L2G 
Discussion of tables 
The assumption that the range that has been assumed for the 
values of fi and n for the spectral forms for S(k) must first be questioned. 
The range of ie is probably more than adequate. However, the relation- 
ship between particle motion spectra and free surface spectra is not known. 
Perhaps n can be even smaller than 4.5 and still yield spectra for the 
free surface that behave over a given range like 1/fP where p is greater 
than 5 as wave observations seem to suggest. 
If these assumed values are reasonable, it would follow that 
a loop ina realization, z = z(x), would be a very rare event. The small- 
est value (except the zero) in Table 5 is 4.7 and the associated proba- 
bility is less than lo, If loops were identified with breaking waves, the 
results would imply that waves shorter than 0.2 feet and n's less than 
5 produce such breakers and this does not seem at all reasonable. 
Stated another way, results based on spectra like K/f£ 
depend very strongly on the high frequency tail of the spectrum where the 
waves are less than 3 inches long and on the fact that the exponent is 
exactly 5 and not 5.1. The original conditions correspond to waves with 
a significant height of 42 feet and with representative lengths of 1500 
to 2000 feet. Breakers in sucha sea certainly occur and surely have 
dimensions exceeding 3 inches. Thus although such loops identify un- 
realistic spectra, the limitations on the spectral form appear to be due 
to effects that occur before such loops even have a chance to attempt to 
form. 
The tables also suggest that equation (49) will be approxi - 
mately correct as to general shape, and that the higher moments are 
both difficult to detect theoretically and to measure in practice. 
Equations (45), (46), and (52) are satisfactory approximations, but the 
approximate higher moments and skewness and kurtosis values will be in 
error by large percentages. The distribution of z as given by equation 
(44) when graphed for two conditions, one for which Le = 0.46 
and n = 5.9, the other for which ie = 4.6 and n = 4.5 can hardly be dis - 
tinguished visually from the normal curve. 
