-ies of passive gaseous tracer dispersion in the atmosphericconvective boundary layer (CBL) with surface and elevatedwind shears. Atmospheric measurement data used forvalidation of these two model techniques are brieflydiscussed as well. A historical overview is given of labo-ratory studies of dispersion in the atmospheric CBL. Modelstudies of tracer dispersion in two CBL types, the (i) non-steady, horizontally homogeneous CBL and (ii) quasi-stationary, horizontally heterogeneous CBL, are reviewed.The discussion is focused on the dispersion of non-buoyantplume emitted from a point source located at differentelevations within the CBL. Approaches towards CBLmodeling employed in different laboratory facilities (watertanks and wind tunnels) are described. The reviewednumerical techniques include Large Eddy Simulation(LES) and Lagrangian modeling. Numerical data ondispersion in the sheared CBL is analyzed in conjunctionwith experimental results from wind-tunnel CBLs.

1. Introduction

Convective boundary layers (CBLs) driven bybuoyancy forcings from the bottom or=and fromthe top and capped by temperature (density)inversions are commonly observed in the lowerportion of earth’s atmosphere (Holtslag andDuynkerke, 1998). During fair-weather daytimeconditions, in the absence of clouds (which is the

case of clear CBL, see op. cit.), the buoyancyforcing in the boundary layer is primarily repre-sented by convective heat transfer from a warmunderlying surface. This feature is an apparentreason for calling the considered boundary-layertype ‘‘convective’’ in the meteorological andother geophysical applications of fluid me-chanics. The term ‘‘convective’’ also emphasizesthe fact that buoyant convection is the mainmechanism of turbulence production in theboundary layer, whilst the contribution of windshear to the generation of turbulence is of sec-ondary importance.

The surface buoyancy forcing generates up-and downward motions that effectively mixmomentum and scalar fields inside the CBL.The fast rising updrafts (convective thermals)typically occupy a smaller percentage of theCBL horizontal cross-sectional area than thebroader, but more slowly descending convectivemotions, or downdrafts (Lenschow, 1998). Dueto active mixing, the wind velocity, potentialtemperature (buoyancy), and concentrations ofatmospheric constituents in the main portion ofthe CBL (often referred to as convectively mixedlayer) do not change considerably with heightwhen averaged over horizontal planes or overtime. A typical CBL can be subdivided into three

separate layers: the surface layer, in which themeteorological variables change fairly rapidlywith height; the mixed layer, where mean verticalgradients of these variables are close to zero; andthe entrainment zone (also referred to as theinversion layer or interfacial layer), where againthe large gradients in meteorological fields areobserved. Across the entrainment zone, the free-atmosphere air, which is more buoyant than theCBL air, is entrained into the convectively mixedlayer as the CBL grows. Such convective entrain-ment is maintained by the penetration of the ther-mals into the stably stratified atmosphere abovethe CBL and subsequent folding of more buoyantair from aloft into the CBL as these overshootingthermals sink back into the mixed layer.

Flow-field and concentration patterns in theatmospheric CBL are strongly variable both intime and in space. However, in the meteorologi-cal boundary-layer studies, two CBL types dif-ferent with respect to their spatial-temporalevolution are usually considered. The first CBLtype (we will call it the non-steady CBL) is (orassumed to be) statistically quasi-homogeneousover a horizontal plane. In this case, the CBLevolution is regarded as a non-stationary process.Most numerical and laboratory CBL studiesreported in the literature have been carried outwithin the assumption of horizontal homogeneityof the layer. Available field measurement data onthe turbulent flow structure and dispersion of pas-sive constituents in the CBL usually also refer tothis CBL type. Another commonly studied caseof the atmospheric CBL is the horizontally evolv-ing CBL, which grows in a neutrally or stablystratified air mass that is advected over a heatedunderlying surface. This type of the CBL (wewill call it the heterogeneous CBL) is a tradi-tional subject of wind-tunnel model studies.Based on the Taylor hypothesis (Willis andDeardorff, 1976b), it is generally possible torelate temporal and spatial scales of dispersiveturbulent motions in the non-steady and hetero-geneous CBLs (Fedorovich et al, 1996).

The turbulence structure and characteristics ofdispersion in the atmospheric CBL have beenrather thoroughly investigated for the case ofCBL without wind shears (hereafter referred toas the case of shear-free CBL). Just a few studieshave been devoted to the investigation of effectsproduced by additional non-convective (or non-

buoyant) forcings that contribute to the CBL tur-bulence regime in conjunction with the dominantbuoyant driving mechanism. Examples of suchforcings are wind shears and surface roughness.In the developed CBL, the momentum fieldinside the layer is well mixed by convectivemotions and, as shown in Garratt et al (1982),the flow regions with strong mean wind gradients(shears) are usually located at the surface (sur-face shear) and at the level of inversion (elevatedshear).

The present paper reviews recent laboratoryand numerical model studies of passive tracerdispersion in the atmospheric CBL with windshears. The atmospheric measurement data avail-able for validation of these model approacheswill be briefly presented as well, although I knowof no major CBL dispersion field experimentsconducted recently. A historical overview willbe given of laboratory models of dispersion inthe atmospheric CBL. Model studies of tracerdispersion in the both aforementioned CBL types(non-steady and heterogeneous) will bereviewed. The discussion will be focused on thedispersion of non-buoyant plume of traceremitted from a point source located at differentelevations within the CBL.

2. Laboratory models of dispersionin the CBL

The pioneering laboratory studies of gaseousplume dispersion in the atmospheric CBL havebeen performed in the 1970s and 1980s by Willisand Deardorff (1976a; 1978; 1981; 1983; 1987),and Deardorff and Willis (1982; 1984). Theseexperiments, conducted in convection water tankheated from the bottom, demonstrated the com-plexity of tracer concentration patterns in theCBL and their sensitivity to the turbulenceregime of the CBL.

In order to imitate a mean wind in the CBL, amodel stack in the quoted laboratory experimentswas towed along the bottom of convection watertank. Apparently, this technique only partiallyaccounts for the effect of wind on the tracer dis-persion. The mean advection of tracer is ade-quately reproduced in this case, while turbulentdiffusive motions generated due to bottom frictionand vertical shears are not taken into account. In anattempt to overcome this limitation of water-tank

4 E. Fedorovich

modeling techniques, an idea of composite watertank was realized in the recent laboratory study ofPark et al (2001). Such composite water tank sys-tem includes a conventional water tank, similar tothe one used in the experiments of Willis andDeardorff, and a moving grid plate for mechanicalgeneration of turbulence near the bottom of thetank, which is intended to simulate the shear-pro-duced turbulence. With mechanically generatedturbulence, the authors of op. cit. managed toachieve rather close agreement between theirlaboratory and CONDORS field experiment(Briggs, 1993) data on the vertical dispersion var-iation as function of distance from the source.

