Simulation of Standing and Propagating Sea Waves . . .
251
∙ LH model is designed to represent a stationary Gaussian field. Normal distribution
of the simulated process (1) is a consequence of the central limit theorem: its
application to the analysis of storm or shallow water waves represents a significant
challenge.
∙ LH model is periodic and need a large set of frequencies to perform long-term
simulation.
∙ In the numerical implementation of the LH model, it appears that convergence rate
of (1) is slow. This leads to a skewed simulated wave energy spectrum and skewed
cumulative distribution functions of various wave parameters (heights, lengths,
etc.). This problem becomes especially significant when simulating complex sea
waves that have a wide spectrum with multiple peaks.
The latter point becomes particularly critical in long-term numerical simulation.
In a time domain computation of the responses of a vessel in a random seaway, the
repeated evaluation of the apparently simple Eq. (1) at hundreds of points on the hull
for thousands of time steps becomes a major factor determining the execution speed
of the code [6]. So, finding a less computationally intensive method for modelling
ocean waves has the potential to increase performance of long-term simulation.
Related Work
Ocean Wave Modelling
Another approach to simulating sea waves involves representing stochastic moving surface as a linear transformation of white noise with memory, which allows to
model stationary ergodic Gaussian random process with given correlation characteristics [7]. The first attempts to model two-dimensional disturbances were undertaken
in [8], which resulted in the development of the resonance theory of wind waves,
and the formal mathematical framework was developed in [9, 10]—the authors built
a one-dimensional model of ocean waves based on autoregressive-moving average
(ARMA) model.
One-dimensional ARMA model does not have some of the LH model deficiencies: it is both computationally efficient and requires less number of coefficients to
converge. In [11] ARMA model is used to generate time series spectrum of which is
compatible with Pierson–Moskowitz (PM) approximation of ocean wave spectrum.
The authors carry out experiments for one-dimensional AR, MA and ARMA models. They mention excellent agreement between target and initial spectra and higher
performance of ARMA model compared to models based on summing large number of harmonic components with random phases. They also mention that in order
to reach agreement between target and initial spectrum MA model require lesser
number of coefficients than AR model. In [12] the authors generalise ARMA model
coefficients determination formulae for multi-variate case.
251
∙ LH model is designed to represent a stationary Gaussian field. Normal distribution
of the simulated process (1) is a consequence of the central limit theorem: its
application to the analysis of storm or shallow water waves represents a significant
challenge.
∙ LH model is periodic and need a large set of frequencies to perform long-term
simulation.
∙ In the numerical implementation of the LH model, it appears that convergence rate
of (1) is slow. This leads to a skewed simulated wave energy spectrum and skewed
cumulative distribution functions of various wave parameters (heights, lengths,
etc.). This problem becomes especially significant when simulating complex sea
waves that have a wide spectrum with multiple peaks.
The latter point becomes particularly critical in long-term numerical simulation.
In a time domain computation of the responses of a vessel in a random seaway, the
repeated evaluation of the apparently simple Eq. (1) at hundreds of points on the hull
for thousands of time steps becomes a major factor determining the execution speed
of the code [6]. So, finding a less computationally intensive method for modelling
ocean waves has the potential to increase performance of long-term simulation.
Related Work
Ocean Wave Modelling
Another approach to simulating sea waves involves representing stochastic moving surface as a linear transformation of white noise with memory, which allows to
model stationary ergodic Gaussian random process with given correlation characteristics [7]. The first attempts to model two-dimensional disturbances were undertaken
in [8], which resulted in the development of the resonance theory of wind waves,
and the formal mathematical framework was developed in [9, 10]—the authors built
a one-dimensional model of ocean waves based on autoregressive-moving average
(ARMA) model.
One-dimensional ARMA model does not have some of the LH model deficiencies: it is both computationally efficient and requires less number of coefficients to
converge. In [11] ARMA model is used to generate time series spectrum of which is
compatible with Pierson–Moskowitz (PM) approximation of ocean wave spectrum.
The authors carry out experiments for one-dimensional AR, MA and ARMA models. They mention excellent agreement between target and initial spectra and higher
performance of ARMA model compared to models based on summing large number of harmonic components with random phases. They also mention that in order
to reach agreement between target and initial spectrum MA model require lesser
number of coefficients than AR model. In [12] the authors generalise ARMA model
coefficients determination formulae for multi-variate case.