6
Introduction
LeBlond, 1989; Meylan & Squire, 1994; Shuchman & Rufenach, 1994; Wadhams et al., 1986). Analysing the modern state of the theory, three principal
research trends can be pointed out: research into water surface gravity waves
in the presence of ice cake (Bukatov & Bukatova, 1993; Lavrenov 1998a,
Kheysin, 1967; Zubakin, 1976; Smirnov, 1996); investigation of surface gravity and internal wave propagation under an elastic layer simulating an ice
sheet (Bukatov & Cherkesov, 1971; Marchenko, 1988); and study of wave
diffraction caused by an ice floe (Kheysin, 1967; Mylan & Squire, 1994). In
most cases these problems are solved with the help of the deterministic approximation. An attempt to solve the problem of wave development caused
by wind action, dissipation due to wave breaking, non-linear energy transfer
in the wave spectrum and wave scattering by ice floes without taking into
consideration their elastic properties was undertaken by Masson & LeBlond
(1989). The approach, elaborated in this monograph, allows the description
of wind wave spectrum evolution in a spatial non-uniform medium using
the geometrical optics approximation theory. It may also be applied to wave
transformation in water with spatially non-uniform ice fields.
In the past few decades, many mathematical wind wave models have been
developed. According to data from the World Meteorological Organisation
(WMO) there were more than 20 models in 1985 without taking into account
the models in the process of development (Marine Meteorology and Related
Oceanographic Activities, 1986). The Meteorological Services in the USA,
Great Britain, Norway, Germany, Japan and other countries used 11 models in their forecasting practice. In 1988 the National Services already used
16 models in their operational practice, and another 14 models were reported
to be used in practical activities (Guide to Wave Analysis and Forecasting,
1988). In 1991, according to WMO information, the National Meteorological
Services in 17 countries, including France, Germany, Greece, Hong Kong, India, Ireland, Japan, Malaysia, Holland, New Zealand, Norway, Saudi Arabia,
Sweden, Great Britain, the USA and Russia used 22 models for official wind
wave prediction. The total number of models used for operational purposes
in different countries was more than 40 (WMO Wave Programme, 1991).
In Russia, the use of numerical modelling of wind waves began after some
delay in comparison with Western countries. This was connected with a lagging behind in computer manufacturing. However, at present there are more
than 20 wind wave models (Abuzyarov, 1981; Theoretical Bases and Methods
for Wind Sea Calculation, 1988; Zaslavskii, 1989b; Catalogue of Applied Computer Programs for Shore Protection, 1989; Matushevskiy & Kabatchenko,
1989, 1991; Yefimov & Polnikov, 1991). These models are significantly different in their objectives, types, characteristics, verification using natural
observations, etc.
In the early 1990s the variety of models increased. There were models
describing wind waves not only on a regional, but also on a global scale
(The WAM Model- A Third Generation Ocean Wave Prediction Model,
1988; Lavrenov & Pasechnik, 1989; Lavrenov & Ryvkin, 1989; Tolman, 1991;
Introduction
LeBlond, 1989; Meylan & Squire, 1994; Shuchman & Rufenach, 1994; Wadhams et al., 1986). Analysing the modern state of the theory, three principal
research trends can be pointed out: research into water surface gravity waves
in the presence of ice cake (Bukatov & Bukatova, 1993; Lavrenov 1998a,
Kheysin, 1967; Zubakin, 1976; Smirnov, 1996); investigation of surface gravity and internal wave propagation under an elastic layer simulating an ice
sheet (Bukatov & Cherkesov, 1971; Marchenko, 1988); and study of wave
diffraction caused by an ice floe (Kheysin, 1967; Mylan & Squire, 1994). In
most cases these problems are solved with the help of the deterministic approximation. An attempt to solve the problem of wave development caused
by wind action, dissipation due to wave breaking, non-linear energy transfer
in the wave spectrum and wave scattering by ice floes without taking into
consideration their elastic properties was undertaken by Masson & LeBlond
(1989). The approach, elaborated in this monograph, allows the description
of wind wave spectrum evolution in a spatial non-uniform medium using
the geometrical optics approximation theory. It may also be applied to wave
transformation in water with spatially non-uniform ice fields.
In the past few decades, many mathematical wind wave models have been
developed. According to data from the World Meteorological Organisation
(WMO) there were more than 20 models in 1985 without taking into account
the models in the process of development (Marine Meteorology and Related
Oceanographic Activities, 1986). The Meteorological Services in the USA,
Great Britain, Norway, Germany, Japan and other countries used 11 models in their forecasting practice. In 1988 the National Services already used
16 models in their operational practice, and another 14 models were reported
to be used in practical activities (Guide to Wave Analysis and Forecasting,
1988). In 1991, according to WMO information, the National Meteorological
Services in 17 countries, including France, Germany, Greece, Hong Kong, India, Ireland, Japan, Malaysia, Holland, New Zealand, Norway, Saudi Arabia,
Sweden, Great Britain, the USA and Russia used 22 models for official wind
wave prediction. The total number of models used for operational purposes
in different countries was more than 40 (WMO Wave Programme, 1991).
In Russia, the use of numerical modelling of wind waves began after some
delay in comparison with Western countries. This was connected with a lagging behind in computer manufacturing. However, at present there are more
than 20 wind wave models (Abuzyarov, 1981; Theoretical Bases and Methods
for Wind Sea Calculation, 1988; Zaslavskii, 1989b; Catalogue of Applied Computer Programs for Shore Protection, 1989; Matushevskiy & Kabatchenko,
1989, 1991; Yefimov & Polnikov, 1991). These models are significantly different in their objectives, types, characteristics, verification using natural
observations, etc.
In the early 1990s the variety of models increased. There were models
describing wind waves not only on a regional, but also on a global scale
(The WAM Model- A Third Generation Ocean Wave Prediction Model,
1988; Lavrenov & Pasechnik, 1989; Lavrenov & Ryvkin, 1989; Tolman, 1991;