Interference effects on wind loading of a row of closely spaced tall buildings

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Journal of Wind Engineering and Industrial Aerodynamics 96 (2008) 562–583 www.elsevier.com/locate/jweia

Interference effects on wind loading of a row of closely spaced tall buildings K.M. Lam, M.Y. H. Leung, J.G. Zhao Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong Received 6 November 2006; received in revised form 5 January 2008; accepted 18 January 2008 Available online 18 April 2008

Abstract Interference effects on a row of square-plan tall buildings arranged in close proximity are investigated with wind tunnel experiments. Wind forces and moments on each building in the row are measured with the base balance under different wind incidence angles and different separation distances between buildings. As a result of sheltering, inner buildings inside the row are found to experience much reduced wind load components acting along direction of the row (x) at most wind angles, as compared to the isolated building situation. However, these load components may exhibit phenomena of upwind-acting force and even negative drag force. Increase in x-direction wind loads is observed on the upwind edge building when wind blows at an oblique angle to the row. Other interference effects on y-direction wind loads and torsion are described. Pressure measurements on building walls and numerical computation of wind flow are carried out at some flow cases to explore the interference mechanisms. At wind angle around 301 to the row, wind is visualized to flow through the narrow building gaps at high speeds, resulting in highly negative pressure on associated building walls. This negative pressure and the single-wake behavior of flow over the row of buildings provide explanations for the observed interference effects. Interference on fluctuating wind loads is also investigated. Across-wind load fluctuations are much smaller than the isolated building case with the disappearance of vortex shedding peak in the load spectra. Buildings in a row thus do not exhibit resonant across-wind response at reduced velocities around 10 as an isolated square-plan tall building. r 2008 Elsevier Ltd. All rights reserved. Keywords: Interference effect; Wind loads; Wind pressure; Sheltering; Channeling; Wind tunnel testing

Corresponding author. Tel.: +852 2859 1975; fax: +852 2559 5337.

E-mail address: [email protected] (K.M. Lam). 0167-6105/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jweia.2008.01.010

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1. Introduction When two or more buildings are placed in close proximity, flow interference occurs and wind loads on each building are modified from its isolated single building situation. Interference effects on wind loading of buildings have been reported in the literature for decades, see Khanduri et al. (1998) for a review. Most investigations were based on wind tunnel experiments and the building configuration being most extensively studied is two square-plan building models placed in different relative positions. Earlier studies used rigid models where mean wind pressures and wind forces were measured (e.g., Blessman and Riera, 1979; Saunders and Melbourne, 1979; Hussain and Lee, 1980; English, 1985). Dynamic behaviors are important for tall buildings so that in later studies, wind-induced dynamic response and loading of buildings were investigated (e.g., Bailey and Kwok, 1985; Taniike, 1992; Zhang et al., 1994). Measurements were made with lumped-mass aeroelastic models (Bailey and Kwok, 1985; Zhang et al., 1994) or through the base-balance technique (Taniike, 1992). A number of important findings on interference have been obtained from the wealth of past studies even though they involved two buildings only. The most common interference mechanisms include sheltering effect, flow channeling, flow asymmetry and wake buffeting. An upstream building generally provides shielding on the downstream building. This normally leads to reduction of mean along-wind force on the downstream building. However, fluctuating wind force may become larger due to turbulence buffeting (Bailey and Kwok, 1985). Presence of a neighbouring building introduces asymmetry in wind flow pattern around the test building, leading to possible highly magnification of wind-induced torsion (Zhang et al., 1994). An upstream building is generally little affected by a downstream building but when two buildings are in very close proximity, wind flow is channelled to sweep through the building gap. Highly negative wind pressure is produced on corresponding building walls and this may modify the wind forces on the upwind building. Interference effect is found to depend on upstream terrain type, with more pronounced effects on a more open exposure (Kareem, 1987). While it is accepted that interference effects depend on the arrangement pattern of buildings and the wind incidence direction, most investigations only reported results for wind incidence normal to the buildings. The building separations being studied were mostly larger than one building width. A notable exception is the experiments of Sakamoto and Haniu (1988) in which forces were measured on two square prisms in a turbulence boundary layer. While tests were limited to flow at normal incidence to the prisms, the two prisms were placed in a large number of relative positions in the tandem, side-by-side and staggered arrangement with a prism separation varying from almost zero to over 10 prism breadths. In the tandem arrangement, the upstream prism was found to experience reduced drag force with the presence of the downstream prism at a clear separation (S) larger than one prism breadth (B). However, when S/Bo1, the drag force on the upstream prism was found to be much larger than the single prism value. Suppression of vortex shedding from the upstream prism was also observed at this close separation. In the side-by-side arrangement, the drag forces on the prisms were found to have the smallest value when S/B is near to 1. At this value of S/BE1, the prisms also experienced the largest lift. The findings in that study suggest that the interference behavior between two buildings at S/Bo1 is different than that at a wider separation.

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High-rise residential developments comprising similar-shaped tall buildings in close proximity are increasingly common in Asian metropolitan cities. Similar-shaped buildings are quite often arranged side-by-side in a row along the coast or harbor front with a separation between neighboring buildings less than one building width. A recent investigation on this building group configuration (To and Lam, 2003) has revealed some interesting interference effects not previously observed in past investigations on two buildings at a larger separation. The present paper reports detailed results further to that preliminary study. The object of study is a group of closely spaced square-plan tall buildings arranged in a row. Interference effects are investigated for every building in the row at all possible wind incidence angles and for a number of clear building separations, all not larger than half the building width. The emphasis on close separations between the buildings is based on the findings of Sakamoto and Haniu (1988) that there may exist unique interference mechanisms different from those at wider building separations. There are two possible arrangement patterns of buildings in the row: parallel side-by-side pattern and diamond diagonal-by-diagonal pattern. This paper reports results of the parallel pattern while results of the diamond pattern will be reported in a future paper. It is expected that the results will provide a database of wind loading of a group of tall buildings in close proximity. The present paper also attempts to explore the interference mechanisms through pressure measurement and computational fluid dynamics (CFD) study.

