Strong wind characteristics and turbulence - Wind Loading of Structures - page 68

Figure 3.5 Normalised spectrum of
longitudinal velocity component (von
Karman-Harris).
In this form, the curve of versus n/Ū has a peak; the value of ℓ u determines the
value of (n/Ū) at which the peak occurs—the higher the value of ℓ u , the higher the value
of (Ū/n) at the peak or λ, known as the 'peak wavelength'. For the von Karman-Harris
spectrum, λ is equal to 6.85 ℓ u . The length scale, ℓ u , varies with both terrain roughness and
height above the ground. The form of the von Karman-Harris spectrum is shown in
Figure 3.5.
The other orthogonal components of atmospheric turbulence have spectral densities
with somewhat different characteristics. The spectrum of vertical turbulence is the most
important of these, especially for horizontal structures such as bridges. A common
mathematical form for the spectrum of vertical turbulence (w ′ ) is the Busch and Panofsky
(1968) form which can be written as:
(3.27)
In this case, the length scale is directly proportional to the height above the ground, z .
The Busch and Panofsky spectrum for vertical turbulence (w ′ ) is shown in Figure 3.6.
3.3.5 Correlation
Covariance and correlation are two important properties of wind turbulence in relation to
wind loading. The latter is the same quantity that is calculated in linear regression
analysis. In the present context, it relates the fluctuating wind velocities at two points in
space or wind pressures at two points on a building (such as a roof).