As a tool for dimensionless analysis and inter-pretation of plume dispersion pattern in thelaboratory CBL, Willis and Deardorff appliedthe Deardorff (1970b) convective (mixed-layer)scaling, further discussed in Deardorff (1985),which since that time has served as standardframework for inter-comparison of CBL disper-sion data from different sources. This scaling hasbeen originally proposed to normalize mean-flowparameters and turbulence statistics in thenumerically simulated pure case of shear-freeCBL. The scaling concept is based on three gov-erning scales for length: zi, velocity: w�, and tem-perature (which should be considered as virtualpotential temperature in the case of clear atmo-spheric CBL): T�. The length scale zi (interpretedas the CBL depth) is taken as the elevation thelevel of the most negative heat flux of entrain-ment within the interfacial layer, the velocityscale is related to zi and to the surface kinematicheat flux Qs as w� ¼ ð�QsziÞ1=3

, where � ¼ g=T0

is the buoyancy parameter (g is the accelerationdue to the gravity, T0 is the reference tempera-ture), and the temperature scale is definedthrough the ratio of Qs to w�: T� ¼ Qs=w�. Forthe purpose of normalization of concentrationpatterns in the CBL with mean wind, the aboveoriginal scaling has to be complemented with thehorizontal length scale Lh ¼ ðzi � UÞ=w�, and theconcentration scale c� ¼ Es=ðzi2 � UÞ, where U isthe mean wind velocity and Es is the tracersource strength in units of volume per unit time(Deardorff, 1985). Two other dimensionlessparameters (numbers) based on the Deardorff(1970b) convective scales are commonly em-ployed to characterize turbulence regime in theCBL developing on the background of stable

stratification (see, e.g., Deardorff et al, 1980;Zilitinkevich, 1991; Fedorovich and Mironov,1994): the Richardson number RiDT related tothe temperature increment DT across the interfa-cial layer: RiDT ¼ �w��2ziDT , and the Richardsonnumber based on the buoyancy frequency N inthe turbulence-free zone above the CBL: RiN ¼N2zi

2w��2.Willis and Deardorff (1978) found in their

water tank experiments that the source locationis an important factor of the concentration distri-bution in the CBL. They have shown, see alsoLamb (1982), that the average centerline of theplume released from an elevated source in theCBL descends quickly downwind of the source.In contrast, the plume released near the surfacerises fast inside the CBL. These observations,which are not consistent with predictions of theGaussian plume model, manifest the specificcharacter of dispersion in the CBL associatedwith the skewed (narrow, fast updrafts versusbroad, slow downdrafts) vertical velocity field.

The water-tank experiments of Willis andDeardorff significantly advanced our understand-ing of dispersion in the CBL, but were limited bymeasurement and data processing techniques.The original tank, which was used in thoseexperiments, no longer exists: it was acquiredby the Fluid Modeling Facility of EPA and pro-foundly modified over the years to such an extentthat nothing remains of the original except fordimensions, as described in Snyder et al (2002).The new tank is equipped with laser-induced-fluorescence and video-imaging systems formaking non-intrusive measurements of tracerconcentrations, as well as with computerizedcontrol system that enables all operation andmeasurement functions to be specified and con-trolled though a single procedure. The main ideabehind the tank renovation has been the estab-lishing of a laboratory tool to study the disper-sion of highly buoyant plumes in the CBL (Weilet al, 2002), which was not sufficiently studiedpreviously in the laboratory. However, a series ofexperiments in the new tank have also been con-ducted with non-buoyant plumes. For the meanconcentration fields and for some other plumedispersion characteristics (for instance, the con-centration intermittency and the lateral dis-persion variation), the new data displayedtrends similar to those found earlier by Willis

Dispersion of passive tracer in the atmospheric CBL with wind shears 5

and Deardorff. A good agreement has been alsofound with field data from Hanna and Paine(1989) on ground-level concentrations and withanalytical predictions for the lateral dispersion inthe CBL. Some discrepancies between the newresults and Willis and Deardorff data have beenattributed by Weil et al (2002) to the insufficientsampling in the early water tank experiments(this sampling problem, however, seems to affectmore the experiments with buoyant plumes).

Another type of laboratory facility employedfor CBL dispersion studies is a saline water tank.An example of such a facility, described inHibberd and Sawford (1994a, b), has been usedfor investigation of various CBL dispersionregimes, in particular the plume fumigation intoa growing shear-free CBL (Hibberd and Luhar,1996). The experiments in the saline tank areperformed in an upside-down fashion (the sourceof negative buoyancy is located at the top) ascompared to the water tank heated from the bot-tom. The saline-tank approach towards CBLmodeling has its own advantages and disadvan-tages. The main advantage is the possibility ofaccurate control of the steadiness of stratificationin a tank without caring about heat losses.The developers of the saline-tank CBL model(Hibberd and Sawford, 1994a) claim that at typi-cal laboratory scales, saline convection cansatisfy the requirements for modeling buoyantplume dispersion under strongly convective(light wind) conditions better than thermal con-vection in heated water tanks.

Nevertheless, the discussed water-tank CBLmodel approaches either omit or treat ratherindirectly the effects of wind shears on the tur-bulence regime and characteristics of dispersionin the atmospheric CBL. With respect to takingthese effects into account, the wind-tunnel modelapproach seems to be the most feasible one. Aseries of laboratory studies of plume dispersionin a sheared CBL have been conducted in spe-cially designed thermally stratified wind tunnelsin different countries of the world, see reviews byMeroney and Melbourne (1992), and Meroney(1998).

First wind-tunnel experiments of this kindhave been carried out in the Colorado State Uni-versity by Poreh and Cermak (1985). They havemeasured parameters of the three-dimensionalplume spread in the horizontally evolving CBL

and found them to be in a fair qualitative agree-ment with atmospheric observations.

A number of wind tunnel facilities capable ofsimulating the atmospheric CBL have been con-structed during the two past decades in Japan.Recent CBL flow and dispersion experimentsconducted in two of these facilities are describedin Sada (1996), and Ohya et al (1996; 1998). Thetunnel used by the latter research team is prob-ably the most technologically advanced facilityamong existing thermally stratified tunnels allover the world. Sada (1996) studied a tracer dif-fusion in a CBL with weak wind shear usingthe thermally stratified wind tunnel of KomaeResearch Laboratory. He found the Deardorff(1970b) convective scaling to be applicable tothe flow and diffusion patterns in the simulatedCBL. The capping temperature inversion in theconducted wind-tunnel experiments was ratherweak. That was a reason for substantial verticalspread of the plume in the upper portion of thewind-tunnel CBL. In the op. cit., the experimen-tally obtained parameters of dispersion were notanalyzed in conjunction with properties of turbu-lence in the simulated CBL, and effects of flowshear on the tracer dispersion in the CBL werenot particularly investigated.