2. Experimental techniques Experiments were carried out in the boundary layer wind tunnel in the Department of Civil Engineering at the University of Hong Kong. The working section was 3.0 m wide and 1.8 m tall. Simulation of natural wind was achieved using triangular spires and 8 m long fetch of floor roughness elements. The minimum configuration of five buildings was chosen as the representative pattern of a row of identical tall buildings. Wind load measurements were made on the center building, the edge building and the second building to cover all typical locations of a building in the row. For easy reference, these building models were labeled A, B and C (Fig. 1). All building models had a square-plan form of breadth B ¼ 10 cm. The height-to-breadth ratio was H/B ¼ 5. The target geometric scale was 1:300, so that the models represented full-scale buildings of height 150 m and width 30 m. ¯ H  6:5 m/s at roof height of the buildings was used in the wind A wind speed at U ¯ H B=n ¼ 4:3  104 . For wind tunnel testing of tunnel tests. The Reynolds number was U sharp-cornered bodies or building models, this was generally accepted to be sufficiently high for flow independence on Reynolds number although some fine flow details may still My y, Fy

y + face

x,Fx

Wind angle θ

A y − face

B

Mz

C

Mx S

B

Fig. 1. Buildings in a row: definition of wind loads and wind direction.

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1.2 Height above wind tunnel floor,z/H

Height above wind tunnel floor,z/H

1.2 1.0

565

power exponent = 0.15

0.8 0.6 0.4 0.2 0.0 0.7 0.8 0.9 1.0 Mean velocity,U/UH Non-dimensional spectral density, nSuu / σu2

0.6

1.1

1.2

power exponent = -0.3

1.0 0.8 0.6 0.4 0.2 0.0 0.05

0.10 0.15 Turbulence intensity

0.20

0.3 ESDU (Lu,x = 0.23m)

0.2

0.1

0.0 10-1

2

3 4 5 5 67 100

2

3 4 5 6 78

2

101

Frequency / mean wind speed, n/U, m-1 Fig. 2. Wind characteristics in wind tunnel: mean wind speed profile, turbulence intensity profile and turbulence spectrum.

be affected by Reynolds number. Fig. 2 shows the wind characteristics measured in the wind tunnel. Mean wind speed profile followed well the power law with a power exponent 0.15. The turbulence intensity varied from a value of about 0.20 near ground to about 0.10 near roof height. These simulated wind conditions were typical of the open land terrain. Turbulence spectrum measured at 1 m height is shown in Fig. 2c and it gave a best-fitted integral scale of turbulence at Lu,xE0.23 m in the wind tunnel. It is known that interference effects are stronger in the open land terrain and weaker in the city terrain. Rows of tall buildings are commonly found in sub-urban residential areas as well as along a coastline or harbor front in rather exposed sites. Thus, the open land terrain was chosen in this study.

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The clear building separation S between two adjacent buildings was a fraction of the building breadth. Tests were carried out at four values of S ¼ {0.5B, 0.25B, 0.125B, 0.1B}. Mean and fluctuating wind loads on individual buildings in the row were measured with a six-component force balance (JR3 Inc.) mounted at the building base. The loads include base shear forces Fx, Fy, and base overturning moments, Mx, My, along body axes (x–y) of the building and torsion Mz about the central vertical axis (Fig. 1). Loading coefficients were used for presentation of wind loads: base shear forces as force coefficients, C F x , C F y , base overturning moments as moment coefficients C M x , C M y , and torsion as C M z : CFx ¼

Fx , ¯ 2H BH ð1=2ÞrU

(1)

CMx ¼

Mx , ¯ 2H BH 2 ð1=2ÞrU

(2)

CMz ¼

Mz . ¯ 2H B2 H ð1=2ÞrU

(3)

Mean loading coefficients were denoted by an over-bar, such as C¯ F x . Root-mean-square (rms) values of force or moment fluctuations were used to derive rms loading coefficients such as C 0F y . In order to understand the generation mechanism of wind loads, measurements of wind pressure on building walls and computation of wind flow by CFD were carried out for some flow cases. The building model for pressure measurement was equipped with 35 pressure taps on each of the four building walls. The taps on a wall were evenly distributed into seven levels and five taps per level. Pressure at all 140 taps on a building model was measured with a multi-point pressure scanning system (with electronic pressure scanners from PSI, Inc. and acquisition unit from Aeroprobe, Inc.). The main purpose of CFD was to visualize the mean wind flow pattern around the building group so as to explore the mechanisms of building interference. Details of the CFD approach had been described in Lam and Zhao (2006) and Lam and To (2006). To reduce the number of computational cells, a row of three buildings was modeled in the computation. A finite volume code FLUENT (Fluent, Inc.) was used to compute the threedimensional turbulent wind flow around the buildings. Turbulence closure was based on the Re-Normalization Group (RNG) k–e model (Yakhot and Orszag, 1986). The computational domain had the size of wind tunnel section at 3 m wide and 1.8 m tall. The length extended from 1.5 m upwind from the center of the building group to 4.5 m downwind. Each building wall was modeled by 40  20 meshes and there were 12 grid points across the width of each building gap. A total of 2.1  106 finite volumes were used to digitize the whole computational domain. For the boundary conditions, the top and two vertical sides of the computation domain were treated with the symmetry plane boundary condition. This boundary condition which specified zero normal velocity and zero normal gradient of flow variables across the boundary was used to simulate the far field flow situation. The ground was modeled as a solid wall with a value of aerodynamic roughness length zo ¼ 0.125 cm, wind tunnel scale. At the inlet face to the computational domain, both mean wind velocity and turbulence intensity varied with height following the power-law profile as in the wind

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tunnel. The power exponent was 0.15 and 0.30, respectively (Fig. 2). For turbulence boundary conditions, turbulent kinetic energy, k ¼ ð1=2Þðs2u þ s2v þ s2w Þ, was obtained from the along-wind turbulence intensity and assuming sv, sw, respectively, at 0.7 and 0.5 times the along-wind su value (s being standard deviation of velocity fluctuations). 3=2 Turbulence dissipation rate e was calculated from  ¼ ðC 3=4 =0:4zÞ with model constant m k Cm ¼ 0.0845. More details can be found in Lam and To (2006) and Lam and Zhao (2006). 3. Results and discussion 3.1. Mean wind loads Fig. 3 shows the variations of mean loading coefficients with wind angle y for Buildings A, B and C. Results at all four values of S/B are shown together with the results of an isolated single building. Moment coefficients are not shown because the wind-angle ¯ M y ðyÞ is almost identical to that of C¯ F x ðyÞ, while C ¯ M x ðyÞ has the same pattern variation of C ¯ as C F y ðyÞ. Therefore, later discussion is made mainly on the shear forces. ¯ F x ðyÞ and C ¯ F y ðyÞ are identical For an isolated single building, wind-angle variations of C but shifted in y by 901. The variation is similar to a sine or cosine curve except for the S/B = 0.5

CFx

Isolated

S/B = 0.25

S/B = 0.125

1

1

1

0

0

0

-1

-1

-1

0

90

180

0

90

180

1

1

0

0

0

0

90

180

0

90

180

0

90

180

CFy

1

S/B = 0.1

C Mz

0

90

180

0

90

180

0.1

0.1

0.1

0.0

0.0

0.0

-0.1

-0.1

-0.1

0

90

180

0

90 180 Wind angle,  (deg.)

