How to model a regular wave using irregular wave input
1. Input

Time series generation parameters

Simulation length, Tdur[s]

Time step, dt [s]


Numerical wave spectrum

Wave height, H [m]

Wave period, T[s]

2. Time series generation parameters

The number of time step must be 2^n

To estimate the actual Tdur that will be used in the time series generation

Number of time steps in FFT:

\(\ln{\frac{T_{dur}}{dt}}=\ln{2^n}= n \ln{2} \Rightarrow n_{actual} = \lceil{{\frac{\ln{\frac{T_{dur}}{dt}}}{\ln{2}}}}\rceil\)


Actual simulation length:

\(T_{dur,actual} = n_{actual} \cdot dt\)


Wave frequency in FFT:

\(\Delta f = \frac{1}{T_{dur,actual}}, \Delta\omega = 2\pi\cdot df\)

3. Numerical wave spectrum

Regular wave frequency

\(\omega_{reg} = \frac{2\pi}{T}\)


Wave energy

\(\frac{1}{2} (\frac{H}{2})^2 = S(\omega) \Delta\omega \rightarrow S(\omega) = \frac{1}{2} (\frac{H}{2})^2 \frac{1}{\Delta \omega}\)

4. Make input

Input frequencies

\(\omega_1 = (\omega_{reg} \Delta\omega/2)(1fac)\)

\(\omega_2 = \omega_{reg}  \Delta\omega/2\)

\(\omega_3 = \omega_{reg}+ \Delta\omega/2\)

\(\omega_4 = \omega_{reg}+ \Delta\omega/2(1+fac)\)


Input wave energy

\(S(\omega_1) = 0.0\)

\(S(\omega_2) = \frac{1}{2} (\frac{H}{2})^2 \frac{1}{\Delta \omega}\)

\(S(\omega_3) = \frac{1}{2} (\frac{H}{2})^2 \frac{1}{\Delta \omega}\)

\(S(\omega_4) = 0.0\)


Fac is a small value ensuring that the wave frequencies are increasing in value, example: fac=0.00005