Introduction
Surface gravity waves have always caused great interest, as they are an example of a well-known, but still very complicated phenomenon. They can easily
be observed, but it is rather difficult to describe them mathematically. Sir
Horace Lamb noted in his letter to the London Mathematical Society in 1904
that waves were almost the first hydrodynamic problem studied systematically on the basis of general equations. It gave an example of activity that
provided efficient evidence of new and unusual analytical methods. Wave
observations on the sea surface and their connection with wind have been
performed from time immemorial. It was quite natural that the pioneers of
theoretical hydrodynamics (J. Lagrange, G. Eiry, G. Stokes and J. Rayleigh)
tried to find an explanation of the elementary properties of surface waves
using the assumption of ideal fluid motion.
Many papers, some of which later became classics, were devoted to solving the problem of surface gravity waves. The well-known Cauchy-Poisson
problem of wave generation caused by an irregular external force in the free
surface of the fluid should be mentioned (Sretenskiy, 1977). Many outstanding
researchers (J. Bussinesk, T. Levi-Civita, G. Stoker, M.S. Longuet-Higgins,
A.l. Nekrasov, S.L. Chaplygin, L.N. Sretensky, N.Ye. Kochin, S.S. Voight,
Ya.N. Sekerzh-Zenkovich, M.A. Lavrentyev, Yu.Z. Aleshkov, V. Zakharov,
E. Pelinovskiy and others) should be mentioned in this connection. Their
studies made a valuable contribution to understanding fluid wave motion
and developed the analytical methods of theoretical studies.
However, real waves on the ocean surface are sufficiently complicated that
theory is never adequate to explain actual observations. J. Rayleigh (1876)
pointed out that the main law of sea waves was the absence of any law. The
irregularity of wind waves made their description difficult.
In 1805, Beaufort was among the first to try to establish a relation between
the wind force and sea surface state. Based on many sea surface observations
during storms he discovered that typical wave heights and periods appeared
at a specific wind speed, i.e. wind of a definite force induced sea waves with
typical elements. As a result his famous scale of waves appeared and it is still
used in modified form (Abuzyarov, 1981).
The problem of wave height correlation with wind speed was formulated
by W. Kelvin (1871), although no real progress was achieved at that time.
By 1850, T. Stevenson carried out surface wave observations in lakes and
Surface gravity waves have always caused great interest, as they are an example of a well-known, but still very complicated phenomenon. They can easily
be observed, but it is rather difficult to describe them mathematically. Sir
Horace Lamb noted in his letter to the London Mathematical Society in 1904
that waves were almost the first hydrodynamic problem studied systematically on the basis of general equations. It gave an example of activity that
provided efficient evidence of new and unusual analytical methods. Wave
observations on the sea surface and their connection with wind have been
performed from time immemorial. It was quite natural that the pioneers of
theoretical hydrodynamics (J. Lagrange, G. Eiry, G. Stokes and J. Rayleigh)
tried to find an explanation of the elementary properties of surface waves
using the assumption of ideal fluid motion.
Many papers, some of which later became classics, were devoted to solving the problem of surface gravity waves. The well-known Cauchy-Poisson
problem of wave generation caused by an irregular external force in the free
surface of the fluid should be mentioned (Sretenskiy, 1977). Many outstanding
researchers (J. Bussinesk, T. Levi-Civita, G. Stoker, M.S. Longuet-Higgins,
A.l. Nekrasov, S.L. Chaplygin, L.N. Sretensky, N.Ye. Kochin, S.S. Voight,
Ya.N. Sekerzh-Zenkovich, M.A. Lavrentyev, Yu.Z. Aleshkov, V. Zakharov,
E. Pelinovskiy and others) should be mentioned in this connection. Their
studies made a valuable contribution to understanding fluid wave motion
and developed the analytical methods of theoretical studies.
However, real waves on the ocean surface are sufficiently complicated that
theory is never adequate to explain actual observations. J. Rayleigh (1876)
pointed out that the main law of sea waves was the absence of any law. The
irregularity of wind waves made their description difficult.
In 1805, Beaufort was among the first to try to establish a relation between
the wind force and sea surface state. Based on many sea surface observations
during storms he discovered that typical wave heights and periods appeared
at a specific wind speed, i.e. wind of a definite force induced sea waves with
typical elements. As a result his famous scale of waves appeared and it is still
used in modified form (Abuzyarov, 1981).
The problem of wave height correlation with wind speed was formulated
by W. Kelvin (1871), although no real progress was achieved at that time.
By 1850, T. Stevenson carried out surface wave observations in lakes and