Fig. 3. Mean wind load coefficients: variation with wind angles and effects of building separation. a: Building A; b: Building B; c: Building C.

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presence of a low-level crest and trough of body force within 7151 from normal incidence. This has been observed in uniform flow over a square cylinder and is caused by re-attachment of separated flow on only one face of the cylinder (Obasaju, 1983). The same form of variation of body forces on a square-plan building model has been reported (Cook, 1990; Blessman and Riera, 1979). The largest force coefficient occurs at normal incidence and has a value about 1.5. The averaged wind speed along the building height is used to derive that force coefficient. Values in Fig. 3 are based on wind speed at building ¯ F x ðy ¼ 0Þ is slightly above 1.0. The torsion C¯ M z ðyÞ exhibits a variation roof height and C similar to the sin(2y) form (Cook, 1990). The largest value here is about 0.08 and the reported value based on height-averaged wind speed was slightly above 0.1 (Cook, 1990). When the building is placed in a row, Fig. 3 shows clearly that its wind loading behavior is modified significantly. Modifications occur mainly on wind load components along x-direction, that is direction along the row. Wind load components along y-direction, Fy and Mx, are also modified, although to a lesser degree. Another evident observation in Fig. 3 is that very similar patterns and levels of wind load modifications from the isolated single building case are found at the four building separations between S/B ¼ 0.1 and 0.5, ¯ F x ðyÞ for all especially for wind loads along x- and y-directions. Curves of C¯ F x ðyÞ and C four values of S/B lie very close to each other, and with narrower separations producing slightly more significant interference effects. For brevity, later discussion on the identification of relevant wind load interference phenomena is mainly based on test results at S/B ¼ 0.25. ¯ M z ðyÞ. For Building A at the Placing a building in a row leads to large changes in torsion C edge, all building separations lead to similar modifications to the moment variation with wind angle, with gradually more pronounced interference effect at a narrower building separation. Buildings inside the row experience lower values of torsion and different building ¯ M z ðyÞ. separation appears to result in different patterns of modifications to C 3.2. Upwind interference on edge building ¯ F x is larger than the isolated single building situation at y between 151 On Building A, C and 451, with the maximum percentage increase between 10% and 25% for the range of S/ B being studied (Fig. 3). At these wind angles, Building A is the edge building at windward end of the row. Few studies on interference effects have reported similar wind load increase on an upwind building at a slight oblique angle of wind incidence. Wind pressure measurement and CFD results can serve to explain this interference phenomenon. Fig. 4 shows the computed wind flow pattern around a row of three buildings on the horizontal plane at mid-height of the buildings. Wind angle is y ¼ 301 and S/B ¼ 0.25. With the buildings so close together, wind flows around the buildings as if they were a single body and the wake behind the row is like a single body wake. However, some wind flow does sweep through the two building gaps at high velocities. This results in highly negative pressure (suction) on the building walls facing the gaps. The left panel of diagrams in Fig. 5 shows the distributions of wind pressure measured on the walls of Buildings A, B and C at y ¼ 301 and S/B ¼ 0.25. The pressure is presented as mean pressure coefficients: C¯ p ¼

p¯ 2

¯H ð1=2ÞrU

.

(4)

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Fig. 4. Computed wind flow pattern around a row of three square-plan buildings at y ¼ 301: CFD velocity vectors on horizontal plane at half building height.

¯ p i are also shown in the figure, as well as in The wall-averaged pressure coefficient values hC Table 1, for each building wall. Wind pressure data are also available from the CFD results in Fig. 4. Computed distributions of C¯ p on walls of the first, second and third buildings are included in Fig. 5, in the right panel. The numerical approach is not expected to be capable of making accurate computation of the pressure on building walls and these data only serve to show the wind pressure distribution pattern and to provide comparison with the more accurate pressure measurement data in the wind tunnel. The location of the first building in the CFD model and the interference effect on it being the edge building in a row should be similar to Building A in the wind tunnel. This similarity is observed in Fig. 5 although negative pressure measured on the rear walls is clearly more negative than the CFD data. Inevitably, there are differences in details of patterns between the pressure contours from measurements (which are drawn from 35 measurement points on one building wall) and the much smoother contours from CFD (which are based on 800 grid points on a building wall). In Fig. 5, the highly negative pressure at the rear wall of Building A is confirmed by pressure measurement. As shown in Table 1, the highly negative wall-averaged pressure coefficient on this wall combines with positive pressure on the front wall to produce a shear ¯ F x ¼ 1:37 which agrees well with the force-balance value (Table 1). force on Building A at C If this were an isolated single building, negative pressure on the rear wall would be much lower in magnitude. Thus, the first upwind edge building experiences an increased value of ¯ F x as compared to the isolated single building. C 3.3. Sheltering effect Sheltering offered by an upwind building is probably the most widely reported interference phenomenon, leading to reduced wind loads on a downwind building. In the

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K.M. Lam et al. / J. Wind Eng. Ind. Aerodyn. 96 (2008) 562–583 1st building (CFD)

y+ (-0.45)

Front (+0.55)

y− (+0.33)

Rear (-0.82)

y+ (-0.50)

Front (+0.63)

y− (+0.27)

Rear (-0.70)

y− (+0.24)

Rear (-0.62)

y− (+0.09)

Rear (-0.44)

2nd building (CFD)

y+ (-0.34)

Front (-0.56)

y− (+0.37)

Rear (-0.73)

y+ (-0.41)

Front (-0.51)

3rd building (CFD)

y+ (-0.29)

Front (-0.46)

y− (+0.32)

Rear (-0.67)

y+ (-0.40)

Front (-0.45)

Fig. 5. Mean pressure coefficients on building walls, y ¼ 301, S/B ¼ 0.25. Left panel: from wind tunnel measurement and right panel: CFD. Wall-averaged pressure coefficient shown in parenthesis for each wall. a: Building A; b: Building B; c: Building C.

