154
STATISTICAL DESCRIPTIONS OF OFFSHORE WAVES
Empirical Forma
Particular forais of deepwater wave spectra in common use are those of
Pierson and Moskowitz (1964) and Bretschneider (1959), which are based on
theory and require sufficient data to fit the constants. The spectra of PiersonMoskowitz are termed wind-speed spectra since wind speed is included directly
in the spectral density function. The spectra of Bretschneider are termed heightperiod spectra since significant height He and the significant or mean apparent
period Tm = 2tt/are used directly in the spectral density function. It is emphasized that in deducing these spectra, use was made of the distribution functions originally derived theoretically by Longuet-Higgins (1952), and supported
by the empirical relations based on the wave data of Putz (1952). These deepwater spectra hâve the form of équation (6.15) in which the constants (Aq.B)
differ, depending on whether the height-double or amplitude-half spectrum assumption is made in reducing the data.
Another spectrum in common use is JONSWAP, which investigators hâve
found appropriate for the design of offshore structures in the North Sea. Unlike the spectra in the form of équation (6.15), which are referred to as fetchunlimited spectra, the JONSWAP spectrum includes the fetch in its formulation,
and is called a fetch-limited spectrum. It is noted that the term fetch, denoted
by X, is the distance from the shoreline of the wave field under considération. A
fetch-limited wave spectrum is one based on a wave field at distance X that has
reached a steady State or time-independent condition. Such a condition can occur in deep water if the wind has blown for a sufficient length of time, out to sea,
and in a direction perpendicular to a regular shoreline. These and other factors
that affect the fetch, together with experimental measures of X appropriate for
fetch-limited spectra, are thoroughly discussed by Young (1999). Useful forms
for both fetch-unhmited and fetch-limited spectra are summarized.
Wind-Speed Spectra. The Pierson-Moskowitz fetch-unlimited spectrahas
the general form
_2
S„(w) = 0.0081
e-B^'
(6.21)
where g is the accélération due to gravity. When the wind speed is known, then
B = 0.74(^)4
(6.22)
where V is the wind speed at a height of 19.5 m above the still water level.
Any consistent set of units for the quantifies g, V, and w are appropriate for
équations (6.21) and (6.22), provided that w is expressed in radians per unit
time.
Significant Wave Height-Period Spectra. When the significant wave
height rather than the wind speed is known, the constant B of équation (6.21),
for H, m units of m/s, is
(6.23)
o
311
STATISTICAL DESCRIPTIONS OF OFFSHORE WAVES
Empirical Forma
Particular forais of deepwater wave spectra in common use are those of
Pierson and Moskowitz (1964) and Bretschneider (1959), which are based on
theory and require sufficient data to fit the constants. The spectra of PiersonMoskowitz are termed wind-speed spectra since wind speed is included directly
in the spectral density function. The spectra of Bretschneider are termed heightperiod spectra since significant height He and the significant or mean apparent
period Tm = 2tt/are used directly in the spectral density function. It is emphasized that in deducing these spectra, use was made of the distribution functions originally derived theoretically by Longuet-Higgins (1952), and supported
by the empirical relations based on the wave data of Putz (1952). These deepwater spectra hâve the form of équation (6.15) in which the constants (Aq.B)
differ, depending on whether the height-double or amplitude-half spectrum assumption is made in reducing the data.
Another spectrum in common use is JONSWAP, which investigators hâve
found appropriate for the design of offshore structures in the North Sea. Unlike the spectra in the form of équation (6.15), which are referred to as fetchunlimited spectra, the JONSWAP spectrum includes the fetch in its formulation,
and is called a fetch-limited spectrum. It is noted that the term fetch, denoted
by X, is the distance from the shoreline of the wave field under considération. A
fetch-limited wave spectrum is one based on a wave field at distance X that has
reached a steady State or time-independent condition. Such a condition can occur in deep water if the wind has blown for a sufficient length of time, out to sea,
and in a direction perpendicular to a regular shoreline. These and other factors
that affect the fetch, together with experimental measures of X appropriate for
fetch-limited spectra, are thoroughly discussed by Young (1999). Useful forms
for both fetch-unhmited and fetch-limited spectra are summarized.
Wind-Speed Spectra. The Pierson-Moskowitz fetch-unlimited spectrahas
the general form
_2
S„(w) = 0.0081
e-B^'
(6.21)
where g is the accélération due to gravity. When the wind speed is known, then
B = 0.74(^)4
(6.22)
where V is the wind speed at a height of 19.5 m above the still water level.
Any consistent set of units for the quantifies g, V, and w are appropriate for
équations (6.21) and (6.22), provided that w is expressed in radians per unit
time.
Significant Wave Height-Period Spectra. When the significant wave
height rather than the wind speed is known, the constant B of équation (6.21),
for H, m units of m/s, is
(6.23)
o
311