height has been assumed at the end of the generat- 
ing area. Actually, this increase will not be sud- 
den but will depend upon the fetch and the wind 
velocity (see figs. 6 and 7). It has been shown 
that the sudden increase in wave height at the 
end of the generating area retains much of its 
sharpness as the disturbance travels through the 
area of decay; it is reasonable to assume, therefore, 
that a gradual increase at the end of the fetch will 
appear as a similar gradual increase in wave 
height at any point in the area of decay. 
If a storm should increase in violence, then 
high and long waves may arrive simultaneously 
with or may overtake lower and slower waves 
which were generated at an earlier time. If the 
higher waves overtake the lower and slower waves, 
a more abrupt increase of wave height can be 
expected at large distances from the generating 
area. 
One inconsistency remains to be explained. 
According to equation (12), the wave period re- 
mains constant near a geometric point travelling 
at half the wave velocity. Therefore no increase 
in wave period should be observed at the energy 
front, and only the low waves arriving ahead of the 
energy front should have periods larger than the 
ones at the end of the fetch. Observations do 
indicate, however, that the period of the signifi- 
cant waves increases with distance from the 
generating area. 
The explanation can probably be found in the 
limitations imposed by the Stokes theory, and by 
the assumption of the constant wave velocity 
made in the section dealing with the propagation 
of a disturbance through a region previously un- 
disturbed. Rossby (1945) has shown that for his 
generalized Stokes waves a dispersion of energy 
from short-period to long-period waves does, in- 
deed, take place. At present it has not been 
found possible to take some of these recent 
theoretical studies into account when dealing with 
significant waves in the decay region, but the 
theory presented here; although incomplete, has 
been found consistent with observations. 
OBSERVATIONS OF THE DECAY OF WAVES 
Little factual infomation is available concern- 
ing the behavior of waves which are no longer 
subject to wind action. It appears that the wave 
period and, therefore, the wave length continues 
to increase while the wave height decreases, and 
beth these changes contribute toward reducing 
the wave steepness. Furthermore, shorter waves 
decay much more rapidly than longer waves, and 
in the area of calm the irregular pattern of steep 
wind waves is transformed into a pattern of regular, 
low undulations known as swell. 
Changes in wave characteristics with distance 
from the generating area depend also upon the 
period of the wave at the end of the generating 
area. No observations are available from which 
all these factors can be derived. A rough check of 
the theory can be obtained by plotting in figure 12 
the nondimensional ratios of (88), (90), and (92) as 
derived from observed values of Tp, tp, and Hp and 
values of H; and 7; computed from weather maps. 
The validity of such a check rests upon the assump- 
tion that the relationships in the generating area 
are well established (figs. 6 and 7) and that the 
weather situations have been analyzed correctly. 
Observations at two widely separated localities in 
the region of decay are desirable for a study of the 
decay of waves without reference to the processes 
of generation. 
31 
Wave height and distance from generating area.— 
Six observations have been plotted in figure 12. 
Three observations marked ‘“MOROCCO” were 
taken by the French Meteorological Service. 
These consisted of wave height and period about 
three times daily. The points in figure 12 rep- 
resent averages of observations at Casablanca, 
Rabat, and Mehedya. Three observations marked 
“BERKELEY” were taken from weather ships, 
and for those the distance of decay is somewhat 
shorter. The agreement between theory and 
observations is fair. 
The following quotation from the British fore- 
casting report is of interest (British Admiralty 
1942): 
But as the forces mentioned in the first paragraph as 
acting on the surface now act against the motion of the 
water, energy is continuously removed from the waves 
and their height diminishes. The rate of diminution of 
height is greater for the shorter waves; it appears, from 
such evidence as is available, that the waves lose roughly 
one-third of their height each time they travel a distance 
in miles equal to their length in feet, e. g., a swell 600 feet 
long and 30 feet high is 20 feet high after 600 miles, 13.3 
feet high after 1,200 miles, 9 feet high after 1,800 miles, 
6 feet high after 2,400 miles, and so on. 
According to this rule: 
Hy 
Hy 
D D _ 6,080 
=0.67 for imme OTe on 
=975, 