The first real opportunity to study in laboratorythe effects of wind shears on dispersion in theCBL was presented in the beginning of the1990s, when a thermally stratified wind tunnelwas completed at the University of Karlsruhe(UniKa), Germany, by M. Rau and his colleagues(Poreh et al, 1991; Rau et al, 1991; Rau andPlate, 1995). Characteristics of turbulent flowin the quasi-stationary, horizontally evolving,sheared atmospheric CBL simulated in theUniKa wind tunnel have been comprehensivelystudied by Fedorovich et al (1996), Kaiser andFedorovich (1998), and Fedorovich and Kaiser(1998). These wind-tunnel experiments haveshown that wind shears can essentially modifythe turbulence dynamics in the CBL and param-eters of turbulent exchange (entrainment) acrossthe capping inversion. Later on, the wind-tunnelstudies at UniKa have been complementedby numerical Large Eddy Simulation (LES)of the CBL flow case reproduced in thetunnel (Fedorovich et al, 2001a, b; Fedorovichand Th€aater, 2001). This combination of numeri-cal and laboratory approaches allowed a detailed

6 E. Fedorovich

quantification of mean flow characteristics andturbulence statistics in the convectively drivenflow modified by surface and elevated windshears. Parallel to the basic CBL flow studies,the UniKa wind-tunnel group conducted a seriesof tracer dispersion experiments in the CBL withwind shears (Th€aater et al, 2001; Fedorovich andTh€aater, 2001).

In order to account for the contribution of windshears to the turbulence regime of the CBL, onehas to complement the list of CBL flow parametersby new quantities that are representative of sheareffects. Dynamic effect of the surface shear iscommonly characterized by the friction velocity

u� ¼ �1=2s , where �s is the near-surface value of

� ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðw0u0Þ2 þ ðw0v0Þ2

q, the turbulent shear stress

magnitude normalized by density. There is nocommonly accepted parameter to characterize theelevated wind shear. A reasonable candidate forthis function could be the entrainment shearvelocity s� ¼ ðDu2 þ Dv2Þðdzi=dtÞ discussed inFedorovich (1995) and applied for parameteriza-tion of the shear effects on the CBL growth in Pinoet al (2003). In the above formula, elevated windshear is expressed in terms of zero-order jumps ofhorizontal wind velocity components u and vacross the entrainment zone. If we now relate velo-city scales u� and s� to the governing velocityscale w� representing the buoyancy forcing, wewill come up with two dimensionless combina-tions u�=w� and s�=w� characterizing, respec-tively, the contributions of surface and elevatedshears, to the turbulence dynamics in the CBL.The first of these combinations can be expressedin terms of the Monin-Obukhov length L ¼�u�3=ð�kQsÞ and the CBL convective length scalezi ratio: u�=w� ¼ �ðkL=ziÞ1=3

, as described, e.g. inFedorovich et al (1996). Following Holtslag andNieuwstadt (1986), the shear contribution to theturbulence production in the CBL (in the absenceof elevated shear) can be neglected if �L=zi<0:1,which gives u�=w� ¼ 0:34 as a conventionalboundary value to distinguish between the regimesof shear and shear-free convection.

3. Modification of CBL flowby wind shears

The effect of surface shear on the CBL flowstructure has been extensively investigated dur-

ing the last two decades by means of numericalLarge Eddy Simulation (LES). The LES tech-nique was for the first time employed in the atmo-spheric CBL studies by Deardorff (1970a). Sincethat time, this technique has been considerablydeveloped and applied to different types of atmo-spheric and industrial boundary-layer flows, seereview papers by Mason (1994), Lesieur andM�eetais (1996), Piomelli and Chasnov (1996).The LES approach distinguishes between large-scale energy-carrying anisotropic motions (largeeddies), which are resolved explicitly on thenumerical grid employed, and smaller subgridmotions, which are assumed to be homogeneousand isotropic, and therefore can be parameterizedwith a universal turbulence closure scheme. Inorder to separate the effects of large eddies andsmall-scale motions in the computational pro-cedure, the initial flow-governing equations de-scribing all scales of motions are filtered, and theterms responsible for the effects of subgrid mo-tions (subgrid-scale stresses and fluxes) appear inthe filtered LES equations as additional sourceterms. It is clear from the nature of LES thatthe success of its application for the reproductionof high Reynolds number turbulent flows essen-tially depends on the complexity of small-scalemotions to be parameterized, and the proportionof energy contents between the resolved and sub-grid scales of motion.

One of the first numerical studies aimed at theevaluation of shear effects in the CBL has beenconducted by Sykes and Henn (1989). Althoughthe CBL case reproduced in this study was notexactly relevant to the atmospheric CBL, theresults obtained have nevertheless provided aquantitative estimate of the ability of an exter-nally applied shear to organize the convectiveeddies into two-dimensional rolls. The combinedeffects of wind shear and buoyancy forces in theatmospheric CBL have been investigated in theLES study by Moeng and Sullivan (1994). Theyobserved a similar re-organization of the turbu-lence structure when the shear-free convectionregime in the boundary layer has been replacedby sheared convection. As the contribution ofwind shear grew, elongated high-low-speedstreaks were formed in the near-surface regionof the simulated boundary-layer flow replacingthe irregular polygonal structure characteristicof the shear-free convective flow. Mason (1992)

Dispersion of passive tracer in the atmospheric CBL with wind shears 7

applied LES to study dispersion of a passive sca-lar in a CBL with wind shear. He found that arelative increase of shear with respect to buoy-ancy led to an increase of short-time dispersionrates. In contrast, the vertical dispersion atgreater time was reduced and took on the char-acter of a simple diffusive process. Mason linkedthis marked change in vertical dispersion to theeffect of a reduced length scale in shear-driventurbulence compared with convective turbulence.All aforementioned LES studies have generallyconfirmed 0.34 to be a critical value of theshear=buoyancy production ratio separatingshear-free and sheared convection regimes inthe CBL.

In a comprehensive LES study of the three-dimensional structure of buoyancy- and shear-induced turbulence in the atmospheric boundarylayer, Khanna and Brasseur (1998) spanned avast range of stability conditions starting froma nearly shear-free CBL (�L=zi ¼ 0:0014,u�=w� ¼ 0:0047) to an almost purely shear-driv-en boundary layer (�L=zi ¼ 2:3, u�=w� ¼ 7:7).Besides the general support of earlier findings byMoeng and Sullivan (1994) concerning the shear-induced alteration of the CBL coherent structure,this study provided further insights into theindividual properties of convective thermals androlls. Based on the comparison of visualizationsof structures with turbulence spectra in thebuoyancy-driven flow, Khanna and Brasseur con-cluded that the shear-dominated near-surface

structure of the unstable surface layer influencesdirectly the global structure of the moderatelyconvective boundary layer.

In Fig. 1, near-surface flow velocity fields inthe shear-free and strongly sheared CBLs fromthe LES study of Conzemius and Fedorovich(2003) are demonstrated. The aforementioneddifferences between the CBL flow structures(cells in the shear-free CBL versus rolls in thesheared CBL) in these two cases are clearly seenin the plots.

