GUIDE WAVE ANALYSIS AND FORECASTING - WMO

52
120 n.mi., estimate the swell heights in the cases
described in Sections 4.4.1 and 4.4.2 with the experience
gained from Section 4.4.3.
Solution 4.4.1:
In Section 4.4.1, the distance to point A is 600 n.mi., or
five times the fetch width. From Figure 3.3, the angular
spreading factor is about 12 per cent. Thus, the characteristic
height of the swell arriving at A should be less
than √0.12 x 12 = 4.2 m.
We can determine the dispersion factor from the
same PNJ graph as before (see Annex IV), but we have
to determine an effective wind speed since only the
wave height is known. The effective wind speed is
determined by following the line for a 15 s period on
the PNJ graph to where it intersects the given wave
height. We can determine the effective wind speed from
the intersection point, in this case 21.5 m/s (43 kn).
Then we determine the E values, and compute the
dispersion factors as in Section 4.3.3. Since the swell
spectrum is broadest at 42 h, the wave heights are highest
at that time. The dispersion factor is about 0.8
giving a multiplier of about 0.9 which leads to a characteristic
wave height of about 3.7 m when angular
spreading is included in the computation.
The height is very small at first, when only long
waves arrive at A. The wave heights are highest in
the period between 40 h and 50 h (see Table 4.6), since
the swell spectrum has its greatest width during that
period.
The distance to point B equals about eight times
the width of the fetch area, which leads to an angular
spreading factor of about 6 per cent; therefore the swell
heights at point B should be no more than 2.9 m.
Considering that the wave dispersion must have
progressed further from point A to point B and that the
smaller components may have been dissipated on their
long journey as a result of internal friction and air
resistance, we can compute, from PNJ, wave dispersion
factors for each arrival time. The widest part of the
spectrum, with the highest heights, passes point B
about 60 h after generation. The dispersion factor for
this time is about 0.6, so the multiplier is about
0.8; therefore, the characteristic swell height will be
about 2.3 m.
Solution 4.4.2:
In Section 4.4.2, the swell spectrum at point A is more
complex. There is a range of generation wave periods
from 12 to 15 s. There is also a limited fetch (180
n.mi.). The highest characteristic waves possible differ
for each of these wave limits.
To determine these wave period limits, we use the
distorted co-cumulative spectra for wind speeds
10–44 kn as a function of fetch from PNJ. To ascertain
the maximum characteristic wave height for the 15 s
waves, we trace the 15 s period line to where it intersects
the 180 n.mi. fetch line and read the wave height
GUIDE TO WAVE ANALYSIS AND FORECASTING
(4.5 m = 14.8 ft). We also find an effective wind speed
for these waves (13 m/s = 26 kn). Likewise we discover
these values for the 12 s waves (characteristic wave
height = 4.8 m = 15.8 ft, and effective wind speed = 14
m/s = 28 kn). The E values (energy proportions) are
determined in the same way as before.
By comparing the 15 s and 12 s wave heights after
the dispersion factors have been taken into account for
each forecast hour, we can show that the waves arriving
at 60 h have the greatest characteristic heights. Recall,
the angular spreading factor at point A is 12 per cent;
this means the highest characteristics possible for
these conditions have a height of about 1.7 m. The
dispersion factor at 60 h is about 0.82 with the multiplier
being about 0.9; thus, the waves arriving at point
A at 60 h can have a characteristic height of no more
than 1.5 m.
4.5 Manual computation of shallow-water
effects
Several kinds of shallow-water effects (shoaling, refraction,
diffraction, reflection, and bottom effects) are
described elsewhere in this Guide. In this section, a few
practical methods are described which have been taken
from CERC (1977) and Gröen and Dorrestein (1976). In
absolute terms, a useful rule of thumb is to disregard the
effects of depth greater than about 40 m unless the waves
are very long, i.e. if a large portion of the wave energy is
in waves with periods greater than 10 s. Distinction is
made between:
(a) Swell originating from deep water entering a shallow
area with variable depth; and
(b) Wind waves with limited wave growth in shallow
water with constant depth.
More complicated cases with combinations of (a)
and (b) will generally require the use of numerical
models.
Section 4.5.1 deals with shoaling and refraction of
swell whose steepness is sufficiently small to avoid wave
breaking after shoaling and focusing due to refraction. In
Section 4.5.2 a diagram is presented for estimating wave
heights and periods in water with constant depth.
4.5.1 Shoaling and refraction of swell in a
coastal zone
In this section, wave decay due to dissipation by bottom
friction and wave breaking is neglected. Shoaling and
refraction generally occur simultaneously; however, they
will be considered separately.
4.5.1.1 Variation in wave height due to shoaling
To obtain the shoaling factor, Ks, which represents the
change of wave height (H) due to decreasing depth
(without refraction), we need to consider the basic rule
that energy flux must be conserved. Since energy is
related to the square of the wave height (Sections 1.2.4
and 1.3.8) and wave energy travels at the group velocity,