2
Introduction
obtained some empirical ratios between the largest wave height and fetch.
75 years later H. Jeffreys (1971) tried to model wave generation by wind under
laboratory conditions. And still in 1956 F. Ursell reasonably mentioned that
wind blowing over the surface of water generated waves by means of physical
processes that could not be considered to be well studied.
At the same time, applied wave prediction problems required the construction of mathematical methods for wind wave estimation. The energy
wave balance equation, proposed by V.M. Makkaveyev in 1937, was one of
the first attempts to apply a mathematical approximation of the evolution of
wind waves in practice. This equation described wind wave energy evolution
in its simplest form, depending on the energy supply due to wind and dissipation. The "energy approach" resulted in the creation of elementary practical
methods for wave calculation and predication. It gave the possibility of estimating wave elements in deep and shallow water depending on wind speed
and direction, duration, fetch and sea depth. Widespread practical methods
and wave prediction were proposed by the Russian scientists V.V. Shuleykin
(1959), Yu.M. Krylov (1956) for deep sea and A.P. Braslavskiy (1952) for
shallow water conditions. The methods of H. Sverdrup and V. Munk (1961),
modified by C. Bretschneider (1958), were worked out in Western countries.
Simultaneously with the study of the physical nature of sea waves,
their statistical properties were investigated. M.S. Longuet-Higgins (1962),
Yu.M. Krylov (1966) and I.S. Brovikov (1954) conducted theoretical studies and I.N. Davidan (1969), Ya.G. Vilenskiy and B.H. Glukhovskiy (1961,
1955) carried out empirical studies on the basis of processing wave records
and visual wave observations. It was established that in spite of the variety
of individual waves, their statistical characteristics (such as the mean height,
mean period, mean length, dispersion, distribution function, correlation function and two-dimensional spectrum) were stable in the quasi-stationary and
quasi-uniform process range.
A synthesis of energetic and statistical regularities of wind waves made
it possible to extend the calculation of sea wave elements. This was used by
G.V. Rzheplinskiy, Yu.M. Krylov and G.V. Matyshevskiy (1969) to create
methods of wind wave calculation for complicated wave formation conditions
at an uneven sea coastline.
A new important achievement in the theoretical description of wind sea
was made in the 1950s. The investigators approached the study of wind waves
in terms of spectra using the modern theory of random functions. Wind waves
were considered to be a probable random process and were described on the
basis of combined application of statistical and hydrodynamic methods. The
Fourier representation of a random wave process allowed one to separate it
into harmonic elements, whose conduct might be considered in terms of the
classical theory of wave motion.
The results of M.S. Longuet-Higgins and co-workers (1957, 196Q-1962,
1964), O.M. Phillips (1957, 1958), J. Miles (1957, 1960) and K. Hasselmann
(1960, 1962, 1963, 1965, 1966) published after 1956, were the basis of the
Introduction
obtained some empirical ratios between the largest wave height and fetch.
75 years later H. Jeffreys (1971) tried to model wave generation by wind under
laboratory conditions. And still in 1956 F. Ursell reasonably mentioned that
wind blowing over the surface of water generated waves by means of physical
processes that could not be considered to be well studied.
At the same time, applied wave prediction problems required the construction of mathematical methods for wind wave estimation. The energy
wave balance equation, proposed by V.M. Makkaveyev in 1937, was one of
the first attempts to apply a mathematical approximation of the evolution of
wind waves in practice. This equation described wind wave energy evolution
in its simplest form, depending on the energy supply due to wind and dissipation. The "energy approach" resulted in the creation of elementary practical
methods for wave calculation and predication. It gave the possibility of estimating wave elements in deep and shallow water depending on wind speed
and direction, duration, fetch and sea depth. Widespread practical methods
and wave prediction were proposed by the Russian scientists V.V. Shuleykin
(1959), Yu.M. Krylov (1956) for deep sea and A.P. Braslavskiy (1952) for
shallow water conditions. The methods of H. Sverdrup and V. Munk (1961),
modified by C. Bretschneider (1958), were worked out in Western countries.
Simultaneously with the study of the physical nature of sea waves,
their statistical properties were investigated. M.S. Longuet-Higgins (1962),
Yu.M. Krylov (1966) and I.S. Brovikov (1954) conducted theoretical studies and I.N. Davidan (1969), Ya.G. Vilenskiy and B.H. Glukhovskiy (1961,
1955) carried out empirical studies on the basis of processing wave records
and visual wave observations. It was established that in spite of the variety
of individual waves, their statistical characteristics (such as the mean height,
mean period, mean length, dispersion, distribution function, correlation function and two-dimensional spectrum) were stable in the quasi-stationary and
quasi-uniform process range.
A synthesis of energetic and statistical regularities of wind waves made
it possible to extend the calculation of sea wave elements. This was used by
G.V. Rzheplinskiy, Yu.M. Krylov and G.V. Matyshevskiy (1969) to create
methods of wind wave calculation for complicated wave formation conditions
at an uneven sea coastline.
A new important achievement in the theoretical description of wind sea
was made in the 1950s. The investigators approached the study of wind waves
in terms of spectra using the modern theory of random functions. Wind waves
were considered to be a probable random process and were described on the
basis of combined application of statistical and hydrodynamic methods. The
Fourier representation of a random wave process allowed one to separate it
into harmonic elements, whose conduct might be considered in terms of the
classical theory of wave motion.
The results of M.S. Longuet-Higgins and co-workers (1957, 196Q-1962,
1964), O.M. Phillips (1957, 1958), J. Miles (1957, 1960) and K. Hasselmann
(1960, 1962, 1963, 1965, 1966) published after 1956, were the basis of the