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Table 1 Measured wall-averaged pressure coefficients and force coefficients Building, wind angle

(a) Along x-direction A, 301/1st B, 301/2nd C, 301 A, 1501/3rd (Single building, 301)

(b) Along y-direction A, 301/1st B, 301/2nd C, 301 A, 1501/3rd

Average Cp on wall

CF x

Front

Rear

Pressure

Balance

CFD

0.55 0.56 0.46 (0.45) 0.55

0.82 0.73 0.67 (0.44) (0.44)

1.37 0.18 0.21 – –

1.22 0.17 0.18 0.07 0.95

1.33 0.11 – 0.01 0.99

Average Cp on wall

CF y

y face

y+ face

Pressure

Balance

CFD

0.33 0.37 0.32 (0.09)

0.45 0.34 0.29 (0.40)

0.78 0.71 0.62 –

0.64 0.68 0.56 0.46

0.77 0.65 – 0.49

Wall-averaged pressure coefficients in parenthesis are from CFD.

present case of five buildings in a row, sheltering mainly affects x-direction wind loads ¯ F x ðyÞ on Buildings B and along the row. It is obvious from Fig. 3 that while variations of C C with wind angle remains grossly similar to that of an isolated single building, the magnitudes are greatly reduced to less than 20% of the latter. At yo901, similar levels of ¯ F x are observed on Buildings B and C, suggesting that one or two upwind reduction in C buildings produce similar degree of protection. When wind blows at y4901, Building B is protected by three upwind buildings on the other side of the row, yet it experiences almost the same level of C¯ F x reduction. Sheltering effect offers protection on inner buildings in the row at all wind angles. The velocity vectors in Fig. 4 can serve to reveal the wind flow pattern around a protected building at y ¼ 301. The second building in the CFD model represents Buildings B or C. Either of its two x-faces is facing a building gap through which high-speed wind flow sweeps. Highly negative wind pressures are produced on both faces as confirmed by the measured ¯ p ¼ 1:0 to  0:9 pressure contours in Fig. 5. For Building B, negative pressure as low as C is measured on its front and rear walls which face a building gap. As shown in Table 1, the wall-averaged pressure coefficient measured on the windward x-face has a less negative value than that on the leeward wall. The combined result is a small force coefficient at C¯ F x ¼ 0:18 which matches very well the force-balance value in Fig. 3. The walls of Building C facing a ¯ p ¼ 0:9 to  0:8. The resulting force gap experience negative pressure as low as C ¯ F x ¼ 0:21. coefficient from the measured wind pressure data is C 3.4. Upwind shear force; negative drag The CFD model in Fig. 4 also represents interference on the edge building in the row at y ¼ 1501 when the most downwind building is taken as Building A. For this third building

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in CFD, the windward x-face (left face in Fig. 4) is under highly negative pressure due to channeled flow through the building gap. Wall-averaged pressure coefficient on it, labeled ¯ p i ¼ 0:45. The other x-face is the outermost building face in the front wall in Fig. 5, is hC row. It is inside the single body wake behind the row of buildings and is only under lowlevel negative pressure at hC¯ p i ¼ 0:44. This means that the windward wall of this building is actually under a higher suction or negative pressure than the leeward wall. This produces ¯ F x ¼ 0:01 acting upwind. an x-shear force which acts upwind and the computed value is C From Fig. 3, this phenomenon of upwind shear force occurs on edge Building A at ¯ F x has small positive values, meaning that Fx is wind angle between 1001 and 1601. C acting towards Building B. This is of the opposite sign as the isolated building case. For S/B ¼ 0.25, value of C¯ F x from force measurements is 0.07 at y ¼ 1501 and reach up to 0.2 around y ¼ 1201. Fig. 6 shows the mean drag and lift forces on the buildings which are derived from the measured mean values of Fx, and Fy. For Building A under the above-described phenomenon of upwind shear force, the mean drag force drops to very low values at y between 1501 and 1701. A more striking observation is that for Building B, the mean drag force even becomes negative at y between 01 and 51. It is believed that at this wind incidence almost parallel to the row, wind flow separates at Building A, and all downwind buildings as well as the building gaps are inside the wake of Building A. Pressure at a point inside the wake depends on its distance from the separated shear layers which extends from the windward edges of Building A. Both windward and leeward walls of Building B are under negative wake pressure but the negative pressure inside the first building gap, between Buildings A and B, is slightly higher than that inside the farther downwind gap. Therefore, the drag force, as well as Fx, on Building B near y ¼ 01, acts upwind. Fig. 3 further shows that this negative drag on Building B near y ¼ 01 becomes larger in magnitude as the building gaps gets narrower. This is because at smaller values of S, windward wall of Building B is nearer to the shear layer and is thus under higher negative pressure. Building C is much farther downstream of flow separation at Building A. Its windward and leeward walls are under negative pressure of similar levels. Thus, negative drag does not occur on Building C which is under very small values of drag or Fx.

Isolated A

B C

1

CL

CD

1

0

0

-1 0

90 Wind angle,  (deg.)

180

0

90 Wind angle,  (deg.)

Fig. 6. Variation of mean drag and lift coefficients with wind angles, S/B ¼ 0.25.

