Hydraulic Structures: Fourth Edition



1

2

a^2 

∞

0

E(f)df

or



1

8

H^2 rms. (14.47)

A fully developed sea is one for which the fetch and the duration of wind

are unlimited, so that the waves do not grow any further for a given wind

speed and the wave field has attained a steady state. The Pierson–

Moskowitz spectrum for the fully developed sea (Pierson and Moskowitz,

1964) is

EPM(f)
g^2 (2π)^4 f^5 exp (^) 

5

4



4

 (14.48)

where 
 is the Phillips constant (equal to 0.0081) and fm0.8772

(g/2πU19.5). U19.5is the wind speed measured at 19.5 m above the sea

surface.

Substituting equation (14.48) into equation (14.47) and performing

the integration, the rms value of the wave heights is

Hrms0.316 , (14.49)

TsTz0.7104/fm.

The Joint North Sea Wave Project (JONSWAP) produced a frequency

spectrum for the developing sea (Hasselmann et al., 1976). The wind

speeds for the JONSWAP wave measurements were taken at 10 m above

the still-water level: U 10 0.93U19.5. The spectrum is

EJ(f)
g^2 (2π)^4 f^5 exp 

5

4



4

^

q (14.50)

where

0.076(gF/U^210 )^ 0.22, qexp[ (f fm)^2 /2^21 f^2 m],

U 10 fm/g3.5(gF/U^210 )^ 0.33,

 1 0.07 for ffm,

 1 0.09 for f'fm,

3.3, TsTz0.777/fm.

f



fm

g
1/2



π^2 f^2 m

f



fm

598 WAVES AND OFFSHORE ENGINEERING