Modification of the CBL turbulence regime bysurface shear has been investigated experimen-tally by Fedorovich et al (1996), and Kaiserand Fedorovich (1998) in the UniKa wind-tunnelmodel of a horizontally evolving CBL. In theseexperiments, surface shear was found to be anessential contributor to the turbulence produc-tion. Values of the surface shear-to-buoyancyproduction ratio u�=w� of 0.3 and larger resultedin a noticeable increase in the variance of veloc-ity fluctuations in the lower portion of the layercompared with their counterparts in the shear-free CBL. Weak roll-like semi-organized mo-tions were identified in the pattern of meanvelocity measured in planes perpendicular tothe mean flow direction. In the bulk of theCBL, buoyancy was found to be the dominantfactor of turbulence production at smaller wavenumbers, while the shear contribution was appar-ently increasing towards large wave numbers.The surface shear forcing in the simulated CBL

Fig. 1. Simulated structure of near-surface u and v (arrows), and w (shaded contours) fields in the case of shear-free CBL (leftplot) and in the CBL with strong (20 m=s) height-constant geostrophic wind (right plot); from Conzemius and Fedorovich(2003)

8 E. Fedorovich

was suggested to be a reason for the elongationand flatness of the production ranges in the mea-sured velocity spectra.

Compared to the effect of shear at the surface,the influence of wind shear across the cappinginversion (elevated shear) on CBL turbulence ismuch less studied. Such elevated shears are typi-cally observed in the atmospheric CBL underbaroclinic conditions (Stull, 1988). The velocityincrements across the inversion layer in this casecan be of either sign depending on the geo-strophic wind change with height in terms ofthe so-called thermal wind (Fedorovich, 1995).According to the zero-order jump CBL model,the contribution of elevated shear to the produc-tion of turbulent kinetic energy in the growingCBL (dzi=dt>0) is essentially positive.

At the same time, wind-tunnel experiments ofFedorovich and Kaiser (1998) have provided anindication that turbulence enhancement in theupper portion of the horizontally evolving CBLwith elevated shears may be accompanied by thedecrease of the CBL growth rate. Due to techni-cal restrictions, the aforementioned experimentscould only be conducted with positive shearacross the inversion layer, when the flow in theouter turbulence-free region had larger meanmomentum than the turbulent flow in the bulkof the CBL. In the complementary LES study,Fedorovich et al (2001b) tried to associate thisdamping effect of elevated shear on the CBLgrowth with the so-called shear sheltering ofturbulence previously considered by Csanady(1978), Jacobs and Durbin (1998), Hunt andDurbin (1999), and in connection with cross-wind effects in the inversion layer by Hunt (1998).

In their LES output, Fedorovich et al have dis-covered what they called the directional effect ofelevated shear on the growth of the horizontallyevolving CBL. In the case of positive wind shearacross the inversion layer (the flow above theinversion possesses a larger momentum thanmean motion in the mixed layer), the CBLgrowth has been found impeded compared tothe case of CBL with the shear-free inversion,just in accordance with the experimental findingsof Fedorovich and Kaiser (1998). On the otherhand, the LES experiments have revealed theactivation of boundary-layer growth in the caseof elevated negative shear when the mean flowabove the inversion possesses a smaller horizon-

tal momentum than mean motion in the mixedlayer. In this way, the effect of negative elevatedshear on the CBL growth turned out to be oppo-site to that of the positive shear.

A subsequent numerical study of Fedorovichand Th€aater (2001) suggested that Fedorovich et al(2001b) had correctly identified the modifica-tions of turbulence structure in the CBL withsheared capping inversion but overlooked themain effect of elevated wind shear on the flowdynamics in the horizontally evolving CBL. Thismain effect was associated with local organizedvertical motions at the CBL top due to accelera-tion or deceleration of the CBL flow caused bymomentum transport across the sheared cappinginversion. The acceleration of the CBL flow (theincrease of the u component of mean motionwith x below the capping inversion) took placein the positive-shear case. Due to the fluid con-tinuity it produced negative (descending) meanvertical motion at the level of inversion. Theopposite happened in the negative-shear case,when the upward transport of momentum acrossthe inversion caused the deceleration of meanflow within the CBL. This deceleration led topositive (ascending) organized vertical motionpushing the capping inversion upwards. In thepositive-shear case, the generated mean verticalmotion opposed the entrainment at the CBL topand thus slowed down the CBL growth, whilst inthe case of negative shear, the organized upwardmotion supported the CBL growth in addition tothe entrainment mechanism.

The discussed effect of elevated shear on theCBL evolution is essentially a feature of the ho-rizontally evolving CBL. Indeed, under the con-ditions of horizontal (quasi-) homogeneity in thenon-steady CBL, there is no internal source ofmean vertical motion at the CBL top that canadversely modify the sign of the CBL growth.Recently, there were several numerical (LES)studies reported that specifically addressed therole of elevated shear in the convective entrain-ment and the CBL development. These studiesarrived at rather mixed conclusions. On onehand, numerical experiments of Pino et al (2003)provided an indication of unconditional enhance-ment of the entrainment and CBL growth rateby the combined effect of surface and elevatedshears. On the other hand, numerical results ofConzemius and Fedorovich (2002) gave no clear

Dispersion of passive tracer in the atmospheric CBL with wind shears 9

indication of wind shear contribution to the CBLgrowth dynamics. A systematic additional inves-tigation of considered effects by Conzemius andFedorovich (2003), who simulated nine CBLflow cases with variable shear and buoyancy forc-ings, has shown that strong wind shear can sig-nificantly enhance the CBL growth rate whenheat flux at the lower surface is weak and thestratification of the atmosphere above the CBLis moderate or weak. If the surface heat fluxand the outer-atmosphere stratification are bothstrong, the effect of shear on the CBL growth,in a relative sense, becomes negligible. Never-theless, shear in this case still exerts a stronginfluence over the turbulence structure withinthe CBL. The conducted numerical experimentsdid not provide any direct support for the Huntand Durbin (1999) theory of turbulence shearsheltering in the case of a CBL-type flow.

Main results recently obtained with laboratoryand numerical models regarding the wind shearinfluence on turbulent flow in the atmosphericCBL may be summarized as follows.

(1) Variances of horizontal velocity componentsin the lower (up to z=zi¼ 0.5) portion of theCBL are noticeably enhanced in the presenceof surface shear.

(2) Surface wind shear does not significantlyaffect the temperature variance and verticalheat flux in the main portion of the CBL.

(3) Longitudinal roll-like structures formed in thesheared CBL additionally contribute to the var-iance of the across-wind velocity component.

(4) Elevated wind shear generates larger var-iances of longitudinal velocity componentin the entrainment zone (interfacial layer)at the CBL top.

(5) Wind shears lead to broader productionranges in the velocity fluctuation spectraextended towards larger wave-number values.

(6) In the horizontally heterogeneous CBL, ele-vated wind shears of different signs have adirectional effect on the entrainment and var-iation of the CBL depth with distance.

4. Plume dispersion in the horizontallyevolving CBL

In this section, the review will be given of recentlaboratory and numerical studies of gaseousplume dispersion in the quasi-stationary, horizon-tally inhomogeneous CBL flow. Laboratory stud-ies of dispersion regimes were conducted in theUniKa thermally stratified wind tunnel in 1996–2001. They were complemented in 2000–2001by LES of dispersion in the considered CBL flowcase.

