GUIDE WAVE ANALYSIS AND FORECASTING - WMO

48
Storm
2
1
Rp
Rp
Rp
t = = = 0. 660 (h).
c 1. 515T
T
g
R p
P
R
GUIDE TO WAVE ANALYSIS AND FORECASTING
Storm
A possible new swell
arriving later
Figure 4.4 — Swell from a distant storm. Waves travelling in
the direction of P have been generated over a
time period D p
(4.4)
These components continue to arrive over a period of D p
hours, then they disappear. D p is determined from
weather charts by examining how long a given fetch
remained in a given area. In the meantime, slower wave
components have arrived and each component is
assumed, in the present example, to last for D p hours.
There is a wave component which is so slow that it starts
to arrive at the moment when the fastest wave component
present is about to disappear (compare boxes 1
and 2 in Figure 4.4). The first wave of the slow component
(box 2) with period T 2 has travelled over a time
of t hours; the last wave of the fast component (box 1)
with period T1 has started out Dp hours later and has thus
travelled over a time of (t – Dp) hours. We have, for the
slow component:
Rp
Rp
T2
= = 0. 660 ( s)
(4.5)
1. 515 t t
and, for the fast component:
or
(4.6)
(Rp is measured in n.mi.; t and Dp in hours.)
T1 and T2 are the limits of all wave periods which
can possibly be present at P at a given time of observation.
Some periods within this range may actually not
be present in the observed wave spectrum; the components
could be dissipated during their long travel
outside the storm area. It can easily be shown from the
above equations that the range of possible wave
frequencies is given by:
Dp
f1 – f2
= 1. 515 .
R
(4.7)
This means that the band width (range) of frequencies of
wave components, which exist at a given point of observation,
is a constant for that point and depends on the
duration of wave generation, D p. The range of frequencies
becomes smaller at greater distances from the storm.
This result, obtained from a schematic model, is indeed
observed. Thus, as the result of wave dispersion, swell
attains a more regular appearance at greater travel
distances.
Example of swell from a distant storm
Problem:
Waves were generated in the direction R for a period of
18 h. The highest wave period generated in the storm
was 15 s. Forecast swell for point A at 600 n.mi. and for
point B at 1 000 n.mi. from the area of generation.
Compute when the first waves arrive and which periods
could possibly be present during the subsequent 36 h.
Solution:
T
R c t– D 1. 515 T1t– D
1 =
= ( ) = ( )
p g p p
Rp
1. 515 t– D
( ) =
p
Rp
0. 660 () s
t– D
At point A, R p = 600 n.mi.; D p = 18 h; T max = 15 s.
From Equation 4.4 the first waves arrive at
t = 0.660 x 600/15 = 26.4 h after the beginning of the
storm. These waves continue for 18 h after they first
arrive.
The range of periods (T 1 – T 2) at point A are
computed for the 36 h subsequent to the arrival time
of the first wave at 6 h intervals beginning with 30 h
after the storm as shown in Table 4.6. The range
of wavelengths can also be given using the relation
λ = 1.56 T 2 (m). The wave components with a period of
15 s disappear after t = 44.4 h.
p
p