Introduction
3
physics of wind wave development. O.M. Phillips proposed a linear spectral
theory of the mechanism of resonance in wave generation due to normal
pressure fluctuations of turbulent wind. A model of the influence of a pressure
harmonic wave on an ideal incompressible fluid surface was further described
by G. Lamb (1947), L.N. Sretenskiy (1977), et al.
The mechanism of wave generation, suggested by J. Miles, was based
on the theory of the instability of the air-water interface in the presence of
a flow with a velocity gradient in the boundary layer. The classical studies by
W. Kelvin (1871) and G. Helmholtz (LeBlond & Maysek, 1981) giving the
solution of the unstable interface problem between two fluids with different,
but constant densities and motion velocities served as a basis of the theory
of J. Miles.
The important part in forming the structure of the wind wave spectrum
is explained with the help of wave-wave interactions. Theoretical studies of
this problem were initiated by M.S. Longuet-Higgins (Ocean Wave Modeling,
1985) and continued by O.M. Phillips (1960). The non-linear wave interaction
for the continuous spectrum case was investigated by K. Hasselmann (1960,
1962, 1963, 1965) and independently by V. Zakharov (1968). As a result of the
four-wave resonance interaction, energy redistribution occurred in the wind
wave spectrum. The complete wave action, energy and wave momentum were
preserved. For a long time, the complicated form of the collision integral did
not allow researchers to obtain correct numerical estimations of non-linear
energy transfer in the wind wave spectrum.
At that time, O.M. Phillips (1958) showed the existence of an equilibrium
or saturating interval in the wind wave spectrum in the high-frequency spectrum range. Governed by intense energy dissipation it reached its upper limit
due to wave crest collapse. As it was shown later (Kitaigorodskii et al., 1975)
the equilibrium interval of the spatial spectrum was an invariant irrespective
of the basin depth or the current.
The results of M.S. Longuet-Higgins also served as a basis for the modern
understanding of wave evolution in non-uniform currents and shallow water.
In particular he was able to show (Longuet-Higgins, 1957) that the spatial
spectrum preserved its value along the trajectory of a wave packet propagating with wave refraction. His studies, performed with R. Stewart, considered
the effects of wave interaction with non-uniform currents. This interaction
was described by the so-called radiation stresses (Longuet-Higgins and Stewart, 1960-1962, 1964). These ideas were further developed by F.P. Bretherton
and C.J.R. Garret (1968) and F.P. Bretherton (1971) showing that the adiabatic invariant-wave action preserved the same value in non-uniform moving
media.
In the 1960s, when powerful computers appeared, wind wave numerical
modelling began to be developed as a result of integrating the spectral energy
balance equation. Elaboration of such models began in Russia (Davidan,
1969; Pasechnik, 1975; Davidan et al., 1975, 1977, 1978; Dzhenyuk, 1976), in
France (Gelci et al., 1963; Fons, 1966; Gelci & Devillaz, 1969, 1975), in the
3
physics of wind wave development. O.M. Phillips proposed a linear spectral
theory of the mechanism of resonance in wave generation due to normal
pressure fluctuations of turbulent wind. A model of the influence of a pressure
harmonic wave on an ideal incompressible fluid surface was further described
by G. Lamb (1947), L.N. Sretenskiy (1977), et al.
The mechanism of wave generation, suggested by J. Miles, was based
on the theory of the instability of the air-water interface in the presence of
a flow with a velocity gradient in the boundary layer. The classical studies by
W. Kelvin (1871) and G. Helmholtz (LeBlond & Maysek, 1981) giving the
solution of the unstable interface problem between two fluids with different,
but constant densities and motion velocities served as a basis of the theory
of J. Miles.
The important part in forming the structure of the wind wave spectrum
is explained with the help of wave-wave interactions. Theoretical studies of
this problem were initiated by M.S. Longuet-Higgins (Ocean Wave Modeling,
1985) and continued by O.M. Phillips (1960). The non-linear wave interaction
for the continuous spectrum case was investigated by K. Hasselmann (1960,
1962, 1963, 1965) and independently by V. Zakharov (1968). As a result of the
four-wave resonance interaction, energy redistribution occurred in the wind
wave spectrum. The complete wave action, energy and wave momentum were
preserved. For a long time, the complicated form of the collision integral did
not allow researchers to obtain correct numerical estimations of non-linear
energy transfer in the wind wave spectrum.
At that time, O.M. Phillips (1958) showed the existence of an equilibrium
or saturating interval in the wind wave spectrum in the high-frequency spectrum range. Governed by intense energy dissipation it reached its upper limit
due to wave crest collapse. As it was shown later (Kitaigorodskii et al., 1975)
the equilibrium interval of the spatial spectrum was an invariant irrespective
of the basin depth or the current.
The results of M.S. Longuet-Higgins also served as a basis for the modern
understanding of wave evolution in non-uniform currents and shallow water.
In particular he was able to show (Longuet-Higgins, 1957) that the spatial
spectrum preserved its value along the trajectory of a wave packet propagating with wave refraction. His studies, performed with R. Stewart, considered
the effects of wave interaction with non-uniform currents. This interaction
was described by the so-called radiation stresses (Longuet-Higgins and Stewart, 1960-1962, 1964). These ideas were further developed by F.P. Bretherton
and C.J.R. Garret (1968) and F.P. Bretherton (1971) showing that the adiabatic invariant-wave action preserved the same value in non-uniform moving
media.
In the 1960s, when powerful computers appeared, wind wave numerical
modelling began to be developed as a result of integrating the spectral energy
balance equation. Elaboration of such models began in Russia (Davidan,
1969; Pasechnik, 1975; Davidan et al., 1975, 1977, 1978; Dzhenyuk, 1976), in
France (Gelci et al., 1963; Fons, 1966; Gelci & Devillaz, 1969, 1975), in the