present in the fetch or to account for waves generated
by a rapidly changing wind.
. E value. E is equal to the sum of the squares of
the individual amplitudes of the individual sine waves
that make up the actual waves. Since it is proportional
to the total energy accumulated in these waves, it is used
to describe the energy present in them and in several
formulas involving wave energy.
l Co-cumulative spectra. The co-cumulative
spectra are graphs in which the total accumulated energy
is plotted against frequency for a given wind speed. The
co-cumulative spectra have been devised for two
situations: a fetch limited wind and a duration time
limited wind.
l Upper limit of frequencies (fu). The upper limit
of frequencies represents the lowest valued frequencies
produced by a fetch or that are present at a forecast point.
This term gets its name from the fact that the period
associated with this frequency is the period with the
highest value.
The waves associated with this
frequency are the largest waves.
l Lower limit of frequencies (fL,). The lower limit
of frequencies represents the highest value frequencies
produced by a fetch or that are present at a forecast point.
This term gets its name from the fact that the period
associated with this frequency is the period with the
lowest value. The waves associated with this frequency
are the smallest waves.
. Filter area. That area between the fetch and the
forecast point through which swell waves propagate.
This area is so termed because it filters the frequencies
and permits only certain ones to arrive at a forecast point
at a forecast time.
l Significant frequency range. The significant
frequency range is the range of frequencies between
the upper limit of frequencies and the lower limit
of frequencies.
The term significant range is
used because those low-valued frequencies
whose E values are less than 5 percent of the
total E value and those high-valued frequencies
whose E values are less than 3 percent of the
total E value are eliminated because of insignificance.
The significant range of frequencies is used to
determine the range of periods present at the forecast
point.
l Propagation. Propagation as applied to ocean
waves refers to the movement of the swell through the
area between the fetch and the forecast point.
. Dispersion. The spreading out effect caused by
the different group speeds of the spectral frequencies in
the original disturbance at the source. Dispersion can
be understood by thinking of the different speeds of the
different frequencies. The faster wave groups will get
ahead of the slower ones; the total area covered is
thereby extended. The effect applies to swell only.
l Angular spreading. Angular spreading results
from waves traveling radially outward from the
generating area rather than in straight lines or banks
because of different wind direction in the fetch.
Although all waves are subject to angular spreading, the
effect of such spreading is compensated for only with
swell waves because the spreading effect is negligible
for sea waves still in the generating area. Angular
spreading dissipates energy.
Wave Spectrum
The wave spectrum is the term that describes
mathematically the distribution of wave energy with
frequency and direction. The wave spectrum consists
of a range of frequencies.
Remember that ocean waves are composed of a
multitude of sine waves, each having a different
frequency. For purposes of explanation, these
frequencies are arranged in ascending order from left to
right, ranging from the low-valued frequencies on the
left to the high-valued frequencies on the right, as
illustrated in figure 6-3.
A particular range of frequencies, for instance, from
0.05 to 0.10 does not, however, represent only six
different frequencies of sine waves, but an infinite
number of sine waves whose frequencies range between
0.05 and 0.10. Each sine wave contains a certain
amount of energy, and the energy of all the sine waves
added together is equal to the total energy present in the
ocean waves. The total energy present in the ocean
waves is not distributed equally throughout the range of
frequencies; instead, in every spectrum, the energy is
concentrated around a particular frequency (fmax), that
corresponds to a certain wind speed. For instance, for
a wind speed of 10 knots (kt) fcnax is 0.248; for 20 kt,
0.124; for 30 kt, 0.0825; for 40 kt, 0.0619. For more
Figure 6-3.-A typical frequency range of a wave spectrum.
6-4
