306
6 Wave Transformation in Shallow Water
(6.61)
(6.62)
(6.63)
where m 0 is the spectrum zero moment, w is the frequency, km is the wave
number of the spectrum maximum, and H is the water depth.
As shown in Problems of Research and Mathematical Modeling of Sea
Wind (1995), a normalized value of the spectrum zero moment at the point
with depth 11 and 18m is correlated with the non-dimensional value of the
spectrum maximum as follows:
(6.64)
where a = a X 10- 3 , a = 2.0.
In order to check this correlation all results, obtained in December 2-4,
are used. The estimation results are shown in Table 6.1.
It is seen (Table 6.1) that the coefficient value a is practically independent
of the non-dimensional frequency at least at WH 0.6-1.6 with depth ll-18m,
where the bottom slope makes up 0.006. The mean value a is equal to 2.04,
corresponding to the value obtained earlier. The mean square deviation is
0.22. This is less in comparison with the observational analysis made in other
conditions (shown below).
The mean value a is increased to 2.57 at the depth 4.5 m, where the
bottom slope is different and makes up 0.025. As seen (see Figs. 6.23 and
6.24), the wave height is not only reduced, but it is considerably increased at
the depth 3.8 and 3.4 m. The mean values are increased to 3.85, after which
wave breaking starts and the wave height is again reduced. The mean value
a is equal to 3.08 at the depth 2.9 m.
In order to analyse the obtained results some other experimental data will
be noted. The main results of the ARSLOE experiment (Bouws et al., 1985,
1987), devoted to the investigation of wave transformation in a coastal zone
lead to the conclusion that it is possible to use the correlation obtained for
the Phillips spectrum (Kitaigorodsii et al., 1975) for approximation of the
one-dimensional spectrum using the wave number spectrum. Having such
results, it is possible to use the following transfer function passing from the
frequency spectrum in deep water to that in shallow water:
( )
(k (w, H))- 3 ok (w, H) /ow
qJ WH =
3
,
(k(w,oo))- 8k(w,oo)j8w
(6.65)
where oo denotes deep water, and His the shallow water depth.
6 Wave Transformation in Shallow Water
(6.61)
(6.62)
(6.63)
where m 0 is the spectrum zero moment, w is the frequency, km is the wave
number of the spectrum maximum, and H is the water depth.
As shown in Problems of Research and Mathematical Modeling of Sea
Wind (1995), a normalized value of the spectrum zero moment at the point
with depth 11 and 18m is correlated with the non-dimensional value of the
spectrum maximum as follows:
(6.64)
where a = a X 10- 3 , a = 2.0.
In order to check this correlation all results, obtained in December 2-4,
are used. The estimation results are shown in Table 6.1.
It is seen (Table 6.1) that the coefficient value a is practically independent
of the non-dimensional frequency at least at WH 0.6-1.6 with depth ll-18m,
where the bottom slope makes up 0.006. The mean value a is equal to 2.04,
corresponding to the value obtained earlier. The mean square deviation is
0.22. This is less in comparison with the observational analysis made in other
conditions (shown below).
The mean value a is increased to 2.57 at the depth 4.5 m, where the
bottom slope is different and makes up 0.025. As seen (see Figs. 6.23 and
6.24), the wave height is not only reduced, but it is considerably increased at
the depth 3.8 and 3.4 m. The mean values are increased to 3.85, after which
wave breaking starts and the wave height is again reduced. The mean value
a is equal to 3.08 at the depth 2.9 m.
In order to analyse the obtained results some other experimental data will
be noted. The main results of the ARSLOE experiment (Bouws et al., 1985,
1987), devoted to the investigation of wave transformation in a coastal zone
lead to the conclusion that it is possible to use the correlation obtained for
the Phillips spectrum (Kitaigorodsii et al., 1975) for approximation of the
one-dimensional spectrum using the wave number spectrum. Having such
results, it is possible to use the following transfer function passing from the
frequency spectrum in deep water to that in shallow water:
( )
(k (w, H))- 3 ok (w, H) /ow
qJ WH =
3
,
(k(w,oo))- 8k(w,oo)j8w
(6.65)
where oo denotes deep water, and His the shallow water depth.