Identification of major spectral peaks can also be a useful step toward 
approximating water velocities and accelerations from a complex record of sea- 
surface elevations, although procedures for doing this are not well established. 
Velocities and accelerations could be estimated for each peak separately, using 
equations in the SPM (Sec. 2.234); then they could be added together to give 
estimates of resultant velocity and acceleration. If direction estimates are 
available, the velocity and acceleration components should’ be added vectorially. 
An alternative approach is to use the nondirectional spectrum to estimate a 
velocity spectrum (Harris, 1972). 
Occasionally, spectra have major secondary peaks which do not represent 
independent wave trains. In particular, when waves are very steep or in very 
shallow water the spectrum will often have secondary peaks at frequencies which 
are integral multiples of the dominant frequency. The secondary peaks indicate 
that additional frequencies are needed to represent the nonsinusoidal wave pro- 
files (the peaks do not necessarily represent independent wave trains). When 
a major secondary peak appears at twice the dominant frequency, its source can 
usually be identified by referring to a plot of the time series from which the 
spectrum was computed. The time series is expected to show wave profiles which 
are clearly nonsinusoidal if the major secondary peak is nonindependent. Coarse 
guidelines for when nonindependent secondary peaks may occur are 
steepness: 2 5 0.008 (5) 
slp 
or 
: d 
relative depth: —» < 0.01 (6) 
B slp 
In cases where both steepness and relative depth approach the above guidelines, 
nonindependent peaks may also be evident. 
b. Frequency and Period. Frequency and period corresponding to major 
secondary spectral peaks, f,; and T,;, usually indicate secondary frequen- 
cies and periods at which major amounts of energy are present. fp2, corre- 
sponding to the second highest spectral peak, is shown in Figure 1. Equations 
(5) and (6) can be helpful in identifying cases where major secondary peaks do 
not represent independent energy concentrations. 
c. Energy and Significant Wave Height. Energy and significant wave height 
corresponding to major secondary spectral peaks, Spz, and Hg7z, indicate the 
relative importance of secondary peaks. Since major secondary peaks often rep- 
resent independent wave trains, Sp; and Hs; can be estimates of the energy 
and significant height of secondary trains. A method used at CERC to estimate 
Spi is to partition the spectrum at its lowest point between every pair of ad- 
jacent major peaks (Fig. 1). The energy between partitions is then totaled by 
t 
Spits aide aeolA)g (7) 
where Kiz is the index representing the lower bound of the peak, and Kz the 
index representing the upper bound of the peak. If (Af)j = Af = constant, then 
16 
