Wind shear exponents

Q. Can you set the wind shear exponent in the WAsP wind profile model?

A. No, you can't. And the reason is that WAsP is based on a logarithmic wind profile governed by the terrain surface roughness length z₀:

U(z) = (u_*/κ) ln(z/z₀)

The wind shear exponent is used in connection with the assumption of a power-law wind profile:

U(z) = U_r (z/z_r)^α

In limited height ranges you may find the best wind shear exponent fit to a certain surface roughness length, and vice versa; but the fit is only approximate since logarithmic and power-law profiles are functionally different. Thus for a small height range around a height z_r  such a fitted relation is:

         α = 1 / ln(z_r /z₀)

Furthermore, one should keep in mind that WAsP does not use a strict logarithmic profile; when WAsP takes terrain inhomogeneities and stability effects into account, the resulting wind profile will in general differ from a simple logarithmic profile.

Q. How does WAsP Engineering calculate the wind shear exponent?

A. WEng calculates the shear from the relation

where velocity and gradient are calculated at the selected height. Unlike data from measurement campaigns, the velocity gradient is not coming from a difference between wind speeds at two heights. This is because the FFT-based flow model LINCOM gives us a computationally faster method based on multiplication of wave numbers and Fourier components followed by inverse Fourier transformation. This provides velocity gradient everywhere in the computational domain.

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