212
5 Wave Evolution in Non-uniform Currents in Deep Water
FA= F (y, f3- n) e [ Jth (y 2 aoho sin (/3)) sin (/3)
- Jth(fj 2 aoh)+vo(.A-.Al)sin(f3)];
at the point B:
(5.89)
(5.90)
In the fourth quadrant (3nl2 < f3 < 2n) it can be presented at the point A
as:
FA=F(y,/3)
at the point B as:
FB = F (fj,/3) .
(5.91)
With the help of the above solution, the moments of the spectra are
calculated numerically. The mean relative values of the wave elements are
determined as: height h = hI ho, period i = T I To and length 5. = .A I .Ao.
The results of numerical wave element calculations in a shear horizontally
non-uniform current in deep water are shown in Figs. 5.25a,b and 5.26. The
relative value of the current velocity VIVa is marked on the horizontal axis.
The left axis boundary corresponds to the initial point, whereas the right one
coincides with a finite point of the current velocity diagram. It is seen (see
Fig. 5.25a) that the wave height is greater than one at the left boundary, but
it is less than one at the right boundary. The phenomenon is due to the wave
reflection effect. The wave height is decreased two-fold at the angle 60°.
The wavelength and the period are also changed in the current, but to
a lesser extent. The general direction of wave propagation in a current is
shown in Fig. 5.26. It is subjected to significant variations at different points
of the current profile.
Diffraction estimations of monochromatic wave elements in a shear
horizontally non-uniform current.
The obtained solution (5.68) is
a spectral generalization of the classic solution derived in the case of the
initial spectrum being prescribed in the form of the Dirac delta function:
Fa (ko, f3o) = 2nmoc5 (ko - k8) c5 (/3o- /38) .
(5.92)
The relative mean wave height h = hlho can be calculated in a current,
using the function (5.92) as the initial boundary spectrum:
5 Wave Evolution in Non-uniform Currents in Deep Water
FA= F (y, f3- n) e [ Jth (y 2 aoho sin (/3)) sin (/3)
- Jth(fj 2 aoh)+vo(.A-.Al)sin(f3)];
at the point B:
(5.89)
(5.90)
In the fourth quadrant (3nl2 < f3 < 2n) it can be presented at the point A
as:
FA=F(y,/3)
at the point B as:
FB = F (fj,/3) .
(5.91)
With the help of the above solution, the moments of the spectra are
calculated numerically. The mean relative values of the wave elements are
determined as: height h = hI ho, period i = T I To and length 5. = .A I .Ao.
The results of numerical wave element calculations in a shear horizontally
non-uniform current in deep water are shown in Figs. 5.25a,b and 5.26. The
relative value of the current velocity VIVa is marked on the horizontal axis.
The left axis boundary corresponds to the initial point, whereas the right one
coincides with a finite point of the current velocity diagram. It is seen (see
Fig. 5.25a) that the wave height is greater than one at the left boundary, but
it is less than one at the right boundary. The phenomenon is due to the wave
reflection effect. The wave height is decreased two-fold at the angle 60°.
The wavelength and the period are also changed in the current, but to
a lesser extent. The general direction of wave propagation in a current is
shown in Fig. 5.26. It is subjected to significant variations at different points
of the current profile.
Diffraction estimations of monochromatic wave elements in a shear
horizontally non-uniform current.
The obtained solution (5.68) is
a spectral generalization of the classic solution derived in the case of the
initial spectrum being prescribed in the form of the Dirac delta function:
Fa (ko, f3o) = 2nmoc5 (ko - k8) c5 (/3o- /38) .
(5.92)
The relative mean wave height h = hlho can be calculated in a current,
using the function (5.92) as the initial boundary spectrum: