Pierson-Moskowitz Spectra

1. Pierson-Moskowitz spectrum

The Pierson-Moskowitz spectrum is given by

\[S(\omega )=\frac{a}{\omega ^5}\exp(-\frac{b}{\omega ^4}) \label{eq-pm-spec}\]

where

\[a = 0.0081 g^2\\ \\ b = \frac{3.11}{H_s^2}\]

and where

\(g\)

acceleration of gravity

The following parameters are given as input:

\(H_s\)

significant wave height

2. Pierson-Moskowitz ISSC spectrum

The spectrum is given by Equation \(\eqref{eq-pm-spec}\) where

\[a = 173.0 \frac{H_s^2}{T_1} \\ \\ b = \frac{691.0}{T_1^4} \label{eq-pm-issc-ab}\]

The following parameters are given as input:

\(H_s\)

significant wave height

\(T_1\)

average period

3. Pierson-Moskowitz spectrum with zero-crossing period

The spectrum is given by Equation \(\eqref{eq-pm-spec}\) and Equation \(\eqref{eq-pm-issc-ab}\) where

\[T_1 = 1.0864 T_z\]

The following parameters are given as input:

\(H_s\)

significant wave height

\(T_z\)

zero upcrossing period