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4 Physical Mechanisms Forming the Wave Spectrum in Deep Water
ceiving energy, but not influencing the interaction directly. The interaction
integral (4.1) can be rewritten in the form of the sum of two items. The first
one does not depend directly on the wave action value N = N(k), which is
a function of the wave vector k. But the second one depends explicitly on
N = N(k). This means that when N(k) = 0 the first item of the non-linear
interaction integral for this component Gnl (k) can be different from zero.
Taking into consideration the aforesaid, it is obvious that if three components are directed along the wind (or, at least, the angle between their
direction and the wind speed is less than 90°), there may be one component
with direction opposite to the wind and it can receive energy from the other
three. It should be noted that the discrete interaction approximation (DIA)
of the non-linear transfer used in the WAM model (Komen et al.,1994) does
not produce this effect at all.
The spectral density of the given component starts growing linearly in
accordance with the integral (4.1). After that its non-linear evolution starts.
As shown above, a more intense development of waves propagating against
the wind occurs with wave development. On the one hand the wind results in
further wave development; on the other hand it creates an energy dissipation
for the spectral components propagating against the wind.
While discussing a report by Phillips "Dynamics of random finite amplitude waves", Barber (1961) mentioned that he remembered standing on the
shore of a lagoon, which was 10m wide. The offshore wind was about 3 ms~ 1 ,
and wind waves with a period of about 1 s developed towards a distant shore.
The water near him was calm and shallow, and he noticed very small waves
with a period of about 1 s approaching him. These waves were propagating
against the wind. He did not know what had caused them. There was no boat
around. Probably, the waves were reflected from the other shore. But there
was a beach there, rather than a wall. In connection with this presentation it
could be suggested that the waves were generated by non-linear interaction
of wind waves.
This is probably one of the first discussions of the physical mechanism of
wave generation propagating against the wind. More precise measurements of
this phenomenon are made later. Thus, the presence of spectral components
propagating against the wind is detected in the high-frequency radar measurements of signals reflected from the sea surface. As shown by the BOMEX
experiment (Crombie, 1972), the amplitudes of such components increase
with distance from the shore.
The first explanation of this phenomenon was suggested by M.S. LonguetHiggins in 1961 as a result of a weak wave non-linear interaction in the wind
wave spectrum. In the paper by Crombie et al. (1978), K. Hasselmann showed
that a non-linear interaction could transfer the energy in the direction opposite to the wind. However, the value of this non-linear interaction is two
orders of magnitude less than its maximum. Unfortunately, it was practically impossible at that moment to obtain a more accurate estimation of
the non-linear interaction in the wind wave spectrum due to the difficulty
4 Physical Mechanisms Forming the Wave Spectrum in Deep Water
ceiving energy, but not influencing the interaction directly. The interaction
integral (4.1) can be rewritten in the form of the sum of two items. The first
one does not depend directly on the wave action value N = N(k), which is
a function of the wave vector k. But the second one depends explicitly on
N = N(k). This means that when N(k) = 0 the first item of the non-linear
interaction integral for this component Gnl (k) can be different from zero.
Taking into consideration the aforesaid, it is obvious that if three components are directed along the wind (or, at least, the angle between their
direction and the wind speed is less than 90°), there may be one component
with direction opposite to the wind and it can receive energy from the other
three. It should be noted that the discrete interaction approximation (DIA)
of the non-linear transfer used in the WAM model (Komen et al.,1994) does
not produce this effect at all.
The spectral density of the given component starts growing linearly in
accordance with the integral (4.1). After that its non-linear evolution starts.
As shown above, a more intense development of waves propagating against
the wind occurs with wave development. On the one hand the wind results in
further wave development; on the other hand it creates an energy dissipation
for the spectral components propagating against the wind.
While discussing a report by Phillips "Dynamics of random finite amplitude waves", Barber (1961) mentioned that he remembered standing on the
shore of a lagoon, which was 10m wide. The offshore wind was about 3 ms~ 1 ,
and wind waves with a period of about 1 s developed towards a distant shore.
The water near him was calm and shallow, and he noticed very small waves
with a period of about 1 s approaching him. These waves were propagating
against the wind. He did not know what had caused them. There was no boat
around. Probably, the waves were reflected from the other shore. But there
was a beach there, rather than a wall. In connection with this presentation it
could be suggested that the waves were generated by non-linear interaction
of wind waves.
This is probably one of the first discussions of the physical mechanism of
wave generation propagating against the wind. More precise measurements of
this phenomenon are made later. Thus, the presence of spectral components
propagating against the wind is detected in the high-frequency radar measurements of signals reflected from the sea surface. As shown by the BOMEX
experiment (Crombie, 1972), the amplitudes of such components increase
with distance from the shore.
The first explanation of this phenomenon was suggested by M.S. LonguetHiggins in 1961 as a result of a weak wave non-linear interaction in the wind
wave spectrum. In the paper by Crombie et al. (1978), K. Hasselmann showed
that a non-linear interaction could transfer the energy in the direction opposite to the wind. However, the value of this non-linear interaction is two
orders of magnitude less than its maximum. Unfortunately, it was practically impossible at that moment to obtain a more accurate estimation of
the non-linear interaction in the wind wave spectrum due to the difficulty