ON WIND VELOCITY PROFILES OVER URBAN AREA. Portuguese Meteorological Institute, Lisboa, Portugal

Transcription

1 N WIND VELCIT PRFILES VER URBAN AREA lara Bezpalcova, bynek Janour, Viktor M. M. Prior 3, Cecilia Soriano 4 an Michal Strizik 5 Charles University, Dept. of Meteorology an Env. Protection, Prague, CR Institute of Theroechanics, Prague, CR 3 Portuguese Meteorological Institute, Lisboa, Portugal 4 Universitat Politècnica e Catalunya (UPC). Barcelona, SPAIN 5 LIDAR s. r. o. Prague, CR INTRDUCTIN The basic paraeters that shoul be concerne for air pollution stuies are win an teperature profiles. There have been nuerous investigations into atospheric bounary layer carrie out, but relatively few of the were carrie out in urban areas in contrast to the fact that the ost irect ipacts of air pollution are felt in cities. The continuous increase of vehicular traffic within ensely populate cities as further pressure on a eteriorating urban air quality in any towns. Therefore, in recent years, bounary-layer eteorologists attention has been irecte towars probles of surface/inertial layer. Velocity an teperature profiles over urban areas above this layer are of interest to esigners of structures, builings in towns, eteorologists etc. This topic is still consiere very coplex. nly a few engineering or icroeteorological rules are general enough to be exporte fro one city to another. The ai of this contribution is to fin a siple universal ean velocity profile for the core of the urban atospheric bounary layer (UABL). bviously the horizontally hoogeneous atospheric bounary layer belongs to the siplest cases. This layer is a theoretical case of the atospheric bounary layer (ABL) with conitions, which in reality are never satisfie siultaneously. In analogy to Wipperann (973) ABL can be efine as a Planetary Bounary Layer (PBL), if: The bounary-layer flow is turbulent, The ean flow an the turbulence properties are stationary, The ean flow an the turbulence properties are horizontally hoogeneous. RSSB SIMILARIT The siplest oel of UABL consists in consiering that the flow over an urban area is siilar to the flow over a rough surface, with a given, large, roughness length z an a efine surface heat flux. In this way we shall oel the UABL as the PBL over a rough surface. Let us non-iensionalize the equations by using the friction velocity u* an the internal scale height of the PBL Hκu*/f., where κ is von áran constant an f enotes the Coriolis paraeter. The equations of otion in tangent-plane co-orinates with the Boussinesq assuption on ey viscosity can be transfore into following for:

2 + x () + y ( ) with (, µ ) following bounary : conitions ( 3 ) : x ( 4 ) yy ( 5 ) ( 6 ) : ( 7 ) (8 ) ( 9 ) Here are: z/h, /(H f), UU/u*, VV/u*, τ x /(ρu* ), τ y /(ρu* ), x U g /, y V g / an µ is a stability paraeter. The set of equations () (3) an bounary conitions (4) (9) epens on three internal paraeters - x, y,, µ. The lower bounary conitions epen on noniensional roughens length: with /(κc g Ro ) () Vg u * Ro an cg () fz V Here the surface Rossby-nuber epens on a non-iensional cobination of the external paraeters V g, f an z. If woul be zero (Ro ) an ey viscosity shoul satisfy the conition ( Ro ) g, () the syste woul be inepenent of Ro, i. e. the profiles (), () an () ust be inepenent on Ro. This is calle Rossby siilarity an the profiles (, x, y, µ), (, x,

3 y, µ), (, x, y, µ) an the iensionless velocity efect coponents κ(u-u g )/u*, κ(v- V g )/u* are universal. However the roughness length is ifferent fro zero an the Rossby siilarity is not existent in the low layer, which has the epth b in the orer of the roughness length an it shoul be relate to the blening height. To assess this epth Wiperann (97) ixing length hypothesis has been use an nuerical solution for varying roughness length an for ifferent theral stratification has been perfore see Janour, Benes(). The exaple of the noniensional Reynols stress profiles for ifferent roughness length is shown on Fig..... e-5 e-6 e-7 ze-7, ze-3, z5e-, ze-, e-8 e-7e-6e a).... e-5 e-6 ze-7, ze-6, ze-5, ze-4, ze-3, e-7 e-7 e-6 e b) Fig. Plot of function -τ/ρu* for a) unstable, b) extreely stable stratification All eterine profiles coincie in the upper part, which eans that the Rossby siilarity exists there. The profiles are splitte in the lower part the Rossby siilarity is not existent. It can be assesse that the height b, where the Rossby siilarity exists, is roughly b,ax (3) The CFD coe Fluent with k- ε oel of turbulence was use to assess the influence of the roughness length too see ozubkova, Drabkova (). The noniensional velocity efect stress for ifferent roughness length (inifferent stratification) is eonstrate on Fig. eonstrating the qualitative siilar results /Hb,,, , agebraic oel Fig. Win efect profiles for ifferent roughness lengths height over the groun at which the groun inhoogeneity is not perceive, over which the various IBLs erge into a layer having an horizontally hoogeneous structure

