248
5 Wave Evolution in Non-uniform Currents in Deep Water
and partially transferred to the low-frequency spectral range by non-linear
wave interaction. The contribution of wave interaction with a horizontal nonuniform current to the source function (i.e. the radiation stresses) can be estimated as Gcur::::; ad~tS = 2~~ S. In this case the energy flux is distributed to
the wave spectrum in all frequencies. The non-linear interaction contribution
can be of less importance.
Thus, a quantitative comparison of these two mechanisms can be used
as a rough estimation of its predominant influence on wave development. It
can be suggested that wave generation is predominant over the wave transformation mechanism when G;n > Gcur· As a result the wave transformation
mechanism prevails in limited water basins (for example, sea straits, river
mouths, etc.) with significant current velocity gradients being observed at
small wind speeds. And, on the contrary, wave generation becomes the determining factor for extensive water areas with small current velocity gradients.
Estimation of wave element transformation in a current changing
along its direction. In the case of a large gradient area it is necessary
to use the wave transformation results (see Sect. 5.4). In order to determine
the wind wave elements for deep water in a counter or fair current, the mean
wave period fo must be found in the area without any current. Then the
parameter v is estimated according to the formula:
v
v = 5.2-_-'
gTo
where V (ms- 1 ) is the current velocity and g = 9.81 ms- 2 .
(5.154)
A positive value of the parameter v is used for a wave propagating opposite
to the current, and negative value for a fair current. The wave components
in a current are determined with the help of Fig. 5.40 by the nomograms
given for different initial directions of wave propagation. The ratio of mean
wave height in a current h to the mean height ho in the absence of current is
determined by curves I (see Fig. 5.40) according to the parameter v, depending on the initial angle of wave propagation relative to the current velocity
direction.
The relative value for the mean wavelength >.j>.0 is determined by
curves II, similarly. 4 The mean relative period is determined by curve III.
The following estimations should be fulfilled. Wind waves with a mean
period fo = 5.3 are assumed to propagate from the open sea area to the
strait. The countercurrent's velocity V is 2 ms- 1 . The parameter v is equal
to 0.2 according to the formula (5.154). The mean wave height is increased
by 218 per cent, the length is decreased by 210 per cent and the period is
increased by 8 per cent according to the nomogram (see Fig. 5.40).
4 If the calculated wave steepness is larger than the ultimate value equal to 1/7, the
wave height corresponding to the ultimate steepness for estimated wavelength
should be used.
5 Wave Evolution in Non-uniform Currents in Deep Water
and partially transferred to the low-frequency spectral range by non-linear
wave interaction. The contribution of wave interaction with a horizontal nonuniform current to the source function (i.e. the radiation stresses) can be estimated as Gcur::::; ad~tS = 2~~ S. In this case the energy flux is distributed to
the wave spectrum in all frequencies. The non-linear interaction contribution
can be of less importance.
Thus, a quantitative comparison of these two mechanisms can be used
as a rough estimation of its predominant influence on wave development. It
can be suggested that wave generation is predominant over the wave transformation mechanism when G;n > Gcur· As a result the wave transformation
mechanism prevails in limited water basins (for example, sea straits, river
mouths, etc.) with significant current velocity gradients being observed at
small wind speeds. And, on the contrary, wave generation becomes the determining factor for extensive water areas with small current velocity gradients.
Estimation of wave element transformation in a current changing
along its direction. In the case of a large gradient area it is necessary
to use the wave transformation results (see Sect. 5.4). In order to determine
the wind wave elements for deep water in a counter or fair current, the mean
wave period fo must be found in the area without any current. Then the
parameter v is estimated according to the formula:
v
v = 5.2-_-'
gTo
where V (ms- 1 ) is the current velocity and g = 9.81 ms- 2 .
(5.154)
A positive value of the parameter v is used for a wave propagating opposite
to the current, and negative value for a fair current. The wave components
in a current are determined with the help of Fig. 5.40 by the nomograms
given for different initial directions of wave propagation. The ratio of mean
wave height in a current h to the mean height ho in the absence of current is
determined by curves I (see Fig. 5.40) according to the parameter v, depending on the initial angle of wave propagation relative to the current velocity
direction.
The relative value for the mean wavelength >.j>.0 is determined by
curves II, similarly. 4 The mean relative period is determined by curve III.
The following estimations should be fulfilled. Wind waves with a mean
period fo = 5.3 are assumed to propagate from the open sea area to the
strait. The countercurrent's velocity V is 2 ms- 1 . The parameter v is equal
to 0.2 according to the formula (5.154). The mean wave height is increased
by 218 per cent, the length is decreased by 210 per cent and the period is
increased by 8 per cent according to the nomogram (see Fig. 5.40).
4 If the calculated wave steepness is larger than the ultimate value equal to 1/7, the
wave height corresponding to the ultimate steepness for estimated wavelength
should be used.