5.5 Wave Element Transformations in Current, Varying Along its Direction
187
- - 1
-----2
- · - J
--* 2
5
Ill
fJ
I-o.*
-O.J
-0.2
-O.f
0
0.1
0.2
O.J'J
Fig. 5.15. Relative change of wave height h/ho (I), period r/ro (II) and length
)..j Ao (III) for different values of parameter n: 1 - n = 5; 2 - n = 8; 3 - n = 10;
4- n = 15; 5- full-scale observations of Zhevnovatiy (1971) for h/ho, 6- Scripps'
institute data
It can be seen from the obtained integral ratios (5.40)-(5.42) that the values: h/h0 , >..j >..o and T fro are functions of the non-dimensional parameters v
and n, giving them a more universal character. The functions hjh0 , >..j>..0
and T /To are not expressed in analytical form. Their estimations are made
numerically.
The numerical results for counter- (v > 0) and fair (v < 0) currents
are shown in Fig. 5.15. The non-dimensional current velocity, i.e. the parameter v, is plotted along the horizontal axis. The relative mean parameter
values (5.40)-(5.42) are shown along the vertical axis. The calculations are
made for different values of the parameter n, equal to 5, 8, 10 and 15, respectively, determining the spectrum width. As shown in the nomogram, the
wave heights in a current are increased monotonically up to some maximum
value defined by the parameter n. Thus, with n = 5 the maximum wave
height is increased up to 2.13 in a countercurrent, achieving in maximum at
the point v = 0.21. After that the height is decreased. The wave energy is
practically equal to zero in the range v > 0.37 due to the large value of the
countercurrent velocity.
The wave height increases more slowly at small v for the parameter values
n = 8, 10 in comparison with that for n = 5. However, with further increase
of the parameter v the wave height is increased to a greater extent than for
n = 5. The height maximum is achieved at larger values v, with the wave
height being sharply decreased after that. The transformation of the wave
heights with n = 15 practically coincides with the solution of (5.37) and
(5.38), obtained for a monochromatic wave.
187
- - 1
-----2
- · - J
--* 2
5
Ill
fJ
I-o.*
-O.J
-0.2
-O.f
0
0.1
0.2
O.J'J
Fig. 5.15. Relative change of wave height h/ho (I), period r/ro (II) and length
)..j Ao (III) for different values of parameter n: 1 - n = 5; 2 - n = 8; 3 - n = 10;
4- n = 15; 5- full-scale observations of Zhevnovatiy (1971) for h/ho, 6- Scripps'
institute data
It can be seen from the obtained integral ratios (5.40)-(5.42) that the values: h/h0 , >..j >..o and T fro are functions of the non-dimensional parameters v
and n, giving them a more universal character. The functions hjh0 , >..j>..0
and T /To are not expressed in analytical form. Their estimations are made
numerically.
The numerical results for counter- (v > 0) and fair (v < 0) currents
are shown in Fig. 5.15. The non-dimensional current velocity, i.e. the parameter v, is plotted along the horizontal axis. The relative mean parameter
values (5.40)-(5.42) are shown along the vertical axis. The calculations are
made for different values of the parameter n, equal to 5, 8, 10 and 15, respectively, determining the spectrum width. As shown in the nomogram, the
wave heights in a current are increased monotonically up to some maximum
value defined by the parameter n. Thus, with n = 5 the maximum wave
height is increased up to 2.13 in a countercurrent, achieving in maximum at
the point v = 0.21. After that the height is decreased. The wave energy is
practically equal to zero in the range v > 0.37 due to the large value of the
countercurrent velocity.
The wave height increases more slowly at small v for the parameter values
n = 8, 10 in comparison with that for n = 5. However, with further increase
of the parameter v the wave height is increased to a greater extent than for
n = 5. The height maximum is achieved at larger values v, with the wave
height being sharply decreased after that. The transformation of the wave
heights with n = 15 practically coincides with the solution of (5.37) and
(5.38), obtained for a monochromatic wave.