DURATION GRAPH 
10° 
8 8 
6 + =! ue =F G 
4 5 it 4 
og [ea aa con iin IE Le cat + + | 3 
2 2 
TT mali v 
Pile) C) 
1 1 
8 i I il a 8 
6 c +S. 6 
‘ tU/ A o 
10"! 4 10 
S) Slamalaal { Na O18 3 
2 2 
e/| © 
Cf, lie el 
o 
1 oe 
& +—+t 1p tue 
GHA ye 8 8 
6 IL + + 6 
+ 
“ JIB ir 4 T 4 
lo? 5 H/ 2 ej 
i aA | 
2 ft 1 a ie 2 
| ese + 
1 JL — 1 
8}—_+ + == T 8 
6 t } | | © BERKELEY SG 
1 =r mr t @ U.S.S. AUGUSTA — 
4 + © EMMONS & CLARKE —7—44 
LO pers! Ih ® DOVER eS 
oe © PARIS 
2 @ KRUMMEL 42 
t 
_| 4+ g Ay ay | | 
i] 1 
1 Mnsinsimeine 3 6 81 Ge 2 6 681 
‘als 
1 2 3°04 Pree gs 3.4 
SS ee ee 
Figure 7.—Wave height and velocity as functions of duration, using nondimensional parameters and relation between minimum duration, 
etch and wind velocity. Theoretical relationships shown by curves; observations by symbols. 
be possible to find solutions for the case U=f(z, t) 
by using numerical methods, but such attempts 
would involve a great deal of time and labor and 
would probably not be justified in view of the 
limited accuracy with which the fundamental 
variables, wind velocity, fetch, and duration, can 
be determined. 
Wind and Wave Energy 
In the theoretical development dealing with 
the growth of waves solutions to equation (55a, b) 
were found under two assumptions: the wave 
period increases continuously (equation 56), and 
the fundamental equation can be split up into two 
equations (57a and 57b). The latter assumption 
specified the manner in which the contributions of 
energy from the two “sources” R; and Ry, are 
distributed to the two ‘energy sinks” Ry and Re. 
The energy budget during the generation of waves 
is further illustrated in figure 9 where the light 
21 
solid curves refer to the energy sources, the dashed 
curves to the sinks, all expressed as percentage 
of Ry, 
li =p Sor (OF (75) 
the total energy dissipated by the wind in the 
lowest 8 to 10 meters. The significant wave has 
an energy income, e’, which must equal its total 
expenditure of energy: 
el any ve nt Re 
Ry Ry Re 
During the very early stages of wave develop- 
ment most of the energy is transmitted by normal 
stress, but for 6 larger than 0.37 transmission by 
tangential stress is domimant. With a 10 m/sec 
wind a wave age of 0.37 is reached in 1.88 hours 
and with a 20 m/sec wind, in 3.75 hours. There- 
fore, the effect of the ncrmal stresses dominates 
for a short time only, and during the greater part 
of the time during which waves grow the effect 
(76) 
