GUIDE WAVE ANALYSIS AND FORECASTING - WMO

ange of directions. Also, waves at different frequencies
will propagate at different speeds. Thus, from a point
source, each component of the spectrum E(f,θ) can be
propagated in the direction θ with a speed c g(f,θ).
3.3.1 Angular spreading
It is often assumed that the directional part of the windwave
distribution has a cos 2 (θ − ψ) form where ψ is the
predominant direction of the waves and θ is the direction
of the spectral component concerned. Most of the
energy is propagated in the mean direction of the sea.
At deviating angles, less energy is transported
and, for all practical purposes, the energy propagated
at right angles to the mean direction is negligible. There
is considerable evidence indicating that the spread
is dependent on the lengths of waves. Several such
formulations for the directional distribution based
on observations have been given. Using the form
cos 2s (θ − ψ)/2, Mitsuyasu et al. (1975) and
Hasselmann et al. (1980) give functional forms for s
which are dependent on the ratio of frequency to peak
frequency. These indicate the narrowest spread at the
peak of the spectrum, with widening at both lower and
higher frequencies. However, there is still uncertainty
with respect to the real functional form of the s para-
WAVE GENERATION AND DECAY 37
2 5 2 5 2 5 2 5 2 5
10 3
10 4
10 5
10 10 2
H c * versus X*
H c * versus t*
T c * versus X*
T c * versus t*
t* and X*
Figure 3.1 — Basic diagram for manual wave forecasting. The curves are drawn for non-dimensional parameters
(H c* = gH c/u 2 ; T c* = gT c/u) (derived from Gröen and Dorrestein, 1976)
H c * T c *
0,24
2
-
10 -1
10 -2
10 -3
meter in simple sea states (e.g. wind-sea generation and
long swells). This is due to the fact that different directional
wave instruments located very close to one
another give widely different results (see for example,
Allender et al., 1989).
Waves which have left the generating area (i.e.
swell) are reduced by the angular spreading. Numerical
models automatically take care of this by splitting the
spectrum into components and propagating each of the
components independently. Manual methods require
more action by the operator. Angular spreading and
dispersion factors must be applied.
As illustrated in Figure 3.2, a point P will receive
wave energy from points all along the front of the fetch.
It is possible to compute the sum of all the contributions.
For a cosine-squared distribution of energy at the fetch
front, results are shown in Figure 3.3. At any fixed
frequency, the curved lines in this diagram represent the
percentages of the wave energy from the fetch front
which reach there. These are the angular spreading
factors. The spatial coordinates are expressed in terms of
the width AB of the fetch area. For example, at a
distance of 2.5 AB along the predominant swell
direction, the wave energy has decreased to about 25 per
cent of the energy per unit area which was present at the
fetch front AB. The reduction in wave height due to
5
2
5
2
10
6,28
1