**2. Atmospheric boundary layer characteristics**

The variation of the mean velocity profile with height can be different over different terrain conditions depending on the friction effects from the earth's surface and the value of roughness length. **Figure 4** shows a schematic of different mean wind profiles over various topographical conditions of a dense urban area, suburban terrain, and over sea surfaces. In **Figure 4**, higher velocity is anticipated in lower altitudes on sea surfaces than the gradient wind in a dense city center.

After recording time series of wind velocity in the lab or in the field, the turbulence spectrum can be obtained accordingly. For the validation of the turbulence spectrum, theoretical spectra are usually used. The Kaimal spectrum is one of the widely used spectra, which is defined as follows [17]:

$$\frac{f\,\mathcal{S}\_{aa}(f)}{\omega\_{\ast}^{2}} = \frac{An}{\left(1 + Bn\right)^{5/3}}\tag{1}$$

*Sc <sup>u</sup>*ð Þ¼ *ζ*, *n*

*DOI: http://dx.doi.org/10.5772/intechopen.92794*

~ *S c*

~ *S c*

The integral length scale of turbulence, *Lu*

ments, as the terrain roughness decreases, *Lu*

suggested by ESDU is defined as follows [19]:

**3. Aerodynamics of low-rise buildings**

**35**

where *Rc*

Davenport:

Maeda and Makino:

where *kr* <sup>¼</sup> <sup>13</sup>ð Þ *<sup>ζ</sup>=zm* <sup>0</sup>*:*<sup>4</sup>

velocity component at any height, *Lu*

*k1* = 1.0, and *k2* = 0.2 [20].

described in Ref. [22]:

∞ð

*Rc*

*Aerodynamics of Low-Rise Buildings: Challenges and Recent Advances in Experimental…*

points, *A* and *B*, respectively; *n* is the frequency; and *ζ* is the distance between the two points *A* and *B*. The cross-spectrum of Davenport is defined in Ref. [21]:

*<sup>u</sup>*ð Þ¼ *ζ*, *n* exp �*kr*

eddy in a turbulent flow [18]. Having the time history of along-wind

*<sup>u</sup>* <sup>¼</sup> *E f* ð Þ*Umean* 4*u*<sup>2</sup> � �

ground [18]. To quantify these changes, the integral length scale formulation

*<sup>u</sup>* <sup>¼</sup> <sup>25</sup>*z*<sup>0</sup>*:*<sup>35</sup>*z*<sup>0</sup>

Bluff body aerodynamics, and in particular fluctuating pressures on low-rise buildings immersed in turbulent flows, are associated with the complex spatial and temporal nature of winds [26]. This complexity mainly comes from the transient nature of incident turbulent winds, and the fluctuating flow pattern in the separation bubble. The flow in the separated shear layer is associated with fluctuations in the velocity field leading to the evolution of instabilities. The flow physics are dependent on upstream turbulence intensity, integral length scale, as well as Reynolds number. The later makes it difficult to scale up loads based on pressure and force coefficients as the process can be highly nonlinear, which is the case, for

*LESDU*

And Counihan formulation used by Refs. [24, 25]:

*Lu*

where *ū* is the standard deviation of the along-wind velocity component and *E*(*f*) is the power spectral density. Studies show that the integral length scale of turbulence may decrease in the flow direction, due to the fact that larger eddies will usually dissipate energy into smaller eddies [23]. According to actual measure-

*Lx*

*<sup>u</sup>*ð Þ¼ *ζ*, *τ E u*½ � *<sup>A</sup>*ð Þ*t uB*ð Þ *t* þ *τ* , *SuA*(*n*), and *SuB*(*n*) are power spectra at two

, *zm* <sup>¼</sup> <sup>0</sup>*:*5ð Þ *zA* <sup>þ</sup> *zB* , *<sup>θ</sup>* <sup>¼</sup> <sup>0</sup>*:*747*ζ=xLu*

*x*

j j *nζ U*

*<sup>u</sup>*ð Þ¼ *<sup>ζ</sup>*, *<sup>n</sup>* exp ð Þ �*k*1*<sup>θ</sup> :* <sup>1</sup> � *<sup>k</sup>*2*θ*<sup>2</sup> � �, (6)

