## Y j

FIGURE 22.52 Velocity components of turbulent wind.

along the mean wind direction, u, is the largest and is therefore the most important for the vertical structures such as tall buildings, which are flexible along the wind direction. The vertical component w is important for horizontal structures, which are flexible vertically such as long-span bridges.

An overall measure of the intensity of turbulence is given by the root mean square value. Thus, for the longitudinal component of the turbulence

10J0

where T0 is the averaging period. For the statistical properties of the wind to be independent on which part of the record is being used, T0 is taken to be 1 h. Thus, the fluctuating wind is a stationary random function, over 1 h.

The value of isu(z) divided by the mean velocity U(z) is called the turbulence intensity cu(z)

which increases with ground roughness and decreases with height.

The variance of longitudinal turbulence can be determined from

where u„ is the friction velocity determined from Equation 22.8 and b, which is independent of the height, is given in Table 22.6 for various roughness lengths.

### 22.5.2.3 Integral Scales of Turbulence

The fluctuation of wind velocity at a point is due to eddies transported by the mean wind U. Each eddy maybe considered to be causing a periodic fluctuation at that point with a frequency n. The average size of the turbulent eddies are measured by integral length scales. For eddies associated with longitudinal velocity fluctuation u, the integral length scales are LUU, Lu, LU describing the size of the eddies in longitudinal, lateral, and vertical directions, respectively. If L£ and LU are comparable to the dimension of the structure normal to the wind, then the eddies will envelope the structure and give rise to well-correlated pressures and thus the effect is significant. On the other hand, if LU and LU are small, then the eddies produce uncorrelated pressures at various parts of the structure and the overall effect of the longitudinal turbulence will be small. Thus, the dynamic loading on a structure depends on the size of eddies.

### 22.5.2.4 Spectrum of Turbulence

The frequency content of the turbulence is represented by the power spectrum, which indicates the power or kinetic energy per unit time, associated with eddies of different frequencies. An expression for the power spectrum is (Taranath 1988)

where f = nz/U(z) is the reduced frequency. A typical spectrum of wind turbulence is shown in Figure 22.53. The spectrum has a peak value at a very low frequency around 0.04 Hz. As the typical range nSU(z, n)

200f

TABLE 22.6 Values of ß for Various Roughness Lengths

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