180

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3.5. Shear force normal to the row The other shear force component Fy acts in the direction normal to the building row. Less dramatic interference effects are observed in Fig. 3 as compared with x-direction wind loads. Buildings B and C are found to experience slightly larger Fy than an isolated single building at 301oyo1501. At y ¼ 0–301 and 150–1801, C¯ F y on the two inner buildings are greatly increased in magnitude. The wind-angle variations remain grossly symmetrical ¯ F y ðyÞ is not symmetrical about y ¼ 901. When about y ¼ 901. For Building A on the edge, C it is at the upwind edge of the row, that is yo901, it experiences an increased lateral shear ¯ F y value of 0.1–0.25. At 901oyo1501, when the force over the isolated building case by a C building is at leeward edge of the row, Fy is much reduced. The change of Fy from negative to positive for y going from 01 to 151 for an isolated single building is not observed for any of the three buildings. This suggests that when a building is placed in a group, reattachment of the separated shear layer at small wind angles cannot occur. As shown in Fig. 4, Fy on a building is due to wind pressure on its two sidewalls, y+ and y faces. Flow patterns at y ¼ 301 show that while most wind flow hits on the windward x-wall of the first building (corresponding to Building A), there is also flow onto the y faces of the buildings (lower building faces in Fig. 4). Fig. 5 and Table 1 show that positive pressure is measured on these walls of Buildings A, B and C. The y+ sides of buildings are in the wake of the row. Separation occurs at the upper corner of the first building and induces highly negative wake pressure on the nearest building face which is the y+ face of Building A. Less negative pressure is induced on y+ faces of the more downstream Buildings B and C which are farther away from the separation shear layer. As shown in Table 1, combination of pressure measured on the two y-faces produces force ¯ F y ¼ 0:78, 0.71 and 0.62, respectively, on Buildings A, B and C. These coefficients at C values agree reasonably well with the force-balance results. The third building in Fig. 4 corresponds to Building A at the opposite wind incidence of y ¼ 1501 where reduced Fy is found. If this third building were alone, flow would separate at its upper corner, producing highly negative pressure on its y+ face. But it is now downwind of other buildings and far from the separation shear layer at upwind edge of the building row. Thus, its y+ face is only under low magnitudes of negative wake pressure. Furthermore, positive pressure on its y face is lower than the more upwind buildings or an isolated building. The resulting Fy is therefore reduced significantly. CFD value is ¯ F y ¼ 0:41 (Fig. 5) and the base-balance data at y ¼ 1501 has an agreeing value at 0.46. C 3.6. Torsional moment ¯ M z ðyÞ exhibits a curve of On an isolated square-plan building, mean torsion coefficient C the sin(2y) form (Fig. 3). At normal wind incidence, mean torsion is zero because of the symmetric flow situation. As the wind angle increases from zero, a positive mean torsion starts to develop. This is caused by two effects as shown by the sketches in Fig. 7a. Firstly, the positive wind pressure on the windward wall develops an asymmetrical distribution. At yo151, for instance, wind hits obliquely on the left wall of the first building sketched in Fig. 7a. The distribution of positive pressure on this wall is asymmetrical with more positive pressure acting on the lower side. This results in a counter-clockwise torsion on the ¯ M z 40 (Fig. 3). Secondly, at this slightly oblique wind incidence, flow building, that is C separates at the two adjacent windward building corners but the separation shear layer

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−

+

0 <  < 15°

A

B

++

75° <  < 90°

C ≈0

All wind directions Fig. 7. Sketch of postulated wind pressure pattern on building walls leading to torsion: (a) isolated single building and (b) row of five buildings.

from the lower corner is nearer to the building lower sidewall as compared with what happens on the upper sidewall. The front part of the lower sidewall is thus under a higher negative pressure than that of the upper sidewall. This results in another contribution to counter-clockwise torsion. As observed in Obasaju (1983), this pattern of separation occurs only at yo151 after which flow separates from two opposite corners of the building instead. This explains why the torsion reaches the largest positive value at wind angles y ¼ 151 (Fig. 3). Similar flow behavior occurs around the other wind quadrants and thus peak positive and negative mean values of torsion occur at wind angles y ¼ 07151 and 907151. ¯ M z ðyÞ on Building A remains positive at For a group of buildings, Fig. 3 shows that C nearly all wind angles and with larger magnitudes than an isolated single building at most wind angles. As sketched in Fig. 7b, there is channeled flow through the gap between Buildings A and B at nearly any wind incidence. Highly negative pressure is induced on the right (rear) wall of Building A. Fig. 5 shows that distribution of pressure on this wall is highly asymmetrical with very high negative pressure near the windward edge. This always produces a large counter-clockwise (positive) torsion on Building A which dominates over contributions from the other three exposed walls. This contribution from the gap wall will be greater as the gap spacing becomes smaller and thus the observed effect of S/B in Fig. 3. Inside the row, Buildings B or C have both two opposite x-faces exposing to channeled gap flow. There is little combined contribution to wind torsion. On the exposed y faces of these buildings, Fig. 4 suggests that wind is directed to flow more along the row than impinging onto the buildings. This reduces the asymmetry of positive pressure distribution of that wall (Fig. 5). It is thus observed in Fig. 3 that wind torsion has very small values on the inner buildings at all wind angles. 3.7. Comparison with available past data There is a wealth of building interference data in the literature but most data are for two square-plan buildings with gap separations mostly larger 0.5B and in either in-line or

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Lift

Drag

1.0

B

A

Interference Factor (IF)

Interference Factor (IF)

A

0.5 B 0.0

1.0 Drag A 0.5 Lift

0.0

-0.5

-0.5 0

2 S/B

4

0

2 S/B

4

Fig. 8. Comparison of present data with past wind tunnel data. Open symbols and curves: past data (Khanduri et al., 1998); solid symbols: present data.

side-by-side arrangement. Khanduri et al. (1998) reviewed these data and proposed best-fit curves for interference effect. Their curves and data used are reproduced in Fig. 8 and ¯ F z and C ¯ F y at y ¼ 01 and 901. For clarity, only results compared to the present results of C at the wider gap separations S/B ¼ 0.25 and 0.5 are plotted. The interference factor (IF) is used to quantify changes in wind loads. It is the ratio of wind load on the building being in a group over wind load on an isolated single building. It is evident that the present data fall within ranges of variation of past data. Blessman and Riera (1979) reported mean wind load data on two tall buildings with separation as small as 0.1B. Measurements were made at wind incidence over full 3601 ¯ F y ðyÞ at S/B ¼ 0.25 in their Fig. A.2 provide a cross directions. Curves of C¯ F z ðyÞ and C reference to the present data on Building A in Fig. 3. Without reproducing their curves, two sets of data are found to show good agreement between each other. 3.8. Fluctuations of wind loads In addition to mean wind loads, fluctuating components are equally important. Fig. 9 shows rms loading coefficients of C 0F z ðyÞ, C 0F y ðyÞ and C 0M z ðyÞ. They represent fluctuations of wind-induced exciting forces only and do not include dynamic magnification of wind loads from wind-induced vibration of the buildings which will be discussed later. For the isolated single building, wind load fluctuations in along-wind direction come primarily from turbulence buffeting and those in across-wind direction from vortex shedding. Vortexinduced load fluctuations are evident from the peaks in the C 0F z ðyÞ curve at y around 901 and in C 0F y ðyÞ at y around 01 and 1801. For buildings in a row, rms wind loads along x-direction are always much lower than the single building case except for Building A at yo901. As discussed earlier, upwind interference effect is found on Building A at y around 301 leading to increased mean x-direction wind loads. The main cause is highly negative

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C'Fx

Isolated

S/B = 0.25

S/B = 0.5

0.3

0.3

0.3

0.2

0.2

0.2

0.1

0.1

0.1

0.0

0.0 0

90

180

S/B = 0.1

0.0 0

90

180

0.3

0.3

0.2

0.2

0.2

0.1

0.1

0.1

0

90

180

0

90

180

0

90

180

C'Fy

0.3

0.0

C'Mz

0.0

0.0 0

90

180

0

90

180

0.04

0.04

0.04

0.02

0.02

0.02

0.00

0.00 0

90

180

0.00 0

90 180 Wind angle,  (deg.)