The UniKa wind tunnel is a facility of theclosed-circuit type, with 10-m long, 1.5-m wideand 1.5-m high test section. The return section ofthe tunnel is subdivided into ten layers, which areindividually insulated. Each layer is 15-cm deepand is driven by its own fan and heating system.In this manner, the velocity and temperature pro-files can be pre-shaped at the inlet of the testsection as shown in Fig. 2. The test section floorcan be heated with a preset energy input to pro-duce a constant heat flux through the CBL bot-tom. The CBL in the tunnel develops throughseveral intermediate regimes that are describedin Fedorovich et al (2001a). The stage of quasi-homogeneous, slowly evolving CBL, which isthe closest counterpart of the atmospheric CBL,is achieved at x� 5.5 m.

At this stage, the value of RiDT is the wind-tunnel CBL model is about 10, which is oneorder of magnitude smaller than typical RiDTvalues in majority of numerical and water-tankCBL models. For most of cases studied in thetunnel, the value of u� was from 0.03 to

Fig. 2. Sketch of modeling the horizontallyevolving, sheared atmospheric CBL in theUniKa thermally stratified wind tunnel

10 E. Fedorovich

0.08 m=s and w� – from 0.15 to 0.20 m=s, andthus the u�=w� ratios were within the range from0.2 to 0.5 (0.02< � L=zi<0:3), that is aroundthe margin for the surface shear effects (see esti-mates in Sect. 3). For the diffusion experimentsin the tunnel, a non-buoyant tracer has been used.As tracer gas, SF6 has been employed. The mix-ture of tracer gas with air was emitted in thecentral vertical plane of the tunnel at 3.32-m dis-tance from the test-section inlet, close to thedownwind edge of established CBL region. Con-centration measurements have been made usingstandard technique based on the electron detectormethod. The measured concentration values havebeen averaged over two-minute time periods. Foradditional information regarding the experimen-tal setup see Fedorovich and Th€aater (2002).

In Fig. 3, the longitudinal concentration distri-bution from a near-ground source in the shearedwind-tunnel CBL is plotted together with itscounterpart from the Willis and Deardorff(1978) water-tank model of the shear-free CBL.From the qualitative point of view, the concentra-tion distributions provided by both experimentaltechniques fairly agree with each other (oneshould keep in mind that the Taylor hypothesiswas employed to enable comparability of thewind-tunnel distribution with the water-tankdistribution). In both CBL models, the plumereleased near the surface rises fast inside thelayer, which is a well-known feature of plumedispersion in the CBL (Lamb, 1982). However,a closer inspection of the plots reveals the

smaller horizontal concentration gradients inthe lower portion of wind-tunnel CBL. This isapparently a result of enhanced longitudinaltransport of tracer by comparatively large hori-zontal velocity fluctuations associated with sur-face shear in the wind-tunnel flow.

In Fig. 4, a concentration distribution measuredin the wind-tunnel CBL with imposed positiveelevated shear (second plot from the top) is com-pared with its analog for the case of CBL with ashear-free upper interface (the uppermost plot).Demonstrated concentration patterns refer to thecentral vertical plane of the tunnel. Concentrationvalues in the plots are normalized as c� ¼c � L2 � U=Es, where L¼ 1 m, U¼ 1 m s�1. Thepresented comparison indicates that in the consid-ered CBL case, the elevated positive shear ampli-fies the effect of stable stratification in obstructingthe plume penetration above the inversion, whichleads to a pronounced blocking of the tracerwithin the CBL. The resulting concentrationlevels at the same elevations along the wind-tun-nel test section are noticeably smaller in the caseof sheared inversion than in the CBL capped by ashear-free density interface. As one may alsonotice, the rise of the maximum concentration linein the case of sheared inversion is delayed in com-parison with the reference shear-free case. Theenhanced horizontal velocity fluctuations insidethe sheared inversion lead to comparativelysmooth horizontal distribution of concentrationin the upper portion of CBL with elevated shear(second plot from the top in Fig. 4).

Fig. 3. Dispersion of a non-buoyant plume in the water-tank model of shear-free CBL (Willis and Deardorff, 1978, left plot)and in the UniKa wind tunnel CBL (Fedorovich and Th€aater, 2002, right plot). The source elevation is z=zi¼ 0.07. Height,length, and concentration are normalized by Deardorff (1970b; 1985) convective scales. The origin of the x-ordinate is at thesource location

Dispersion of passive tracer in the atmospheric CBL with wind shears 11

In the CBL with positive elevated shear, theground concentrations are generally higher thanin the CBL flow with a shear-free inversion layer(compare two lower plots in Fig. 4). This is aresult of accumulation of tracer in the congestedand more shallow boundary layer affected by theelevated wind shear.

Further results from the described wind-tunnelexperiments, summarized in Fedorovich andTh€aater (2002), indicate that the cross-stream con-centration distribution in the sheared CBL dis-plays features of plume channeling, which ispresumably caused by longitudinal semi-orga-nized roll-like motions in the CBL with shear.

A numerical study of dispersion in the UniKawind-tunnel CBL was conducted by means of theLES code described Fedorovich et al (2001a)with an added dispersion simulation block(Th€aater et al, 2001). The Eulerian method con-sidered in Nieuwstadt (1998) was employed forincorporation of the tracer transport in the LESframework, and the balance equation for the

tracer concentration c was taken in the form:

@c

@tþ @ðui � cÞ

@xi¼ @

@xi

��c

@c

@xi� ðcui � c � uiÞ

�þ Sc;

where i¼ 1, 2, 3; t stands for the time, xi ¼ðx; y; zÞ are the right-hand Cartesian coordinates,�uui ¼ ð�uu;�vv; �wwÞ are the resolved-scale componentsof the velocity vector, �cc is the resolved-scale con-centration of the tracer, Sc is the source term, and�c is the molecular diffusivity of the tracer. Theoverbar signifies the grid-cell volume average.The quantities Fsi ¼ cui � �cc � �uui are the com-ponents of the subgrid concentration flux,respectively, which were parameterized asFsi ¼ �Kcð@�cc=@xiÞ. The value of subgrid turbu-lent diffusivity Kc was assumed to be equal to thesubgrid thermal diffusivity. The latter quantitywas parameterized through the product of sub-grid length scale and square root of the sub-grid turbulence kinetic energy as described inFedorovich et al (2001a). Zero-gradient boundaryconditions are employed for �cc at the walls of

Fig. 5. Numerically simulated concentration distributionsin the wind tunnel CBL with positive elevated wind shear(PS) and in the basic flow case (Basic case) without ele-vated shear. The source is at the ground level in both cases.The origin of the x-ordinate is at the source location. Thecapping-inversion and shear-zone elevations at x¼ 0 are300 mm

Fig. 4. Longitudinal concentration distributions measuredin the CBL with positive elevated wind shear (PS) and inthe basic CBL flow case without elevated shear (denoted asBasic case). The source is at the ground level in both cases.The origin of the x-ordinate is at the source location. Thecapping-inversion and shear-zone elevations at x¼ 0 are0.3 m

12 E. Fedorovich

simulation domain (the wind-tunnel test section),and the radiation condition was applied at the out-let. In the grid cell containing the source, the sourceterm had the form: Sc ¼ Es=D3, where Es is thesource strength and D3 ¼ DxDyDz is the grid-cellvolume. In all other grid cells of the simulationdomain, the value of Sc was set equal to 0.

