Sletringen wind spectrum

The Slentringen wind spectrum is given by

\[S(f,z) = \bar{u}_{r}^p\{\frac{a_1(\displaystyle \frac{z}{z_r})^{-q}}{(B_1+f)^{5/3}}+\frac{a_2}{(B_2^n+f^n)^{5/(3n)}}\}\]

where

\[\begin{array}{l} \displaystyle n=n_0+n_1e^{-c_n\rho }\\\\ \displaystyle B_1=b_1\frac{\bar{u}_r}{z}\\\\ \displaystyle B_2=b_2\bar{u}_re^{c_{b2}\rho }\\\\ \displaystyle \rho =\frac{\gamma }{(\displaystyle \frac{\bar{u}_r}{10~\mathrm {\displaystyle m/s}})^\varepsilon } \end{array}\]

and

\(\gamma\)

is the temperature stability parameter, recommended values are in the range \(\displaystyle \mathrm{ 10 ~ \frac{K}{km} - 20 ~ \frac{K}{km} }\)

The values for the parameters have been derived from the Sletringen measurements as shown below.

Parameter	Value
\(\mathrm {a_1}\)	\(\mathrm {2.03\cdot 10^{-5}}\)
\(\mathrm {a_2}\)	\(\mathrm {1.18\cdot 10^{-5}}\)
\(\mathrm {\varepsilon }\)	\(\mathrm {1.40}\)
\(\mathrm {p}\)	\(\mathrm {3.07}\)
\(\mathrm {q}\)	\(\mathrm {1.50}\)
\(\mathrm {b_1}\)	\(\mathrm {1.82\cdot 10^{-2}}\)
\(\mathrm {b_2}\)	\(\mathrm {3.56\cdot 10^{-4}}\)
\(\mathrm {c_{b2}}\)	\(\mathrm {0.293}\)
\(\mathrm {n_0}\)	\(\mathrm {0.281}\)
\(\mathrm {n_1}\)	\(\mathrm {0.428}\)
\(\mathrm {c_n}\)	\(\mathrm {0.183}\)

Parameter

Value

\(\mathrm {a_1}\)

\(\mathrm {2.03\cdot 10^{-5}}\)

\(\mathrm {a_2}\)

\(\mathrm {1.18\cdot 10^{-5}}\)

\(\mathrm {\varepsilon }\)

\(\mathrm {1.40}\)

\(\mathrm {p}\)

\(\mathrm {3.07}\)

\(\mathrm {q}\)

\(\mathrm {1.50}\)

\(\mathrm {b_1}\)

\(\mathrm {1.82\cdot 10^{-2}}\)

\(\mathrm {b_2}\)

\(\mathrm {3.56\cdot 10^{-4}}\)

\(\mathrm {c_{b2}}\)

\(\mathrm {0.293}\)

\(\mathrm {n_0}\)

\(\mathrm {0.281}\)

\(\mathrm {n_1}\)

\(\mathrm {0.428}\)

\(\mathrm {c_n}\)

\(\mathrm {0.183}\)