the definition requires further refinement because 
the composition of the “‘one-third highest waves” 
depends upon the extent to which the lower waves 
have been considered. Experience so far indicates 
that a careful observer who attempts to establish 
the character of the higher waves will record values 
' which approximately fit the definition. It is also 
found that the-concept of ‘‘significant waves’’ is 
essential for the purpose of forecasting. 
The significant waves behave differently com- 
pared to the classical waves in a single finite 
train. The wave crests in such a train maintain 
their identity, that is, the waves are conserva- 
tive, and according to (12): 
OCMC OC es 
Of 2Or me () 
A steady state (0C/Ot=0) cannot exist simul- 
taneously with an increase of wave velocity (or 
period) with distance in fetch; nor can a transient 
state exist during which the wave velocity (or 
period) increases with the time but remains uniform 
over an area (OC/Ox=0). 
These conclusions are in contrast with ordinary 
experience as to the behavior of the significant 
waves. When a wind of constant velocity has 
blown for a long time over a limited stretch of 
water, such as a lake, a steady state is established. 
At any fixed locality the significant waves do not 
change with time, but on the downwind side of 
the lake they are higher and longer than on the 
upwind side. If, on the other hand, a uniform 
wind blows over a wide ocean, waves grow just 
as fast in one region as in any other region and the 
significant waves change with time but do not 
vary in a horizontal direction. 
The discrepancy between the behavior of signifi- 
cant waves and individual waves must lie in the 
fact that the crests of significant waves do not 
maintain their identity: in the storm area signifi- 
cant waves are not conservative. The implica- 
tions of this conclusion are as yet not clear but 
it is possible that the significant waves represent 
interference patterns which in a given locality 
are formed by ever-changing combinations of 
wave trains. In all events, relationships between 
waves and wind, fetch, and duration which shall 
agree with empirical results must be based on a 
study of significant waves. Such a study repre- 
sents a radical departure from the study of the 
conservative waves of the classical theory. 
Energy Budget of Conservative and of Signifi- 
cant Waves 
The transient (or unsteady) state will be dis- 
cussed first. The total energy per unit crest 
width of a wave equals EL, where E is the mean 
energy per unit surface area. The energy added 
each second by the normal pressure of the wind 
equals +RyL (30) and that added by the tan- 
gential stress equals R,L (37). 
Only half the energy, the potential energy, 
travels with the wave (18). Kinetic energy is 
constantly gathered at the forward edge of the 
wave, and left behind at the rear edge. This 
feature can be illustrated by considering a paral- 
lelepiped of unit width, extending to a depth 
below which wave motion is negligible, and whose 
forward and rear edges travel beneath two ad- 
jacent crests (fig. 4). At the forward edge of the 
moving paralielepiped energy is gained at the rate 
CELL 2(c%) 
and at the rear edge energy is lost at the rate 
CE/2. 
The total energy budget can therefore be 
writien: 
see =| Rr Bvt alee) lz 
The rate at which the wave length increases and, 
therefore, at which the parallelepiped ‘‘stretches”’ 
is determined by the difference in speed between 
the adjacent wave crests: 
dL Bete 
(43) 
dL oC _ 
dt Or 
Since C?=gL/2r, this equation can also be 
written 
oC 2dC 
== Gidi (44) 
and (43) takes the form: 
dE E _ COE _ 
In this form the above equation applies to a train 
of conservative waves, but not to significant waves 
because experience shows that under the stated 
conditions the energy of the significant waves is 
independent of z: 
(46) 
13 
