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4 Physical Mechanisms Forming the Wave Spectrum in Deep Water
negative for waves propagating faster than the wind speed. In this case the
wave phase speed projection onto the wind direction is compared with the
wind speed. If the dynamical wind pressure on the frontal wave surface is
higher in comparison with the rear surface pressure, this leads to the appearance of energy flow directed from the waves to the wind. Secondly, the
integral energy flow to the waves becomes 2-3 times lower in case of fully developed wind sea. It is determined by the energy outflux from low-frequency
components propagating faster than the wind speed and a relatively small
influx to the waves with velocity being close to the wind speed. Thirdly, in
the high-frequency range, a greater energy flux compared to Snyder's formula
(4.34) is estimated with the help of the approximation (4.39a) since Bu in
(4.39b) is proportional to a~ at aa > 2. The difference in the integral value
of this wind wave energy input and Snyder's ratio becomes smaller for the
initial stage of wind sea development. It should be noted that the value of
the wind wave energy input function used in the WAM model (Komen et al.,
1994) is also much smaller in comparison with Snyder's value.
Since there is not only an energy flux from the wind to the waves, but also
a flux from the waves to the wind in the wave/wind interaction mechanism
(4.39), it becomes possible to use this mechanism for achieving a more rapid
spectrum shape stabilization at the developed wave stage.
The parameter approximation Bu is compared with observational data.
Their consistency within the confidence interval of the measurement results
is shown by Chalikov & Belevich (1995). Additionally a quadratic dependence
of the parameter Bu on the frequency a a for large values is confirmed.
The values U>. and C>. are defined at the level of the "apparent" wavelength in the approximation of the wind wave energy input function ( 4.39) As
the wind speed and the resistance coefficient are changed with height, the introduction of the parameters u).. and c).. eliminates the ambiguity of choosing
the readout level, typically existing in every calculation scheme. It reduces
the number of determining parameters. Also it corresponds to the physics of
the process, since the layer of the air flow /wind interaction becomes thinner
with increasing frequency. In other words, what happens beyond this layer is
not essential for the given wave.
The prevalent part of the momentum flux, connected with waves, is determined to be formed within the high-frequency spectrum range. The surface
resistance can be taken into account with the help of the wind sea model
using the roughness parameter z0 . Its value is dependent on the energy of the
high-frequency components. This can be related to the Phillips parameter a
for the JONSWAP spectrum approximation by the ratio:
Zo = xa 1 1 2 A,
( 4.41)
where A = u; I g, X is a parameter in the range 0.15-Q.25 and u* is the
frequency velocity. The relation ( 4.41) can be considered as a generalization
of the well-known relation of Charnock (1955), taking into account the sea
surface state.
4 Physical Mechanisms Forming the Wave Spectrum in Deep Water
negative for waves propagating faster than the wind speed. In this case the
wave phase speed projection onto the wind direction is compared with the
wind speed. If the dynamical wind pressure on the frontal wave surface is
higher in comparison with the rear surface pressure, this leads to the appearance of energy flow directed from the waves to the wind. Secondly, the
integral energy flow to the waves becomes 2-3 times lower in case of fully developed wind sea. It is determined by the energy outflux from low-frequency
components propagating faster than the wind speed and a relatively small
influx to the waves with velocity being close to the wind speed. Thirdly, in
the high-frequency range, a greater energy flux compared to Snyder's formula
(4.34) is estimated with the help of the approximation (4.39a) since Bu in
(4.39b) is proportional to a~ at aa > 2. The difference in the integral value
of this wind wave energy input and Snyder's ratio becomes smaller for the
initial stage of wind sea development. It should be noted that the value of
the wind wave energy input function used in the WAM model (Komen et al.,
1994) is also much smaller in comparison with Snyder's value.
Since there is not only an energy flux from the wind to the waves, but also
a flux from the waves to the wind in the wave/wind interaction mechanism
(4.39), it becomes possible to use this mechanism for achieving a more rapid
spectrum shape stabilization at the developed wave stage.
The parameter approximation Bu is compared with observational data.
Their consistency within the confidence interval of the measurement results
is shown by Chalikov & Belevich (1995). Additionally a quadratic dependence
of the parameter Bu on the frequency a a for large values is confirmed.
The values U>. and C>. are defined at the level of the "apparent" wavelength in the approximation of the wind wave energy input function ( 4.39) As
the wind speed and the resistance coefficient are changed with height, the introduction of the parameters u).. and c).. eliminates the ambiguity of choosing
the readout level, typically existing in every calculation scheme. It reduces
the number of determining parameters. Also it corresponds to the physics of
the process, since the layer of the air flow /wind interaction becomes thinner
with increasing frequency. In other words, what happens beyond this layer is
not essential for the given wave.
The prevalent part of the momentum flux, connected with waves, is determined to be formed within the high-frequency spectrum range. The surface
resistance can be taken into account with the help of the wind sea model
using the roughness parameter z0 . Its value is dependent on the energy of the
high-frequency components. This can be related to the Phillips parameter a
for the JONSWAP spectrum approximation by the ratio:
Zo = xa 1 1 2 A,
( 4.41)
where A = u; I g, X is a parameter in the range 0.15-Q.25 and u* is the
frequency velocity. The relation ( 4.41) can be considered as a generalization
of the well-known relation of Charnock (1955), taking into account the sea
surface state.