EM 1110-2-1100 (Part II)
30 Apr 02
(b) There are many forms of wave energy spectra used in practice, which are based on one or more
parameters such as wind speed, significant wave height, wave period, shape factors, etc. Phillips (1958)
developed an equation for the equilibrium range of the spectrum for a fully-developed sea in deep water,
which became the basis of most subsequent developments. Phillips' equilibrium range is often written in
terms of the angular frequency ω and is of the form
E(ω) ' αg 2ω&5
(II-1-153)
where α is the Phillips' constant (= .0081) and g the gravitational acceleration.
(c) One commonly used spectrum in wave hindcasting and forecasting projects is the single-parameter
spectrum of Pierson-Moskowitz PM (Pierson and Moskowitz 1964). An extension of the PM spectrum is the
JONSWAP spectrum (Hasselmann et al. 1973, 1976); this is a five-parameter spectrum, although three of
these parameters are usually held constant. The relationship between PM and JONSWAP spectra is shown
in Figure II-1-38. Other commonly used two-parameter wave spectra forms, including those proposed by
Bretschneider (1959), ISSC (1964), Scott (1965), ITTC (1966), Liu (1971), Mitsuyasu (1972), Goda (1985a),
and Bouws et al. (1985) are essentially derivatives of the PM and JONSWAP spectra. A six-parameter wave
spectrum has been developed by Ochi and Hubble (1976). The utility of this spectrum is that it is capable
of describing multi-peaks in the energy spectrum in a sea state mixed with swell (Figure II-1-39). Only the
parametric wave spectra forms most often used in coastal engineering will be briefly discussed here.
(d) The equilibrium form of the PM spectrum for fully-developed seas may be expressed in terms of
&4
2πUw f
0.0081g 2
E(f) '
(II-1-154)
exp &0.24
g
(2π)4 f 5
where Uw is the wind speed at 19.5 m above mean sea level. The PM spectrum describes a fully-developed
sea with one parameter, the wind speed, and assumes that both the fetch and duration are infinite. This
idealization is justified when wind blows over a large area at a constant speed without substantial change in
its direction for tens of hours.
(e) The JONSWAP spectrum for fetch-limited seas was obtained from the Joint North Sea Wave
Project - JONSWAP (Hasselmann et al. 1973) and may be expressed as
2
f
&1
fp
&4
exp &
αg 2
f
2σ2
exp &1.25
γ
E(f) '
fp
(2π)4 f 5
(II-1-155)
&0.33
&0.22
g 2F
gF
1#γ#7
fp ' 3.5
;
α ' 0.076
;
3
2
U10
U10
σ ' 0.07 for f # fp
and σ ' 0.09 for f > fp
Water Wave Mechanics
II-1-89
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