Fig. 9. Fluctuations of wind loads: rms wind load coefficients. a: Building A; b: Building B; c: Building C.

pressure induced on the leeward x-face which is exposed to the channeled gap flow (Fig. 4). Result in Fig. 9 shows that not only mean value of Fx is increased but rms value is also higher. This suggests that channeled flow through the gap is highly unsteady leading to largeamplitude fluctuating pressure. This conjecture seems ill posed when it is observed that rms values of C 0F z for Buildings B and C are much lower than the single building values while both x-faces of these buildings are facing a building gap. It is noted, however, that mean loads on these inner buildings are lower even by a greater degree than the single building values (Fig. 3). Actually, it is the ratio of rms value to mean value, or the fluctuation intensity, which can better measure the degree of fluctuations of wind loads or wind pressure. When the fluctuation intensities are computed and compared, not shown here for brevity, it is found that Fx on all buildings at all wind angles have higher fluctuation intensities than the single building case. Another important observation in Fig. 9 is that the high values of C 0F x at y around 901, which are caused by vortex shedding on an isolated single building, are no longer evidently found on buildings in a row at all four building separations. This suggests that vortex shedding from tall buildings becomes impaired or much less coherent when they are so closely spaced side-by-side (Sakamoto and Haniu, 1988). Along y-direction, rms values C 0F y on the buildings do not differ much from the single building values as for their mean values. At y ¼ 01, wind blows along the row and the

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vortex-induced high values of C 0F y observed on an isolated single building can still be weakly found on Buildings A and B for S/B40.125. On Building C, this is found only at the widest building separation S/B ¼ 0.5. When wind blows from the other side of the row, at y ¼ 1801, no peak value of C 0F y is found on Buildings A or B at any building separation. It appears that when the buildings are closely arranged in-line to wind flow, coherent vortex shedding from the buildings is impaired but with a wider separation, some forms of across-wind load fluctuations remain in action for the more upwind buildings. For rms torsion on an isolated building, it is interesting to note that the largest levels of fluctuations are found at wind angles where mean torsion is nearly zero. On Building A, while mean torsions greater than the single building case are found at y4901, the corresponding value of C 0M z ðyÞ are lower. Torsions on Buildings B and C generally have much lower rms values. 3.9. Wind load spectra Power spectral densities (PSD) of base wind loads at S/B ¼ 0.25 are shown in Fig. 10 for ¯ 2H B2 HÞ2 , are plotted some selected wind angles. Normalized PSD, nS MM ðnÞ=ðð1=2ÞrU ¯ H where n is frequency. Spectra at other building against non-dimensional frequency nB=U separations exhibit similar characteristics and are not presented. For the isolated squareplan building, moment spectra in across-wind direction shows the dominant sharp spectral ¯ H  0:1 which is caused by strong vortex shedding from the building. This is peak at nB=U observed in Mx at y ¼ 01 and 1801 and My at y ¼ 901. Along-wind spectra are mostly affected by turbulence buffeting and do not exhibit any sharp spectral peaks. When wind blows along the row of buildings, at y ¼ 01 and 1801, across-wind moment spectra Mx of all buildings no longer exhibit the vortex shedding spectral peak at ¯ H  0:1. This implies that coherent vortex shedding does not occur on the buildings nB=U when they are located in close proximity. Strong across-wind response which is typical for an isolated tall building is thus not expected to occur on buildings in a row. Spectra on Buildings A, B and C are broad-banded in very similar shapes, that is containing similar distribution of power levels over frequencies. Spectra of Buildings A and B at y ¼ 01 have almost the same spectral levels while spectrum of Building C farther downwind has lower power levels. Drop in spectral levels continues to the fourth and last buildings in the row, that is, Buildings B and A at y ¼ 1801. Similar drops on spectral power levels are observed on the along-wind moment spectra My of buildings going from upwind to downwind but there are also changes in shapes of spectra. At y ¼ 01, the most upwind Building A has an along-wind moment spectrum almost the same as that of an isolated single building. Spectrum of Building B has lower spectral powers at the lower frequency end. This drop in spectral levels at lower frequencies is even more pronounced for Building C. On the other hand, there seems to be increase in spectral levels at high-frequency end of the spectra. This may be because when a building is behind other buildings, incoming wind contains more intense fine-scale turbulence leading to high-frequency oscillations in wind forces. The fourth and last building in the row are represented by Buildings B and A at y ¼ 1801. When wind blows normal to the row (y ¼ 901), across-wind moment is My. No sharp spectral peak of vortex shedding is clearly observed on any building. Yet for edge Building A, there seems to be some concentration of spectral powers remaining around ¯ H  0:1. The open exposure of this building at its free end may preserve some nB=U

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578  = 0° : 1

1

n SM M x

0.01

n SM M

x

y

0.1

0.01

0.01

0.0001

0.001

0.001

1e-005

0.01

0.1

 = 90° : 1 0.1

0.0001 0.01

0.1

1e-006 0.01

0.01

n SM M y

0.1

0.0001

0.001

0.001

1e-005

 = 180° : 1

0.0001 0.01

1

n SMxMx

0.1

0.01

n SMyMy

0.001

0.01

0.01

0.0001

0.001

0.001

1e-005

 = 30° : 1

0.0001 0.01

0.1

n SMy My

0.1

0.001

0.01

0.01

0.0001

0.001

0.001

1e-005

0.1 nB/U

0.0001 0.01

0.1 nB/U

z

0.1

n SM M z

0.1

0.01

n SM M

1e-006 0.01

0.01

1 n SMx Mx

0.1

z

0.1

0.1

z

1e-006 0.01

0.1

0.01

n SM M

0.001

0.01

0.1

0.1

z

y

0.01

0.01

z

0.001

1

n SMxMx

n SM M z

y

0.1

A B C Isolated

z

1e-006 0.01

0.1 nB/U

Fig. 10. Wind moment spectra at normal wind incidence and y ¼ 301, S/B ¼ 0.25. Power spectral densities shown in normalized values (see text).

degree of vortex shedding which is less periodic and of much weaker strengths. Along-wind moment spectra Mx, mainly caused by turbulence buffeting, have similar shapes as an isolated building but with lower levels.

