=20— 
The construction may even turn out to be considerably simpler 
than that employed by Tick [1961] because only low frequencies are in- 
volved. 
In the above process, T is to be a fraction of a second after 
G =O), 5) is to be a foot or so below the free surface. The first two 
pairs will yield an estimate of the instantaneous speed of acrest. If 
x, (a, 0,0) exceeds this value, then the crest could be considered to be a 
breaking crest. The other terms should yield some information on the 
size of the region of unstable motion. A range of possible spectral forms 
can be used to construct this vector process and some idea of the fraction 
of breaking waves in the total can be gained. 
However, from the results given above on the linear random 
model and on the periodic second order irrotational model, the results 
obtained from such a construction will probably not be quantitatively cor- 
rect as they may yield waves that are too high physically by a factor of 
two, even for irrotational waves to second order. 
Breakers in a random sea 
Whitecaps and breakers in deep water are an integral part of the 
problem of wave generation. Many photographs of waves in deep water show 
such breaking waves. The equations governing the wave motion fail locally 
and a breaker is produced. The water in the breaking part of a wave is 
certainly governed by physical laws that are completely different from 
those that govern the wave motion. A breaker is probably produced when 
the water particle speed exceeds the speed of the crest, but other effects 
such as the wind actually blowing off the crest of a wave before this re- 
quirement is met may also play an important part. 
Moreover, the turbulence produced by a breaking wave, governed 
by eddy viscosity laws, will tend to damp out the higher frequency linear 
components in the spectrum of the wind generated sea. The absence of the 
local chop in the wake of a ship illustrates this effect. 
Whenever a breaker disorganizes the fluid motions, there is 
a mass of water moving forward at the crest of the waves. This effect 
may contribute to both the drift current at the surface and to the growth 
of the lower frequency waves. 
