GUIDE WAVE ANALYSIS AND FORECASTING - WMO

54
1.8
1.6
1.4
Ks
1.2
1.0
0.8
Example:
For a deep water wavelength λ 0 = 156 m and T 0 = 10 s,
then k 0 = 0.04 m –1 , and for T 0 = 15 s, k 0 = 0.018 m –1 .
Table 4.10 shows the shoaling factor K s for a
number of shallow depths. It also shows that the height
of shoaling waves is reduced at first, but finally increases
up to the point of breaking which also depends on the
initial wave height in deep water (see also Figures 4.7(a)
and (b)).
4.5.1.2 Variation of wave height due to refraction
In the previous example, no refraction was taken into
account, which implies propagation of waves perpendicular
to parallel bottom depth contours. In natural
conditions this will rarely occur. So the angle of incidence
with respect to the bottom depth contours usually
differs from 90°, which is equivalent to α, the angle
between a wave crest and the local isobath, being different
from 0°. This leads to variation of the width between
wave rays. Using Snell’s law,
H
=
H
The refraction factor is:
0
cg
c
g
cos α
.
cos α
0 0
Kr = cos α0
cos α
GUIDE TO WAVE ANALYSIS AND FORECASTING
0.01 0.1 1
h/λo
(4.13)
with α 0 the angle between a wave crest and a local
isobath in deep water. Figure 4.8, taken from CERC
(1984), is based on Equation 4.13. For a given depth and
wave period the shallow-water angle of incidence (solid
lines) and the refraction factor (broken lines) can be read
off easily for a given deep-water angle of incidence α 0. It
is valid for straight parallel depth contours only.
Problem:
Given an angle α0 = 40° between the wave crests in deep
water and the depth contours of the sloping bottom, find
α and the refraction at h = 8 m for T = 10 s.
h
TABLE 4.10
Wavenumber k and shoaling factor Ks for two wave
periods, at several depths, h, in metres, using
Equations 4.11 and 4.12
T = 10 s, k 0 = 0.04 m –1
Figure 4.7(b) —
A graph of shoaling factor
K s versus h/λ 0 (derived from
CERC, 1984)
T = 15 s, k 0 = 0.018 m –1
(m) k (m –1 ) K s k (m –1 ) K s
100 0.040 1.00 0.018 0.94
50 0.041 0.95 0.021 0.92
25 0.046 0.91 0.028 0.98
15 0.055 0.94 0.035 1.06
10 0.065 1.00 0.043 1.15
5 0.090 1.12 0.060 1.33
2 0.142 1.36 0.095 1.64