Numerically simulated concentration distribu-tions for the basic CBL flow case with the shear-free inversion and for the CBL with imposedpositive elevated shear are presented in Fig. 5.There is an overall agreement between the mea-sured (Fig. 4) and computed (Fig. 5) concentra-tion distributions with respect to their integralparameters. However, some important fine detailsof the tracer dispersion in the CBL such asplume-rise rate and surface concentration patchi-ness are rather poorly reproduced by the LES.The noted deficiencies are presumably due toinsufficient spatial resolution of the conductednumerical simulations and spurious effects ofthe employed low-order advection scheme.

5. Plume dispersion in the non-steadyCBL with shear

A comprehensive numerical study of passivetracer dispersion in the non-steady, horizontally(quasi-) homogeneous CBL has been reported byDosio et al (2003). Following the Eulerian meth-odology, they added a conservation equation tothe set of governing LES equations, previouslyemployed for simulation of a variety of flowregimes in the atmospheric boundary layer.Similar methods to describe the tracer disper-sion in the LES of CBL were previously usedby Wyngaard and Brost (1984), Haren andNieuwstadt (1989), Schumann (1989), and Hennand Sykes (1992). A different approach towardsupgrading the LES for investigation of dispersionin the sheared CBL was exploited earlier byMason (1992), who employed the Lagrangianframework to calculate the concentration patternsbased on the LES-generated flow fields (seeSect. 6).

Wyngaard and Brost (1984) were first todemonstrate that properties of turbulent transportof the passive scalar emitted near the CBL bot-tom (bottom-up diffusion) are rather differentfrom the transport of a scalar emitted at theinversion level (top-down diffusion). This

suggested bottom-up/top-down decompositionturned out to be very useful for the analyses ofdispersion patterns in the shear-free CBLs. How-ever, the concept and associated scaling stillawait extension for the case of sheared CBL withboth surface- and elevated-shear contributions tothe diffusive turbulent motions.

Dosio et al (2003) put numerical investigationof tracer dispersion in the CBL on a systematicbasis and simulated dispersion regimes corre-sponding to four different values of geostrophicwind and three different values of surface heatflux in the simulation domain with a horizontalcross-section of 10 km� 10 km. The range ofu�=w� in these numerical experiments was from0.02 to 0.59. Thus, the CBL cases spanned in thestudy were from the practically shear-free CBLto the CBL with very significant contributionof surface shear to the turbulence production.Dispersion of plumes emitted from both thenear-surface source (zs=zi ¼ 0:078, where zs isthe source height) and the elevated source(placed almost in the middle of the CBL atzs=zi ¼ 0:48) was studied.

Results of the aforementioned numericalexperiments for the CBL cases with u�=w� inthe range from 0.02 to 0.21 have shown verygood agreement with experimental data availablefrom the laboratory (water-tank) and field studiesof dispersion from a near-surface source in theweakly sheared CBL, see left-hand panels inFig. 6. Presented plots demonstrate the compar-ison of the computed vertical, �z and �z

0, andhorizontal (lateral), �y, dispersion parameterswith experimental data. These dispersion param-eters were evaluated in the following way:

�z2 ¼

Ðcðz� �zzÞdVÐ

cdV; �z

02 ¼Ðcðz� zsÞdVÐ

cdV;

�y2 ¼

Ðcðy� �yyÞdVÐ

cdV;

where �zz and �yy are the mean plume height and themean plume horizontal position, respectively.The dimensionless distance from the source, X,in the plots is defined based on the Deardorff(1970b, 1985) convective scaling explained inSect. 2 of the present paper.

At short distances from the source (X<1), thesimulation results for �z

0 were found to fit wellwith the expression �z

0=zi ¼ 0:52X6=5, which is

Dispersion of passive tracer in the atmospheric CBL with wind shears 13

very close to the classical approximation �z0=zi ¼

0:5X6=5 (Lamb, 1982). For the horizontal disper-sion parameter �y, the LES results were in a goodagreement with the laboratory data for X<2.Besides that, they followed very closely theestablished analytical dependencies of �y=zion X discussed in the literature (Lamb, 1982;Briggs, 1985; Gryning et al, 1987).

Rather satisfactory agreement was also foundbetween the LES results and experimental datafor the plume emitted from the elevated source(right-hand panels in Fig. 6). For the verticalplume dispersion, only �z values are shown inthe plots because the mean plume height in thiscase does not noticeably deviate from the initialrelease height and thus �z

0 � �z. The power-lawdependence on X for �z=zi retrieved from theLES confirmed the parameterization suggestedby Lamb (1982) for dispersion from elevatedreleases at X<2=3: �z=zi ’ 0:5X. The normal-ized lateral dispersion parameter �y=zi as a func-tion of X in the LES experiments with theelevated source followed approximately the sameanalytical curve as in the case of near-surfacerelease, except for the region of small X, wherethe plume was spreading laterally slightly faster

in the case of the near-surface release due to theenhanced horizontal fluctuations at the surface.This was found consistent with the unifiedparameterization suggested by Lamb for bothreleases at X>1: �y=zi ’ ð1=3ÞX2=3.

The LES results of Dosio et al (2003) are ofspecial interest with respect to quantification ofthe surface-shear effect on the dispersion of aplume emitted at different elevations within theCBL. In order to account for the shear in thenormalized concentrations patterns, the authorsof op. cit. used a modified velocity scale wm

introduced through the empirical formula wm3 ¼

w�3 þ 5u�3 first suggested by Zeman andTennekes (1977) for determination of velocityscale in the CBL with surface shear. The distancefrom the source x is then normalized asXm ¼ ðwm=ziÞðx=UÞ.

Numerical data presented in Fig. 7 (left-handpanels show results for the near-surface releaseand panels to the right refer to the elevatedrelease) indicate that wind shear can consider-ably modify longitudinal variations of meanplume height and both vertical and lateral disper-sion parameters in the CBL. As was mentionedin Sect. 3 of the present paper, the horizontal

Fig. 6. Horizontal changes of the plume height and dispersion parameters �z, �z0, and �y in the almost shear-free CBL with

near-surface (left-hand panels) and elevated (right-hand panels) sources; from Dosio et al (2003). The LES results from op.cit. are shown by solid lines with standard deviations indicated by vertical bars. Experimental data of Willis and Deardorff(1976), Weil et al (2002), and Briggs (1993) are shown by filled circles, � symbols, and diamonds, respectively. The dashedlines represent 6=5 and 1 power laws for �z

0 and �z (see explanations in the text), and the Gryning et al (1987) parameteriza-tion for �y. The dashed-dotted line illustrates the simulated meandering component as compared with the water-tank data ofWeil et al (2002) shown by open triangles

14 E. Fedorovich

velocity fluctuations throughout a significant por-tion of the CBL are considerably enhanced bysurface wind shear. These turbulence regimechanges, in addition to the faster longitudinaltransport of tracer by larger mean velocities, leadto relatively less effective vertical dispersion inthe sheared CBL and, consequently, to the slowerplume rise with distance and smaller values ofthe vertical dispersion parameter �z. At the sametime, the lateral spread of the tracer in thesheared CBL is intensified by enhanced horizon-tal velocity fluctuations, and the horizontal dis-persion parameter grows with distance faster thanin the case of shear-free CBL. The discussedshear effects on the tracer plume released at thesurface are perfectly illustrated by the LESresults shown in the left-hand panels of Fig. 7.Shear effects on dispersion in the CBL were gen-erally less pronounced in the case of elevatedrelease (right-hand panels in Fig. 7).

