shown to be in agreement with empirical evidence. 
Table 5 
Wave Periods for Wind of Given Velocities 
and Duration 
Wind velocity Wave periods, seconds 
Beaufort | m/sec 20 hours 30 hours | 40 hours 
scale 
4 5.3- 8.5 3.9- 4.9 4,5- 5.9 5. 0-6. 5 
5 8. 6-11.0 5.0- 5.9 6.0- 6.9 6. 6-7.7 
6 11. 1-14.1 6. 0- 6.9 7.0- 8.0 7.8-9.0 
7 14. 2-17. 2 7.0- 7.8 FoR Ee ey As Py eee 
8 17. 3-20. 8 7.9 8.8 QNS—LON Sy |e eae a 
9 20. 9-24. 4 8.9- 9.7 LOND eee 
10 24. 5-28. 5 OES 1047 epee ea eee a= 
ll 28. 6-32. 7 AQ OSES Gil tet eee ey |e ee 
L 
According to the Atlas of Climatological Charts 
of the Oceans (U. S. Weather Bureau, 1938), 
wind velocities exceeding 7 Beavfort are not 
frequent over the oceans. For the stormy part of 
the North Pacific in winter the frequency of such 
high wind velocities exceeds 15 percent in only a 
few regions, and in the North Atlantic it reaches 
25 percent in only one area. The duration of 
these winds is usually between 20 and 30 hours. 
Therefore, waves of periods longer than 8.9 
seconds would not be produced on more than 15 to 
25 percent of the days in winter; waves of periods 
exceeding 12 seconds would never be formed . 
because wind velocities of 10 to 11 Beaufort occur 
rarely and are of short duration. It follows that 
if the waves proceeded without change in period 
the periods of the swells on the coasts of southern 
California and of northwest Africa would exceed 
35 
8.9 seconds in 15 to 25 percent of the cases and 
would never exceed 12 seconds. 
Gutenberg (1929) has commented upon the 
problem of the increase of wave period and calls 
it a truly geophysical phenomenon noticeable 
only over long distances and periods of time. He 
finds that earthquake waves, microseismic and 
ordinary sound waves increase in period in a 
manner similar to the one characteristic of water 
waves. For seismic waves the increase might be 
associated with the internal viscosity of the 
transinitting medium. 
Although the “kinematics” of the increase in 
wave period is now fairly well understood, due 
mostly to studies by Rossby (1945), the physical 
causes of the phenomenon remain obscure. The 
explanation may lie in an analogy with the 
Cauchy-Poisson problem of impulsive wave gen- 
eration (Lamb, 1932, p. 384). Due to the impul- 
sive generation a spectrum of wave periods is 
present at all times and the longer and faster 
waves will run ahead of the shorter and slower 
waves. The entire wave train stretches, result- 
ing in an increase of wave period: However, the 
Cauchy-Poisson problem deals with a momentary 
generation of waves as, for example, waves 
caused by a pebble dropped in water. In storm 
areas the process of wave formation must be a 
semicontinuous one and it represents a much 
more difficult problem. This paper may serve 
to clarify the relationships between wind, sea, 
and swell, but it leaves a number of fundamental 
questions unanswered. 