4 Let us efine the epth b corresponing to bounary layer thickness δ as that istance for which ifference of velocity efect for rough surface with an for sooth surface is less than n%. The estiation of the blening height fro CFD ata are plotte in Fig. 3. blening height assessent DELTA[-],4,3,,,,, [-] DELTA% DELTA5% DELTA% Fig. 3. Blening height b assessent CMPARISN WITH EPERIMENTS There have been relatively few available experients perfore in urban areas to test the above-introuce urban velocity profile: Jones et all. (97) use a captive balloon to carry easureent instruents for win an other eteorological agnitues above Liverpool urban area. The bounary layer epth an the epenence of power-law inex on stratification ha been assesse; Dobbins (976) selecte ata fro low-level sounings over Cabrige, U. S. A. an eterine the ata on the basis of an Ekan-like variation of the win vector with altitue; raiosouning launche by SERVEI DE METERLGIA DE CATALUNA (Catalan Meteorological Service) in Barcelona; raiosouning launche by INSTITUT e METERLGIA (Portugal hyroeteorological institute) in Lisboa, Èvora an Neves Corvo; SDAR (an LIDAR) easureents for win (an concentrations) above Prague for CST 75 project by LIDAR s. r. o., CR. Exaples of preliinary coparisons of our siulation with above-entione results are presente on Fig. 4 an 5 for inifferent stratification. /Hb,9,8,7,6,5,4,3,, nu erical si ulation pow er ean profile Fig. 4 Coparison of velocity efect profiles insie the UABL siulation with raiosouning launche in Barcelona.

5 /Hb,9,8,7,6,5,4,3,, Lisboa-65 LISBA-64 LISBA-64 LISBA-69 LISBA-668 LISBA-678 nuerical siulation ean profile Fig. 5 Coparison of velocity efect profile insie the UABL siulation with raiosouning launche in Lisboa. CNCLUSINS The horizontally hoogeneous atospheric bounary layer over rough surface with a large, roughness length z has been investigate to oel the siplest cases of the UABL over flat plain. The Rossby siilarity has been eonstrate for the core of the urban atospheric bounary layer (UABL). It eans that the profiles (, x, y, µ), (, x, y, µ), (, x, y, µ) an velocity efect coponents κ(u-u g )/u*, κ(v-v g )/u* are universal an inepenent on surface characteristics for > B. It can be conclue that the Rossby siilarity cannot be use for non-iensional coponents of the velocity. The conclusion is in contrast to Rafailiis (997) results that conclue fro win tunnel siulations that the win above an urban fetch is influence by the presence of the builings only within 3 cobine builing heights above groun. The altitue of the Rossby siilarity lower liit corresponing to the blening height was estiate. Coparisons of our siulation with epirical results pointe out coplexity of the topic, e. g.: scattere raiosouning ean velocity efect profiles (averaging tie T~ inute) are copare with the siulate ones (T~5 inutes). Artificial ean profile eterine fro the ata sets sees to be ore suitable for coparison - see fig 5; influence of topography is ore iportant across the Barcelona Internal-Sub-Layer - see fig. 4. REFERENCES Dobbins R. A.,977: bservations of the Barotropic Ekan Layer over an Urban Terrain, Bounary_layer Meteorology, Janour., Benes M., : Nuerical siulation of the Planetary-Bounary-Layer Equations, Workshop on Urban Bounary Layer Paraetrisations, űrich. Jones P. M., e Larringa M. A. B., Wilson C. B., 97: The Urban Win Velocity Profile, Atospheric Environent 5, 89. ozubkova M., Drabkova S., : Influence of the wall roughness on the win profile an concentration of pollutants in the atosphere, Seinar Topical probles of flui echanics, pp Wipperann F., 97: Epirical Forulae for the Universal Functions M (µ) an N(µ) in the Resistance Law for Barotropic an Diabatic Planetary Bounary Layer, Beitrage zur Physik er Atosphere, 45, Wipperann F.: 973: The Planetary Bounary Layer of the Atosphere, Deutscher Wetterienst.