TM No. 377 



In the classical theory of progressive surface waves, the total wave energy 

 per unit horizontal area is given by (see Lamb, 19U5): 



E T = 3 f A . (v-21) 



where Q = 98O cm sec , p is the density of sea water, and A is the amplitude 

 of the wave (equal to half the wave height^H/2). The kinetic energy Ej^ of the 

 wave equals the potential energy Ep, or: 



Ek^B p = fc J^ (v-22) 



It is worthwhile to attempt to evaluate E p using average values of the 

 observed wave heights. During the BBELS observations, visual estimates were made 

 of wave height (h) and wave length (l), and these are listed in table V-2. The 

 values obtained are manifestly very subjective, and statistical interpretation 

 of them is difficult. 



Consider first the wave height observations. What was actually done was 

 to scan the sea surface from the lower catwalk (shown in figure TV-18), located 

 some 18 meters above the water, and to estimate the distance from the visible 

 crests to the trough. This method of observation gives approximate values of 

 maximum wave height Hm, but it is difficult to derive anything more than rough 

 estimates of the average wave height (see Pearson, Neumann, and James, 1955). 



A somewhat arbitrary decision was made to define the "average wave height" 

 as 0.5 Hm, and these values are listed in table V-2. Using these Hm/2 values 

 and equation (V-2l), the estimates of wave potential energy, designated Ep (h/2), 

 were obtained. These estimates range from 1.77 to 5.18 X 105 erg cm-2„ They 

 are very similar in magnitude to the kinetic energy values (Ekw). Note that in 

 BBELS-11 Ep (h/2) shows a similar increase with the respective values of Ekw 

 In view of the crudeness of the instrumentation and the obvious shortcomings of 

 both the data and perhaps its interpretation, the similarity of Ekw with Ep (h/2) 

 is startling. 



It may reasonably be objected that the choice of using average wave heights 

 of l/2 Hm was made so as to produce similar magnitudes of E^w an ^- Ep (h/2). Let 

 us therefore estimate the mean wave height by another method. Note in table IV- 3 

 that values were recorded of wave length. These were somewhat more accurate than 

 wave height, since the distance between the main west legs of the BBELS (15 m) 

 could be used as a reference. From the observed values of wave length L, inter- 

 polated values of average wave height (designated by h) were obtained using 

 table II-2 (from Marks, 196U). These values are tabulated as H(l) in table V-2, 

 and are very similar to those for Hm/2. Values of corresponding potential energy, 

 designated as Ep (S), are shown in the last column of table V-2. These values 

 of Ep (fi) are still similar to both E^ w and E p (h/2) in most cases. 



12k 



