Isaacs—Faughn-Schick—Sargent: Deep-Sea Moorings 277 
effect on a mooring with a buoyant pennant. A submerged float will move in a 
reduced orbit, which can be estimated from tables such as those of Wiegel (1954). 
It should be kept in mind that there may be large differences between the be- 
havior in the real sea and the behavior in ideal waves. No matter how appealing 
the customary assumption of regular trochoidal waves from the standpoint of 
simplicity, such an assumption may exaggerate elementary motions (as rolling 
and pitching) on the one hand, and may fail to give satisfactory explanations of 
such matters as slamming and lurching on the other. It is necessary also to take 
into account the extreme conditions met during storms, when waves are steep and 
confused, and often break. 
In a breaking deep-sea wave or comber, a moored surface float is struck by a 
cascade of water perhaps % the height of the wave. This cascade moves essentially 
at the wave (phase) velocity for a distance of about 14 of a wave length. The 
following wave may also break, subjecting the mooring to extreme stress and 
excursion. 
The size of waves is controlled by the velocity, the fetch, and the duration of 
winds. The Marine Climatic Atlas of the World (U.S. Navy, 1955-1959) shows 
for each region of the ocean the percentage frequency of wind of each Beaufort 
force from 2 through 9. Tables relating wave size to wind are given in Wind Waves 
at Sea, Breakers and Surf (USN HO, 1947, pp. 17-18). 
If the greatest height (H.) of the waves producing deep-sea combers is esti- 
mated for a region, the wave length (Ly), the period (T), and the velocity (Co) 
may be approximated as follows: 
L,=7 H, feet (for the steepest storm waves) 
T= (L,/5.12)1/?, or T=1.1(H.)?/? seconds 
Cy) =L,/T, or C)=6.0 (H.)*/? feet per second 
(See Sverdrup, Johnson, and Fleming, 1942, pp. 525-527.) 
Thus, in an area known to experience wave heights of 25 feet in storms, it may 
be estimated that the mooring will be struck from time to time by a cascade of 
water traveling at about 30 feet per second, and that this cascade will persist for 
about 60 feet. In such a breaking sea, a second comber is very likely to follow the 
first. This wave is likely to peak up during its passage through the wake of the 
previous comber and to begin breaking approximately at the point where the 
previous comber ceased breaking. Thus it is essential that the surface float be 
subject to enough restoring force to be pulled through the first comber at a rate 
that permits it to escape the following comber. 
In storms in the deep sea, the dominant waves and winds are most likely to be 
in the same direction. Consequently, the wind stress may be considered as impos- 
ing an initial load or restoring force on the surface float that is being carried out 
of position by a breaking wave. This is because the steep approaching comber 
shields the surface float from the wind, and hence some of the resisting force in 
the mooring (which a moment previously resisted the wind drag) begins to move 
the float toward the approaching comber, and the float, if boat-shaped, is oriented 
by this effect. This condition does not necessarily obtain near fast-moving storm 
centers, of course, but a mooring has survived the close passage of the eye of one 
of the fast-moving chubascos of Mexican waters, where wind velocities were esti- 
mated at about 100 knots. 
