GUIDE WAVE ANALYSIS AND FORECASTING - WMO

TABLE 4.6
Ranges of swell periods and wavelengths at point A for
arrival time after storm beginning
Arrival time (h) Periods (s) Wavelengths (m)
30 15.0–13.2 351–272
36 15.0–11.0 351–189
42 15.0–9.4 351–138
48 13.2–8.2 272–105
54 11.0–7.3 189–83
60 9.4–6.6 138–68
66 8.2–6.0 105–56
For point B, R p = 1 000 n.mi.; D p = 18 h; T max = 15 s.
The first waves arrive 44 h after the beginning of
the storm. Table 4.7 shows the same information as
Table 4.6, but now for point B, starting at 48 h and
ending at 84 h. The wave components with a period of
15 s disappear after t = 62 h.
Rather long forecast times have been given for both
points to demonstrate the gradual change of wave
periods. In practice, the shorter waves may not be
noticeable after two to three days’ travel time, and also
after displacement of the storm in the case of a tropical
cyclone. A cyclone does not, however, generate swell in
all directions; this depends on the structure of the wind
fields in the cyclone.
4.4.2 Distant storm with long fetch
Forecasting the waves from a distant storm with long fetch
is a more complicated case, since the distance travelled by
individual wave components inside the wave-generating
area will generally not be the same for the various components.
The longer and larger waves will generally be
found in the downwind part of the storm area.
For all practical purposes, one may choose an appropriate
mean value for the distance S (see Figure 4.5) and
apply a corrected duration Dp´ by adding to Dp the time
needed by wave components to cover the distance S:
S
S
Dp′ = Dp
+ = Dp
+
c 1. 515T1 gi
TABLE 4.7
Same as Table 4.6 except at point B
WAVE FORECASTING BY MANUAL METHODS 49
(4.8)
Arrival time (h) Periods (s) Wavelengths (m)
48 15.0–13.8 351–297
54 15.0–12.2 351–232
60 15.0–11.0 351–184
66 13.8–10.0 297–156
72 12.2–9.2 232–132
78 11.0–8.5 189–113
84 10.0–7.9 156–97
S
O
Storm edge
Figure 4.5 — Swell from a quasi-stationary, distant storm, in
which the waves travel over a distance R p , and
the generation area has a long fetch
in which c gi is the group speed of the component considered.
It can be shown that in this case the range of wave
frequencies of the swell does not remain constant for a
given point P, but increases slightly as the larger components
disappear, and the spectrum consists of
progressively smaller components.
Example of swell from distant storm with long fetch
Problem:
Referring to Figure 4.5, waves were generated in the
direction R. The “mean” generation fetch is 180 n.mi.
for waves with periods between 12 and 15 s; Rp =
600 n.mi.; Dp = 18 h. Find the wave conditions at P.
Solution:
The corrected duration for waves with T = 15 s, is
Dp = 18 h + (0.660 x 180/15) = 18 h + 8 h = 26 h. This
component arrives at P, 26.4 h after the storm as before,
but disappears 26 h later. Likewise the corrected duration
for generation of waves with T = 12 s is Dp = 27.9 h. The
travel time for this component to arrive at point P is
t = 0.660 x (600/12) = 33 h. The last waves with T = 12 s
pass point P at t = 33 h + 27.9 h = 60.9 h.
The ranges of periods and wavelengths are
reflected in Table 4.8.
Comparison of the examples in Sections 4.4.1 and
4.4.2 shows that, in the latter, the wave spectrum remains
TABLE 4.8
R p
Ranges of swell periods and wavelengths at point P for arrival
times after the beginning the storm
Arrival time (h) Periods (s) Wavelengths (m)
30 15.0–13.2 351–272
36 15.0–11.0 351–189
42 15.0–9.4 351–138
48 15.0–8.2 351–105
54 14.1–7.3 310–83
60 12.0–6.6 225–68
66 10.4–6.0 169–56
P
R