| t=O HOURS 
sy eases | een |e 
| 
HEIGHT,H,IN METERS 
HEIGHT, H,IN METERS 
800 
1200 1600 
DISTANCE, 0, IN KM 
+=24 HOURS 
sth tS 
8coO 
1200 
ISTANCE, 0, IN KM 
Figure 8.—Growth of wave height with time and distance from beginning of fetch. 
of the tangential stress is more important. The 
ratio between the total amounts of energy trans- 
ferred by tangential and normal stresses depends 
upon £ only: 
0. 7 10 1. 369 
Ratio between total 
amounts of energy 
transferred by tan- 
gential and normal 
SUTeSSES ee ee ae ee . 87 1% 2. 84 4. 43 
For 6<1 the larger portion of the energy goes 
toward increasing the wave height, for B=1 the 
energy consumed in the increase of wave height 
and wave velocity are nearly equal, but for very 
old waves the larger portion of energy is required 
for the increase of wave velocity. 
Again it must be emphasized that as yet no 
physical significance can be attached to the split- 
up of the fundamental energy equation. This 
split-up leads, in what appears to be the simplest 
mathematical manner, to solutions consistent 
with empirical evidence, and therein lies its chief 
justification. Solutions to (55) can perhaps be 
based on other considerations such as the increase 
of wave period, but the msults obtained here are 
in svch good agreement with observations that 
the main features in figure 9 can be regarded as 
22 
significant. Any other attempts to find solutions 
must lead to similar results. 
A very small portion, about 1 percent, of the 
wind energy dissipated in the lowest layer is 
transferred to the sea for maintaining the pure 
wind current. Another fraction goes into forma- 
tion and maintenance of the significant waves. 
For any “given value of 8 this fraction equals 
{(76), (39), and (40)]: 
= 7S B’[l+a(1—B)?] (77) 
where 
§ 
Omani (78) 
Actually, a number of waves of different veloci- 
ties and directions are present simultaneously, so 
that the total percentage, «, of the wind energy 
going into the formation of waves may be two or 
three times the energy needed for the formation 
of the significant waves, that is, 10 to 15 percent 
of the wind energy dissipated in the lowest layer 
may go toward increasing and maintaining the 
energy of waves. 
With o=2.50 and y?=2.6 107%, one obtains 
s=0.013 (79) 
