Wave Spectra

To create an irregular wave train for load calculations, the user must specify a suitable wave spectral formula $S_{\zeta} (f) $. This function will depend on the location of the turbine being modelled and the prevailing meteorological and oceanographic conditions. Bladed allows the wave spectrum to be specified in one of two ways: as a JONSWAP /Pierson-Moskowitz spectrum or as a user-defined lookup table.

JONSWAP/ Pierson Moskowitz spectrum

There are different versions of the JONSWAP formula. The version used in Bladed is based on an expression by (Goda, 1979).

\[ \begin{equation} S_{\zeta} (f)=\alpha_{2} H_{s}^{2} T_{p} \left (\frac{f}{f_{p}}\right)^{-5} \ exp \left[ -1.25 \left(\frac{f}{f_{p}}\right)^{-4} \right] \gamma ^{\beta} \end{equation} \]

where \(f\) is the wave frequency (in Hz), \(H_{s}\) is the significant wave height, \(T_{p}\) is the peak spectral period, \(f_{p}={1}/{T_{p}}\) , and \(\gamma\) is the JONSWAP peakedness parameter,

\[ \begin{equation} \alpha_{2}=\frac{0.0624}{0.230+0.0336 \gamma -\frac{0.185}{1.9+ \gamma}} \end{equation} \]

\[ \begin{equation} \beta=exp \left [-0.5 \left(\frac{\frac{f}{f_{p}}-1}{\sigma} \right)^{2} \ \ \right] \end{equation} \]

and

\[ \begin{equation} \begin{aligned} \sigma =0.07 &\text{\ \ \ \ \ \ \ for } & f \leq f_{p} \\ \sigma =0.09 &\text{\ \ \ \ \ \ \ for } & f \gt f_{p} \end{aligned} \end{equation} \]

The Pierson-Moskowitz spectral density function may be regarded as a special case of the JONSWAP spectrum with

\[ \begin{equation} S_{\zeta} (f)=0.3123 H_{s}^{2} T_{p} \left(\frac{f}{f_{p}} \right)^{-5} \ exp \left[ -1.25 \left(\frac{f}{f_{p}}\right)^{-4} \ \ \right] \end{equation} \]

If the JONSWAP / Pierson-Moskowitz option is selected, the user is required to enter values for \(H_{s}\), \(T_{p}\), and \(\gamma\).

User-defined spectrum

A user-defined spectrum may be entered in the form of a lookup table. Up to 100 pairs of $S_{\zeta} (f) $ and \(f\) may be entered. The values of $S_{\zeta} (f) $ at the lowest and highest frequencies entered should be zero. At frequencies between the specified values of \(f\) , values of $S_{\zeta} (f) $ are linearly interpolated.

Last updated 10-09-2024