Employing Venkatram’s (1988) idea of decom-position of lateral dispersion variance in ‘‘b’’buoyancy- and ‘‘s’’ shear-related parts �y

2 ¼�yb

2 þ �ys2, and using the shear-contribution pa-

rameterization similar to the one that Luhar (2002)suggested for a coastal fumigation model, Dosioet al (2003) came up with a practicable expression

of �ys2 for the case of near-surface release, (see eq.

(32) in their paper), and a recommendation to use�yb

2 in the form proposed by Gryning et al (1987).Based on the LES data, rather feasible parameter-izations were also developed for the verticaldispersion parameters �z and �z

0. These parame-terizations took into account surface-shear effectsin the CBL cases with near-surface as well as withelevated plume releases, (see eqs. (35), (37), and(38) in Dosio et al, 2003).

Based on their LES results, Dosio et al (2003)concluded that the main effect of (surface) windshear on the tracer dispersion in the atmosphericCBL is represented by a reduction of the verticalspread of a tracer, whereas its horizontal spreadis enhanced. Consequently, the ground concen-trations are strongly influenced as the increasedwind tends to advect the plume for a longer time.The tracer, therefore, reaches the ground atgreater distances from the source.

6. Lagrangian models of dispersionin the sheared CBL

According to the Lagrangian modeling meth-odology, the dispersion process is regarded asthe change of the concentration when traveling

Fig. 7. Effects of surface wind shear on the plume height and dispersion parameters �z and �y in the CBL with near-surface(left-hand panels) and elevated (right-hand panels) sources; from Dosio et al (2003). The solid lines (cases B1–B5) showsimulated parameters of the plume in the practically shear-free (u�=w��0.21) CBL. The dashed lines (SB1–SB2) correspondto the CBL cases with moderate shear (u�=w� ¼ 0.27 and u�=w� ¼ 0.34). The dashed and dotted lines refer to the strongly-sheared CBL cases (u�=w� ¼ 0.46 and u�=w� ¼ 0.47). The case of nearly-neutral boundary layer (indicated as NN) isrepresented by u�=w� ¼ 0.59

Dispersion of passive tracer in the atmospheric CBL with wind shears 15

with a passive particle that moves with theturbulent flow (Nieuwstadt, 1998). The probabil-ity that a single particle released at time t0from position rs � ðxs; ys; zsÞ, that is the sourcelocation, arrives at r � ðx; y; zÞ at time t is givenby pðr; t; rs; t0Þ. Accordingly, the mean con-centration c at ðr; tÞ is given by cðr; tÞ ¼ÐÐÐ

pðr; t; rs; t0Þc0ðrsÞdrs, where c0ðrsÞ is theinitial particle concentration distribution at rs.In the case of a point source with unit strengthat r0, the initial distribution is given by c0ðrsÞ ¼�ðrs � r0Þ, where � is the Dirac delta function.The integration provides cðr; tÞ ¼ pðr; t; rs; t0Þ,which means that in this case the mean concen-tration is equivalent to the single-particle prob-ability density. The probability density functionis calculated by releasing a large number of par-ticles and, particle positions at each time beingknown, computing the number of particles withina given volume around r. The particle position rpis found by integrating drp ¼ uLdt, where uL isthe Lagrangian velocity of the particle.

The method to calculate the Lagrangian veloc-ity is rather model-specific. Lagrangian models,employed in air pollution applications, use forthis purpose the prescribed mean turbulent flowcharacteristics and parameterized turbulencestatistics derived from measurement data or/andfrom some flow model output, see review byWilson and Sawford (1996). When applied tocalculation of concentration fields in the CBL,such Lagrangian models typically require speci-fication of parameterizations for variances of thewind velocity components, components of thevertical turbulent shear stress, the turbulencekinetic energy (TKE) dissipation rate, the thirdmoment of the vertical velocity fluctuations, andprobability density distribution of these fluctua-tions. In the Lagrangian models, based on theLES-derived flow fields, the Lagrangian velocityis evaluated from the resolved velocity fields incombination with contribution from the subgridvelocity variances. The first model of this typewas developed by Lamb (1978).

A representative example of applied Lagrangianmodel based on the parameterized description ofCBL turbulence is the model of Rotach et al(1996), and de Haan and Rotach (1998). Thisrandom-walk type Lagrangian model is particu-larly designed to cover the whole flow regimes inthe atmospheric boundary-layer flow with com-

bined surface-shear and buoyancy turbulence-gen-eration mechanisms. In order to account for boththese mechanisms, the probability density function(PDF) of the particle velocities is constructed as aweighted sum of a skewed (characteristic of theCBL flow) and a Gaussian PDF (representativeof the velocity field in the neutral boundary layer),using the so-called transition function Ft. Thefunction Ft is a continuous function of the inver-sion height zi, hydrostatic stability expressed interms of the Monin-Obukhov length scale L, andthe current height z of each particle. It is specifiedin such a way that in fully convective conditionsand sufficiently far away from underlying surface,Ft is set equal to unity, which corresponds to thesituation, when the horizontal and vertical velocityfluctuations are not correlated. For neutral condi-tions and when approaching the surface, the distri-butions of u and w fluctuations are assumed to bejointly Gaussian, and Ft ¼ 0. Due to limited dataavailability, the transition function has originallybeen calibrated from near-ground atmosphericmeasurements only. In a recent attempt byKastner-Klein et al (2001) to improve the parame-terization for Ft, as well as parameterizations forother turbulence characteristics employed in themodel, the wind-tunnel data on the statistics ofvelocity fluctuations and on the TKE dissipationrate in the sheared CBL from Fedorovich et al(1996), Kaiser and Fedorovich (1998), andFedorovich et al (2001) were additionally invoked.

The comparison of the original and newparameterizations for the velocity variances ispresented in Fig. 8. It is clear from the firstglance that only for the vertical velocity variancethe original parameterization from Rotach et al(1996) works appropriately. For the horizontalvelocity variances, the original parameterizationsproduce too large values of u02 and v02 in the mainportion of the CBL and do not account for thefast decay of variances with height in the near-surface region of the flow.