*<sup>x</sup>* can be calculated using the approach

*f*!0

*<sup>u</sup>*ð Þ *ζ*, *τ* exp ð Þ �*j*2*πnτ dτ:* (4)

� �, (5)

� �<sup>2</sup> <sup>þ</sup> <sup>2</sup>*πnζ=<sup>U</sup>* � �<sup>2</sup> n o<sup>1</sup>*=*<sup>2</sup>

, is a measure of the size of the largest

*<sup>x</sup>* increases with the height above

*<sup>C</sup>* <sup>¼</sup> <sup>300</sup>ð Þ *<sup>z</sup>=*<sup>300</sup> <sup>0</sup>*:*46þ0*:*074 ln *<sup>z</sup>*<sup>0</sup> (9)

�0*:*<sup>063</sup> (8)

,

(7)

�∞

in which *f* is *nU*/*z*. One can obtain the spectrum, *Suu*, in the along-wind direction by considering *A* to be 105 and *B* to be 33 [14, 18]. For the lateral and vertical spectra, different values for the parameters *A* and *B* are suggested [14, 18].

The Engineering Science Data Unit (ESDU) spectrum is proposed based on a new von Karman spectrum, covering the full frequency range, as follows [19]:

$$\frac{f\,\mathbb{S}\_{\text{uu}}(f)}{\sigma\_{\text{u}}^{2}} = \beta\_{1} \frac{2.987 n\_{\text{u}}/a}{\left[1 + \left(2\pi n\_{\text{u}}/a\right)^{2}\right]^{5/6}} + \beta\_{2} \frac{1.294 n\_{\text{u}}/a}{\left[1 + \left(\pi n\_{\text{u}}/a\right)^{2}\right]^{5/6}} F\_{1} \tag{2}$$

For more details regarding the ESDU spectrum and definition of different terms, readers are referred to Ref. [19]. The nondimensional cross-spectrum of u-component is defined in Ref. [20]:

$$
\tilde{S}\_u^\xi(\zeta, n) = \frac{S\_u^\xi(\zeta, n)}{\sqrt{S\_{uA}(n)}\sqrt{S\_{uB}(n)}},\tag{3}
$$

#### **Figure 4.**

*Mean wind speed profiles over different terrains according to Davenport's power law profiles (adapted from Ref. [16]).*

*Aerodynamics of Low-Rise Buildings: Challenges and Recent Advances in Experimental… DOI: http://dx.doi.org/10.5772/intechopen.92794*

$$S^\epsilon\_u(\zeta, n) = \int\_{-\infty}^{\infty} R^\epsilon\_u(\zeta, \tau) \exp\left(-j2\pi n\tau\right) d\tau. \tag{4}$$

where *Rc <sup>u</sup>*ð Þ¼ *ζ*, *τ E u*½ � *<sup>A</sup>*ð Þ*t uB*ð Þ *t* þ *τ* , *SuA*(*n*), and *SuB*(*n*) are power spectra at two points, *A* and *B*, respectively; *n* is the frequency; and *ζ* is the distance between the two points *A* and *B*. The cross-spectrum of Davenport is defined in Ref. [21]:

Davenport:

**2. Atmospheric boundary layer characteristics**

*Aerodynamics*

the widely used spectra, which is defined as follows [17]:

*f Suu*ð Þ*f σ*2 *u*

u-component is defined in Ref. [20]:

**Figure 4.**

*Ref. [16]).*

**34**

¼ *β*<sup>1</sup>

~ *S c <sup>u</sup>*ð Þ¼ *ζ*, *n*

*f Saa*ð Þ*f u*2 ∗

<sup>¼</sup> *An*

in which *f* is *nU*/*z*. One can obtain the spectrum, *Suu*, in the along-wind direction

The Engineering Science Data Unit (ESDU) spectrum is proposed based on a new von Karman spectrum, covering the full frequency range, as follows [19]:

For more details regarding the ESDU spectrum and definition of different terms, readers are referred to Ref. [19]. The nondimensional cross-spectrum of

> *Sc <sup>u</sup>*ð Þ *<sup>ζ</sup>*, *<sup>n</sup>* ffiffiffiffiffiffiffiffiffiffiffiffiffi

*Mean wind speed profiles over different terrains according to Davenport's power law profiles (adapted from*

by considering *A* to be 105 and *B* to be 33 [14, 18]. For the lateral and vertical spectra, different values for the parameters *A* and *B* are suggested [14, 18].

