210
5 Wave Evolution in Non-uniform Currents in Deep Water
Grodskiy et al., 1989; Dulov & Kudryavtsev, 1989, 1992; Kudryavtsev et. al.,
1995; Dulov et al., 1996, 1998). They propose a method of determining the
wind wave spectrum, using photographic negatives (Bolshakov et al., 1988).
The observed wave fields are compared with the solution of the refraction
equations for waves in a current. In some cases of quasi-uniform wave developing conditions the current effect is identified in the fields of integral characteristics of the two-dimensional wind wave spectra. Although this problem
is sufficiently difficult and not completely investigated, in general it seems to
be quite promising.
In this section an attempt is undertaken to explain the spatial nonuniformity of a wind wave field in the frontal zone characterized by large
current velocity gradients. The reverse problem, namely, the estimation of
the current velocity with the help of wave spectra based on aerial photography data can be solved using the proposed mathematical model.
For example, using the direction of the spectrum maximum of reflected
waves and the corresponding part of the direct wave spectrum, the current
direction and velocity at which this reflection occurred can be easily estimated. The current direction can be determined with the help of the mirror
reflection condition:
(5.82)
where (32 is the propagation direction of the reflected waves, equal to 40°,
and (31 is the direction of the corresponding direct waves, equal to 140°.
Using the kinematic relations (5.63), (5.64), the current velocity variation
at the two-flow boundary in the wave reflection area is estimated as:
"V _ {"g1- jsin ((JI) ~
_1
u
-yk sin(f31)
1.2ms .
(5.83)
As can be seen, these estimations are in good agreement with full-scale
observations. The error in determining the latter is within the range of 25 per
cent, which is mainly connected with the discreteness of spectra presentation,
their variability and error in determining the angle (31.
So, if it were possible to identify the direct, reflected and transmitted
spectral components not only in the spectral maximum, but also in a wider
frequency range, the accuracy of determining the current velocity with the
help of aerial photographs would be increased, by specifying the methods of
initial data processing and analysis.
Wave element estimation in currents with transversal horizontal
velocity shear. The numerical estimation of mean wave elements will be
made in a shear horizontally non-uniform current with a maximum at the
point Xm· In order to do so, the earlier obtained spectral solution is used.
It should be taken into account that there is no wave reflection at the flow
points x > Xm· The wave elements are determined by numerically integrating
the corresponding spectral moments (5.71), (5.74), (5.75), (5.77)-(5.81).
5 Wave Evolution in Non-uniform Currents in Deep Water
Grodskiy et al., 1989; Dulov & Kudryavtsev, 1989, 1992; Kudryavtsev et. al.,
1995; Dulov et al., 1996, 1998). They propose a method of determining the
wind wave spectrum, using photographic negatives (Bolshakov et al., 1988).
The observed wave fields are compared with the solution of the refraction
equations for waves in a current. In some cases of quasi-uniform wave developing conditions the current effect is identified in the fields of integral characteristics of the two-dimensional wind wave spectra. Although this problem
is sufficiently difficult and not completely investigated, in general it seems to
be quite promising.
In this section an attempt is undertaken to explain the spatial nonuniformity of a wind wave field in the frontal zone characterized by large
current velocity gradients. The reverse problem, namely, the estimation of
the current velocity with the help of wave spectra based on aerial photography data can be solved using the proposed mathematical model.
For example, using the direction of the spectrum maximum of reflected
waves and the corresponding part of the direct wave spectrum, the current
direction and velocity at which this reflection occurred can be easily estimated. The current direction can be determined with the help of the mirror
reflection condition:
(5.82)
where (32 is the propagation direction of the reflected waves, equal to 40°,
and (31 is the direction of the corresponding direct waves, equal to 140°.
Using the kinematic relations (5.63), (5.64), the current velocity variation
at the two-flow boundary in the wave reflection area is estimated as:
"V _ {"g1- jsin ((JI) ~
_1
u
-yk sin(f31)
1.2ms .
(5.83)
As can be seen, these estimations are in good agreement with full-scale
observations. The error in determining the latter is within the range of 25 per
cent, which is mainly connected with the discreteness of spectra presentation,
their variability and error in determining the angle (31.
So, if it were possible to identify the direct, reflected and transmitted
spectral components not only in the spectral maximum, but also in a wider
frequency range, the accuracy of determining the current velocity with the
help of aerial photographs would be increased, by specifying the methods of
initial data processing and analysis.
Wave element estimation in currents with transversal horizontal
velocity shear. The numerical estimation of mean wave elements will be
made in a shear horizontally non-uniform current with a maximum at the
point Xm· In order to do so, the earlier obtained spectral solution is used.
It should be taken into account that there is no wave reflection at the flow
points x > Xm· The wave elements are determined by numerically integrating
the corresponding spectral moments (5.71), (5.74), (5.75), (5.77)-(5.81).