Both original and modified turbulence parame-terizations were incorporated in the Rotach et al(1996) Lagrangian model, and the model sensi-tivity to the turbulence parameterizations wasstudied for different locations downwind of thesource. As reference data, the wind-tunnelconcentration measurements and LES resultsdescribed in Fedorovich and Th€aater (2002), andTh€aater et al (2001) were used. In Fig. 9, mean

16 E. Fedorovich

Fig. 8. Comparison of different Lagrangian-model parameterizations for velocity component variances with wind-tunnel andLES data of Fedorovich et al (1996; 2001a) for the sheared CBL. Asterisks and crosses present, respectively, wind-tunnelmeasurements at 2.3 m and 4.0 m downwind of the source location. The LES data at 2.3 m downwind of the source are givenby dotted lines. Dashed lines show original parameterizations of the Rotach et al (1996) Lagrangian model. Solid lines presentthe modified parameterizations

Fig. 9. Dimensionless mean concentration profiles along the plume centerline at different dimensionless distances x� down-wind of the ground-level source. The nondimensionalzation is carried out with Deardorff (1985) convective scales. TheRotach et al (1996) Lagrangian model predictions with original turbulence parameterizations and with new turbulenceparameterizations are presented by dashed and solid lines, respectively. The wind-tunnel measurements and LES calculationsare shown by markers and by short-dashed lines, respectively

Dispersion of passive tracer in the atmospheric CBL with wind shears 17

concentration profiles from the Lagrangianmodel runs with original and new turbulenceparameterizations are shown at ten locationsalong the sheared CBL in comparison withwind-tunnel and LES profiles for the case ofthe ground-level source. The comparison clearlyindicates that with modified turbulence parameter-izations implemented, the Lagrangian model ofRotach et al (1996) is generally capable of success-fully predicting dispersion from a ground source inthe atmospheric CBL with moderate surface windshear. Only at the first two locations does the modelversion with original parameterizations seem toperform better that the version with new parame-terizations. At larger distances from the source, themodel with original parameterizations consider-ably overestimates concentration values in thelower portion of the CBL. Both model versions failto reproduce the maximum in the concentrationprofile that develops at x� � 1:02. A similar max-imum within this range of distances can be identi-fied in the concentration profiles from LES.However, the vertical dispersion of tracer in LESat small distances from the source appears to be toolarge in comparison with the wind-tunnel data.This is apparently another deficiency of theemployed LES based on the Eulerian approach,(see also discussion in Sect. 4).

The main advantage of the Lagrangian LES-based dispersion modeling approach is its capa-bility to ensure, numerically, in an easier andmore predictable manner, the conservation ofmass of the tracer and its positive definiteness,and to minimize the spurious effects of numer-ical diffusion and dispersion (Nieuwstadt,1998). This feature of the Lagrangian approachmakes it especially useful for LES of disper-sion in the sheared CBL characterized by fastadvection of the tracer. Under such conditions,LES based on the Eulerian methodologyusually requires special nonlinear numericalschemes, which make its less computationallyefficient.

Recently, a LES-based Lagrangian modelstudy of dispersion in CBLs with varyingdegrees of wind shear was reported by Weilet al (2001). For simulating the CBL turbulentflow, they employed the LES code of Moengand Sullivan (1994) with the subgrid turbulenceclosure described in Sullivan et al (1994).The Lagrangian velocities of the particles were

calculated from the sum of resolved velocitiesand random subgrid-scale velocities using adetailed stochastic model of Thomson (1987).The LES runs were conducted for �zi=L ¼ 5:5(strongly sheared CBL), 16, and 106 (almostshear-free CBL). Only the case of ground-levelsource was investigated.

It was found that the curves of the normalizedmean plume (subscript p) height zp=zi versusdimensionless downstream distance X ¼ xw�=ðUziÞ for different �zi=L collapse to essentiallythe same one for X<0.1 (with zp=zi / X), butexhibit a natural ordering by stability for largerdistances. The normalized plume height for thecase of weak shear was the largest followed bythose for moderately and strongly sheared CBLs.This result is consistent with the LES data ofDosio et al (2003) obtained using the Eulerianmethod for the simulation of the tracer dispersion(see Fig. 7). In the simulated CBL case withstrong shear ð�zi=L ¼ 5:5Þ, the normalizedplume height zp=zi was following X2=3 depen-dence over the range of distances 0.25<X<0.9.This was found close to the well-knownbehavior of surface release in the neutral bound-ary layer.

The dependence of the surface crosswind-inte-grated concentration, Cy, on X showed a generalconsistency with the plume-height variation. Forweak shear ð�zi=L ¼ 106Þ, the decrease of Cy

with X (/ X�2) was greater than expected inthe absence of along-wind diffusion (/ X�5=4),which allowed Weil et al (2001) to conclude thatthis diffusion was important in the simulated weak-shear case. With strong shear ð�zi=L ¼ 5:5Þ, Cy

varied as X�2=3 within the same range of X, wherethe dependence of zp=zi on X was close to theneutral-layer behavior.

Weil et al (2001) compared their simulatedcrosswind-integrated concentrations with fielddata from the Prairie Grass and CONDORS(Briggs, 1993) experiments and found that simu-lated Cy followed the average data trend fordifferent �zi=L rather well, although there wasa considerable scatter in the field data forX>0.3.

7. Concluding remarks

The state-of-the-art laboratory and numericalmodel approaches towards the description of

18 E. Fedorovich

dispersion processes in the atmospheric con-vective boundary layer with surface and ele-vated wind shears have been reviewed. In thereview of numerical models, emphasis waslaid on the Large Eddy Simulation (LES) ofdispersion. Presently, LES is primarily usedas a scientific tool. However, one may expectthat with growing computer power, this simula-tion technique will be employed more frequent-ly as an applied research tool in dispersionstudies.

The reviewed results of laboratory and nu-merical studies have indicated that wind shearscan have a significant impact on various char-acteristics of dispersion in the CBL. Theplume height, ground-level concentration, ver-tical and horizontal dispersion parameters, andcrosswind-integrated concentrations in the CBLare all affected to a certain extent by windshears. The continued development of LESand the forthcoming implementation of DirectNumerical Simulation (DNS), which seems tobe not very remote, in the studies of atmo-spheric dispersion on surface- and boundary-layer scales, will provide researchers with dataon more detailed dispersion characteristics suchas concentration fluxes, variances, and higher-order statistics.

The analyses and interpretations of these newnumerical data will not be conclusive andcomplete without new laboratory and fieldexperimental data available for verification ofnumerical simulations. As was mentioned in theIntroduction, there were no major field experi-ments organized during the last decade specifi-cally designed to study the tracer dispersion inthe sheared CBL, and the author of this reviewhas heard of no plans within the atmospheric dis-persion community of putting together suchan experiment in the near future. Laboratorystudies of dispersion (both with water tanks andwind tunnels) are also losing ground all over theworld due to their high costs and non-attractive-ness to researchers of the younger generation,who tend to seek only numerical solutions toscientific problems. In this sense, the future ofboundary-layer dispersion studies cruciallydepends on the readiness of the scientific com-munity, and society in general, to invest moneyand effort in the adequate experimental facilitiesand programs.

Acknowledgements

The author gratefully acknowledge productive discussionswith Petra Kastner-Klein, Johannes Th€aater, and RobertConzemius in the course of preparation of this review.Many thanks also to Natascha Kljun for the plots with theLagrangian model data. The reviewed research was partiallysupported by the Deutsche Forschungsgemeinschaft (DFG)within the Project Ji 18=5 and National Science Foundation(USA) within the grant ATM-0124068.

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Author’s address: E. Fedorovich, School of Meteorology,University of Oklahoma, 100 East Boyd, Norman, USA(E-mail: fedorovich@ou.edu)

Dispersion of passive tracer in the atmospheric CBL with wind shears 21