be obtained from (30) depends mainly upon the 
knowledge of the ‘sheltering coefficient’”’ s, and 
upon the extent to which it remains constant. 
Especially during the early stages of growth, a 
variation in s might be expected. A detailed 
theoretical and experimental investigation of 
energy transfer by normal stress would be highly 
desirable because the accuracy to which Ry can 
be evaluated is less than the corresponding ac- 
curacy for Ry. Fortunately, the term Rr plays a 
more important part in the development of waves 
than Ry (see p. 23). 
Friction 
The effect of molecular viscosity is small com- 
pared to the wind effects. Collecting constants, 
by putting A=2y’p'/p and a=s/2y?, equations 
(30), (87) and (7) become: 
Pp= EAgU-1p-8 (39) 
|Ry|= HAgU-'B-*a(1— 8B)? (40) 
i 2 
Re ait RU 6 (41) 
From equations (39), (40), and (41): 
| iy an eee Aug 
RrtRy  pA[l ta(1—8)*] 
U-p- 
With »=1.8X10-?, g=980, p=1, A=6.5X10-° 
and a=2.5, as will be shown later: 
Ru ow 109X710! 
RrptRy 1: 2.5(1—p)- 
For U=500 and g=0.1 (C=50): 
Wmba 
THEORY FOR THE 
ane: : 
Significant” and ‘Conservative’? Waves 
In the last sections we have tacitly assumed the 
existence of infinite trains of waves, but in the 
oceans we have to deal with trains of finite length. 
Within the gencrating area there always exist a 
large number of such trains of waves of different 
lengths, traveling with the wind or at small angles 
with the wind direction. From interference and 
criss-crossing there results an extremely irregular 
appearance of the sea surface, but the larger waves 
For U=1,000 and B=0.1 (C=100): 
For all but very small values of 8 and for moder- 
ate and large values of U, Ru is small compared to 
R;+ fy and can be neglected when dealing with 
the growth of waves. 
After waves have left the storm area and travel 
through regions of calm, the effect of ordinary vis- 
cosity is still negligible. An 8 second wave, for 
example, would have to travel more than 2 years 
and could complete 10 ‘‘equatorial round trips’ 
before its height would decrease by 63 percent 
(1/e=0.37). 
It may be argued that the rapid decay of waves 
could be explained by introducing an eddy vis- 
cosity, as is done in order to account for the low 
velocities of wind driven currents. When dealing 
with wind currents the eddy viscosity has been 
found to be from 1,000 to 100,000 times as large as 
the ordinary viscosity, but when dealing with 
waves the introduction of an eddy viscosity seems 
undesirable for the following reasons: 
1. The decrease of particle velocity with 
depth would be much more rapid than is shown 
by equation (5), which has been verified by 
observations. 
2. The eddy viscosity applicable to wind cur- 
rents gives much too rapid a decrease of wave 
height, and it would be necessary to introduce 
a smaller coefficient applicable only to wave 
motion. 
3. The observed decrease of wave height can 
be explained as the effect of air resistance 
against the advancing wave. 
Assuming, therefore, that dissipation takes 
place by ordinary viscosity only, the effect of 
friction is neglected. 
GROWTH OF WAVES 
12 
can be recognized and the theoretical relationships 
between period, length, and velocity apply to 
these (Kriimmel 1911, Sverdrup et al, 1942). 
Because of the simultaneous presence of many 
trains the wave characteristics have to be de- 
scribed by some statistical terms. For that 
purpose it has been found convenien: to introduce 
“the average height and period of the one-third 
highest waves.’’ The waves’ defined in this 
manner are called “the significant waves,’ but 
