WAVE VELOCITY AGAINST WIND VELOCITY 
COMPARISON BETWEEN THEORY AND OBSERVATION 
LEGEND 
THEORY 
UNLIMITED FETCH 8 
UNLIMITED DURATION 
—-"—— UNITED BY FETCH 
—++— LIMITED BY QURATION 
EMPIRICAL RELATIONS 
WAVE VELOCITY, GC, IN GM/SEC 
1500 2000 2500 3000 
WIND VELOCITY, U,IN CM/SEC 
Figure 11.—Wave velocity as function of wind velocity only. 
Cornish has discussed the relation between wind 
and wave velocity in great detail, and his conclu- 
sions are based on a lifetime of careful observations 
THEORY FOR THE 
Energy Budget 
After the waves have left the generating area 
they travel through a region of calm where the 
wind velocity is small compared to the wave 
velocity. The waves receive no energy by normal 
pressure but, on the contrary, they meet an air 
resistance. The loss of energy due to the air 
resistance, according to (30b), equals 
Ry= ~) lk’ -! sp'gH’C (84) 
The transfer of energy due to tangential stress (37) 
can be neglected: 
Therefore, from equation (57) 
Ru=—(1+2) Ry, Ro=ZRw (86a, b) 
and the decay of waves is derived from (86) with- 
out any further assumptions. 
27 
at sea. It is possible that his conclusions were 
somewhat influenced by Jeffreys, according to 
whom waves can grow only if their velocity is less 
than that of the wind (31), but this limitation no 
longer holds when the transmission of energy by 
tangential stress is taken into account (41). 
Observations from the trade-wind regions where 
the wind blows with nearly uniform and moderate 
velocity over large areas are highly instructive. 
Some of these observations, which have been 
plotted in figure 5, are collected in table 4. They 
were obtained by Paris (Kriimmel, 1911, p. 52, 
80) and Schumacher (1939) and show clearly that 
the wave velocities may exceed wind velocities in 
the generating area. 
Table 4 
Average Wave Characteristics in Trade Wind 
Regions 
Bees 
er 
Observa- U Cc 
table A 8 8 
ipa Locality tions made | cm/ cem/ 
pew by— sec | sec | C/U} H/L 
pen- 
dix 2 
32| Trade winds, North Atlantic_| Meteor_-__ 935) 858] 0. 93/0. 029 
17|2oaee C6 Co eee st dolitees 670) 780} i. 16} .024 
33 | see Oe al ee Ud ee Parise 590) 1,120) 1.90} .029 
34) Trade winds, Indian Ocean--|--.do_-___-- 720) 1,260) 1.75} .029 
39] Western Pacific Ocean---_-_-- Desf (ae ee Tes 860] 1, 240} 1.44] .030 
47| Westerlies, South Atlanti Pde 1,240) 1,400) 1.13} .032 
75| Westerlies, Indian Ocean_--_}--_do------- 1,490) 1,500) 1.01} .045 
WiC hinal sea sss seen eneeenee ido = 1,300) 1,140) . 88] .042 
DECAY OF WAVES 
Wave period and distance from the generating 
area.—Substitution of (49a), (50a), and (84) in 
equation (86b) gives 
1 ,pdC_rl 
2 ‘det a8 
From (4), (6), and (78), again writing A=2y’p’/p, 
one obtains 
GC 9 AgrO™, de 
Integrating from s=F (end of fetch) tor=F+D 
(end of decay distance): 
Tees D 
4 1-+169*Ar( os) 
where 7'p and 7; are the wave periods in seconds, 
respectively, at the end of the decay distance and 
at the end of the fetch. 
Travel time and distance from a generating area.— 
To obtain the travel time, tp, from the end of the 
sp’ g?EC 
dT 87’ 
=o (87) 
(88) 