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Fig. 10 also shows moment spectra at y ¼ 301 where upwind interference is observed and discussed. Increase in spectral levels over the isolated building case is observed on My of Building A at all frequencies. Spectra of My for more downwind buildings have much lower spectral power especially at the low frequency end. The other moment Mx is more related to across-wind actions and characteristics similar to those at y ¼ 01 are observed. At normal wind incidence, the torsion spectrum on an isolated single building exhibits ¯ H  0:09 and 0.2. These peaks are not observed at two broad spectral peaks at nB=U oblique wind incidence at y ¼ 301. When buildings are placed in close proximity, spectra of Mz have much lower power levels with disappearance of the first spectral peaks but the second peaks remain. 3.10. Wind-induced dynamic building responses Fluctuating moments measured with the base balance on wind tunnel model can be used to estimate wind-induced dynamic response of a tall building (Tschanz, 1982). The generic square-plan buildings in this study are treated as mildly dynamic and typical full-scale dynamic properties are borrowed from a real 52-storey reinforced concrete residential building of similar size and shape. Same dynamic properties are assumed in x- and y-directions. Natural frequencies of the first and second vibration modes are n0,x ¼ n0,y ¼ 0.238 Hz (full-scale value). The third mode is in the torsional direction j with natural frequency at n0,j ¼ 0.415 Hz. For simplicity, the vibration modes are assumed uncoupled. A value of critical damping ratio at z ¼ 0.01 is used for structural damping. Assuming same linear mode shape in x or y and a constant mode shape in j, base moment spectra in Fig. 10 approximate PSD of the generalized wind forces. They are then combined with dynamic properties of the building to obtain the deflection spectra in x, y and j. Areas under these spectra give rms values of deflections at building top floor. Computation follows the standard procedures in modal analysis and a description of the procedures can be found in Swaddiwuhipong and Khan (2002). Fig. 11 shows how rms deflections sx, sy and sj vary with wind speed. Wind speeds are ¯ H =ðn0;x BÞ or U ¯ H =ðn0;j BÞ. Results are shown at three wind shown as reduced velocities, U angles only, at normal wind incidence where largest along- and across-wind responses are expected to occur, and at y ¼ 301 where upwind interference occurs on Building A. Response curves of sx and sy for the isolated single square-plan building at normal ¯ H =n0 B ¼ 10. At this wind incidence exhibit the expected across-wind resonance near U speed, frequency of vortex shedding from the building matches the natural frequency of lateral building vibration, resulting in resonant building deflections in across-wind direction. Along-wind deflections and non-resonant across-wind deflections generally increase with the square of wind speed as evidently observed from the log–log plots. When the building is placed in a row, wind-induced responses are modified. In most situations, wind-induced responses are of smaller magnitudes than the isolated building case and vortex-induced across-wind resonance does not occur. When wind blows along the row of buildings, y ¼ 01, along-wind responses of Building A are similar to the single isolated building but Building B downstream exhibits much lower amplitude of sx. Response of Building C is even much lower. This implies that sheltering effect reduces overall strength of turbulence buffeting which has been shown in spectra of My in Fig. 10. Unlike the isolated single building, those spectra on all three ¯ H  0:2 at the high-frequency end. This leads buildings exhibit a broad peak around nB=U

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Isolated A

10-1

10-2

10-2

10-3

10-5

10-2 10-3 

10-1

10-4

10-3

10-4

10-4

10-5

10-5 1

10

10-6 1

U/nxB

10

1

U/nyB 10-1 10-1

10-2

10-2

10-3 10-4

10-2 10-3 

10-1

y /B

x /B

10 U/nB

 = 90° :

10-3

10-4

10-4

10-5

10-5 10-6

10-5 1

10

1

U/nxB

10

1

U/nyB

 = 30° :

10 U/nB

10-1 10-1

10-2

10-2

10-3 10-4 10-5

10-2 10-3 

10-1

y /B

x /B

B C

10-1

y / B

x /B

 = 0° :

10-3

10-4

10-4

10-5

10-5 1

10 U/nxB

10-6 1

10 U/nyB

1

10 U/nB

Fig. 11. Wind-induced dynamic response of translational and torsional deflections at different reduced velocities, S/B ¼ 0.25.

to some resonant responses of sx at reduced velocities between 4 and 6. At these wind speeds, along-wind responses of Buildings B and C approach similar levels as the isolated single building case. For sy, no resonant across-wind responses at reduced velocities about 10 are observed on all three buildings. At very high reduced velocities, sy of Building A becomes larger than the single isolated building and this is due to the higher spectral densities in its Mx spectrum at the lower frequency end (Fig. 10).