> 2*:*987*nu=α* <sup>1</sup> <sup>þ</sup> ð Þ <sup>2</sup>*πnu=<sup>α</sup>* <sup>2</sup> h i<sup>5</sup>*=*<sup>6</sup> <sup>þ</sup> *<sup>β</sup>*<sup>2</sup>

ð Þ <sup>1</sup> <sup>þ</sup> *Bn* <sup>5</sup>*=*<sup>3</sup> (1)

1*:*294*nu=α*

*SuA*ð Þ *<sup>n</sup>* p ffiffiffiffiffiffiffiffiffiffiffiffiffi *SuB*ð Þ *<sup>n</sup>* <sup>p</sup> , (3)

<sup>1</sup> <sup>þ</sup> ð Þ *<sup>π</sup>nu=<sup>α</sup>* <sup>2</sup> h i<sup>5</sup>*=*<sup>6</sup> *<sup>F</sup>*<sup>1</sup> (2)

The variation of the mean velocity profile with height can be different over different terrain conditions depending on the friction effects from the earth's surface and the value of roughness length. **Figure 4** shows a schematic of different mean wind profiles over various topographical conditions of a dense urban area, suburban terrain, and over sea surfaces. In **Figure 4**, higher velocity is anticipated in lower altitudes on sea surfaces than the gradient wind in a dense city center. After recording time series of wind velocity in the lab or in the field, the turbulence spectrum can be obtained accordingly. For the validation of the turbulence spectrum, theoretical spectra are usually used. The Kaimal spectrum is one of

$$\tilde{S}\_{\mathfrak{u}}^{\xi}(\zeta, n) = \exp\left(-k\_r \frac{|n\zeta|}{\overline{U}}\right),\tag{5}$$

Maeda and Makino:

$$\tilde{S}\_{\mathfrak{u}}^{\xi}(\zeta, n) = \exp\left(-k\_1 \theta\right). \left(\mathbb{1} - k\_2 \theta^2\right), \tag{6}$$

where *kr* <sup>¼</sup> <sup>13</sup>ð Þ *<sup>ζ</sup>=zm* <sup>0</sup>*:*<sup>4</sup> , *zm* <sup>¼</sup> <sup>0</sup>*:*5ð Þ *zA* <sup>þ</sup> *zB* , *<sup>θ</sup>* <sup>¼</sup> <sup>0</sup>*:*747*ζ=xLu* � �<sup>2</sup> <sup>þ</sup> <sup>2</sup>*πnζ=<sup>U</sup>* � �<sup>2</sup> n o<sup>1</sup>*=*<sup>2</sup> , *k1* = 1.0, and *k2* = 0.2 [20].

The integral length scale of turbulence, *Lu x* , is a measure of the size of the largest eddy in a turbulent flow [18]. Having the time history of along-wind velocity component at any height, *Lu <sup>x</sup>* can be calculated using the approach described in Ref. [22]:

$$L\_u^x = \left[\frac{E(f)U\_{mean}}{4\overline{u}^2}\right]\_{f\to 0} \tag{7}$$

where *ū* is the standard deviation of the along-wind velocity component and *E*(*f*) is the power spectral density. Studies show that the integral length scale of turbulence may decrease in the flow direction, due to the fact that larger eddies will usually dissipate energy into smaller eddies [23]. According to actual measurements, as the terrain roughness decreases, *Lu <sup>x</sup>* increases with the height above ground [18]. To quantify these changes, the integral length scale formulation suggested by ESDU is defined as follows [19]:

$$L\_u^{ESDU} = \mathfrak{Z} \mathfrak{z}^{0.35} z\_0^{-0.063} \tag{8}$$

And Counihan formulation used by Refs. [24, 25]:

$$L\_u \, ^\text{C} = \mathbf{300} (z/\text{300})^{0.46 + 0.074 \ln z\_0} \tag{9}$$
