Introduction
7
Komen et al., 1994). There were more models taking into account the effect of
an uneven seabed (Hasselmann & Collins, 1968; Collins, 1972; SWIM Group,
1985; Gutshabash & Lavrenov, 1987, 1988; Khandekar, 1989; Tolman, 1991)
and spatially non-uniform currents (Hurghes & Grant, 1978; Kato & Sato,
1978; Sakai & Iwagaki, 1983; Booij et al., 1984; Gutshabash & Lavrenov, 1986;
Holthuijsen et al., 1989; Khandekar, 1989). However, it should be noted that
there were considerable discrepancies even between the results of the most
advanced models.
This variety of mathematical models indicates that wind waves remain
a very complicated object for investigation, and its theory is far from being
completed. It is difficult to create one universal model optimal for all cases.
That is why different approaches and methods have a right to exist. On the
other hand, a large variety of models help us to better understand wind waves
and develop model implementations using modern computers.
In 1985, due to a large number of different models, the SWAMP International Working Group (Sea Wave Modelling Project) proposed its own classification having made a comparison between the earlier developed models
(Ocean Wave Modelling, SWAMP group, 1985). This classification was based
on differentiation into types of source function presentation in the spectral
energy density equation and, mainly, on the accuracy of the non-linear energy
transfer estimation in the wind wave spectrum.
The participants of this group decided to initiate the development of
a more advanced wind wave model. Thus, a new International Working Group
WAMDI (Wave Modelling Group) was created with G. Komen, L. Cavaleri,
M. Donelan, K. Hasselmann, S. Hasselmann, P. Janssen, etc. The first paper
was published in 1988 (The WAM Model- A Third Generation Ocean Wave
Prediction Model, 1988). The decision to combine the efforts of scientists from
different countries for developing a wind wave model revealed, on the one
hand, the importance of the problem and, on the other hand, its complexity.
It was decided to develop a new model based on the following principles.
Firstly, it was necessary to use the most accurate approximation of the integral of non-linear energy transfer preserving the same cubic operator structure as the original expression (S. Hasselmann & K. Hasselmann, 1981). The
proper formula was named a "discrete interaction approximation" (Komen et
al., 1994). Secondly, the source function was to be supplemented with a more
precise dissipation mechanism. The dissipation function (Komen et al., 1984)
was obtained from a series of numerical computations of the energy balance
equation with accurate collision integral estimation. The wind wave energy
input mechanism was taken according to experimental data (Snyder et al.,
1981). The mathematical problem was solved in spherical variables, allowing
the use of this model as a global one. In addition, there was an attempt to
generalise the model for the shallow water case. The model took into account
refraction and bottom friction. The non-linear energy transfer function took
into account the corresponding correction describing non-linear wave interac-
7
Komen et al., 1994). There were more models taking into account the effect of
an uneven seabed (Hasselmann & Collins, 1968; Collins, 1972; SWIM Group,
1985; Gutshabash & Lavrenov, 1987, 1988; Khandekar, 1989; Tolman, 1991)
and spatially non-uniform currents (Hurghes & Grant, 1978; Kato & Sato,
1978; Sakai & Iwagaki, 1983; Booij et al., 1984; Gutshabash & Lavrenov, 1986;
Holthuijsen et al., 1989; Khandekar, 1989). However, it should be noted that
there were considerable discrepancies even between the results of the most
advanced models.
This variety of mathematical models indicates that wind waves remain
a very complicated object for investigation, and its theory is far from being
completed. It is difficult to create one universal model optimal for all cases.
That is why different approaches and methods have a right to exist. On the
other hand, a large variety of models help us to better understand wind waves
and develop model implementations using modern computers.
In 1985, due to a large number of different models, the SWAMP International Working Group (Sea Wave Modelling Project) proposed its own classification having made a comparison between the earlier developed models
(Ocean Wave Modelling, SWAMP group, 1985). This classification was based
on differentiation into types of source function presentation in the spectral
energy density equation and, mainly, on the accuracy of the non-linear energy
transfer estimation in the wind wave spectrum.
The participants of this group decided to initiate the development of
a more advanced wind wave model. Thus, a new International Working Group
WAMDI (Wave Modelling Group) was created with G. Komen, L. Cavaleri,
M. Donelan, K. Hasselmann, S. Hasselmann, P. Janssen, etc. The first paper
was published in 1988 (The WAM Model- A Third Generation Ocean Wave
Prediction Model, 1988). The decision to combine the efforts of scientists from
different countries for developing a wind wave model revealed, on the one
hand, the importance of the problem and, on the other hand, its complexity.
It was decided to develop a new model based on the following principles.
Firstly, it was necessary to use the most accurate approximation of the integral of non-linear energy transfer preserving the same cubic operator structure as the original expression (S. Hasselmann & K. Hasselmann, 1981). The
proper formula was named a "discrete interaction approximation" (Komen et
al., 1994). Secondly, the source function was to be supplemented with a more
precise dissipation mechanism. The dissipation function (Komen et al., 1984)
was obtained from a series of numerical computations of the energy balance
equation with accurate collision integral estimation. The wind wave energy
input mechanism was taken according to experimental data (Snyder et al.,
1981). The mathematical problem was solved in spherical variables, allowing
the use of this model as a global one. In addition, there was an attempt to
generalise the model for the shallow water case. The model took into account
refraction and bottom friction. The non-linear energy transfer function took
into account the corresponding correction describing non-linear wave interac-