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At y ¼ 901 when wind blows normal to the row, all buildings have much smaller acrosswind responses of sx, almost one order of magnitude lower, when compared to the isolated single building. Disappearance of resonant responses at reduced velocities near 10 implies that coherent vortex shedding cannot occur in this situation. Some weakly resonant response around reduced velocity 10 remains on Building A which is the end member of the row. In along-wind direction, location of buildings in a row does not result in significant interference effect. Thus, similar response characteristics of sy are observed on all buildings as the isolated single building. Upwind interference at y ¼ 301 also applies to building dynamic responses. Fig. 11 shows evidently that Building A has sx larger than an isolated single building at all reduced velocities. Buildings B and C downstream have much lower amplitudes of rms deflections but they exhibit resonant responses at reduced velocities between 4 and 6 due to the highfrequency broad spectral peak in their My spectra (Fig. 10). Responses of buildings along y direction have smaller differences. At normal wind incidences, torsion spectra Mz of an isolated single building exhibit two ¯ H  0:09 and 0.2. Response curves of sj therefore broad spectral spectra centered at nB=U show two weakly resonant response ranges centered roughly at reduced velocity 5 and 10. It should be noted that actual wind speed corresponding to reduced velocity 10 in this torsional mode is 1.74 times wind speed at reduced velocity 10 in translational mode, 1.74 being ratio of n0,j/n0,x. At y ¼ 01, Buildings A and B have similar responses of sj as the isolated single building while Building C has responses of much lower amplitudes. At y ¼ 901, all buildings have much lower sj than the single isolated building. At y ¼ 301, upwind interference on Building A applies to sj as well, with response amplitudes higher than those of a single building at all reduced velocities. Buildings B and C show much smaller responses. 4. Conclusions This paper reports wind tunnel measurement results on five closely spaced square-plan buildings arranged in a row. A number of wind interference mechanisms unique to closely spaced tall buildings and at wind angles other than normal incidence are identified and explained. Data and findings of this paper are relevant to the design of residential developments in large metropolitan cities. It is found that while sheltering effect remains the key interference effect at many wind incidence angles, other interference effects are in action at some wind flow cases by which some member buildings experience wind loads greater than an isolated single building. This is most evidently observed on the edge building in the row when wind blows at a slight oblique angle to the row, for instance, at y ¼ 301. Wind flow patterns around a row of buildings at this wind angle are visualized with CFD. They show that strong channeling of wind flow through the building gaps occurs as a result of the close proximity of buildings. This leads to highly negative pressures on building walls facing a gap. Occurrence of these negative pressures is confirmed by pressure measurement in the wind tunnel. For the upwind edge building in the row, this much higher suction pressure on its leeward wall leads to increase in wind load components acting along direction of the row. This interference effect resulting in wind load increase on an upwind building has scarcely been reported. For the most downwind building in the row at oblique wind incidence, large suction is induced on its windward wall which faces a gap flow but not on its free leeward

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wall. This results in a wind force acting upwind. When wind blows along the row of buildings, inner buildings are in the wake of the first building and thus experience very small drag forces. In extreme cases, the drag force can become negative on the second building. Wind loads at direction normal to the row are expected to experience smaller interference effect. While this is only partly true for mean wind loads, fluctuating wind loads are found to be largely modified. The most important interference effect on fluctuating wind loads is the destruction of coherent regular vortex shedding from the buildings at normal wind incidence when they are closely located in a row. The sharp spectral peak of vortex shedding observed on an isolated square-plan building is no longer found in the across-wind load spectra of buildings being in a row. As a result, windinduced responses of the buildings do not exhibit across-wind resonant behavior at the typical reduced velocity near 10 as an isolated tall building. In general, similar patterns of interference are observed at different building separations between 0.1B and 0.5B, with wind load modifications becoming slightly more significant at smaller separations. It is believed that the same interference mechanisms which are described in this paper are in action at all these close building separations. However, when the separation is wider than one building breadth, the interference behaviors observed in this study are not expected to occur, probably with the exception of sheltering effect. Acknowledgment The investigation is supported by a research grant (HKU7014/02E) awarded by the Research Grants Council of Hong Kong. References Bailey, P.A., Kwok, K.C.S., 1985. Interference excitation of twin tall buildings. J. Wind Eng. Ind. Aerodyn. 21, 323–338. Blessman, J., Riera, J.D., 1979. Interaction effects in neighbouring tall buildings. In: Proceedings of the 5th International Conference on Wind Engineering, Colorado State University, Fort Collins, CO, pp. 381–395. Cook, N.J., 1990. The Designer’s Guide to Wind Loading of Building Structures. Part 2. STATIC Structures. Building Research Establishment Publications, Butterworths, London, UK. English, E.C., 1985. Shielding factors from wind-tunnel studies of mid-rise and high-rise structures. In: Proceedings of the 5th US National Conference on Wind Engineering, Texas Tech University, Lubbock, TX, vol. 4A, pp. 49–56. Hussain, H., Lee, B.E., 1980. A wind tunnel study of the mean pressure forces acting on a large group of low-rise buildings. J. Wind Eng. Ind. Aerodyn. 31, 41–66. Kareem, A., 1987. The effects of aerodynamic interference on the dynamic response of prismatic structures. J. Wind Eng. Ind. Aerodyn. 25, 365–372. Khanduri, A.C., Stathopoulos, T., Bedard, C., 1998. Wind-induced interference effects on buildings—a review of the state-of-art. Eng. Struct. 20 (7), 617–630. Lam, K.M., To, A.P., 2006. Reliability of numerical computation of pedestrian-level wind environment around a row of tall buildings. Wind Struct. 9 (6), 473–492. Lam, K.M., Zhao, J.G., 2006. Interference effect of wind loads on a row of tall buildings. In: Proceedings of the 4th International Symposium on Computational Wind Engineering, Yokohama, pp. 817–820. Obasaju, E.D., 1983. An investigation of the effects of incidence on the flow around a square section cylinder. Aeronaut. Q. 34, 243–259. Sakamoto, S., Haniu, H., 1988. Aerodynamic forces acting on two square prisms placed vertically in a turbulent boundary layer. J. Wind Eng. Ind. Aerodyn. 31, 41–66.

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Saunders, J.W., Melbourne, W.H., 1979. Buffeting effects of upwind buildings. In: Proceedings of the 5th International Conference on Wind Engineering, Colorado State University, Fort Collins, CO, pp. 593–605. Swaddiwuhipong, S., Khan, M.S., 2002. Dynamic response of wind-excited building using CFD. J. Sound Vib. 253, 735–754. Taniike, Y., 1992. Interference mechanism for enhanced wind forces on neighbouring tall buildings. J. Wind Eng. Ind. Aerodyn. 42, 1073–1083. To, A.P., Lam, K.M., 2003. Wind-induced interference effects on a group of buildings. In: Proceedings of the 11th International Conference on Wind Engineering, Texas Tech University, Lubbock, TX, pp. 2405–2410. Tschanz, A., 1982. Measurement of total dynamic loads using elastic models with high natural frequencies. In: Workshop on Wind Tunnel Modeling Criteria and Effects, NBS, Gaithersburg, MA. Yakhot, V., Orszag, S.A., 1986. Renormalization-group analysis of turbulence. Phys. Rev. Lett. 57, 1722–1724. Zhang, W.J., Kwok, K.C.S., Xu, Y.L., 1994. Aeroelastic torsional behaviour of tall buildings in wakes. J. Wind Eng. Ind. Aerodyn. 51, 229–248.