time of 103 sec (= 16.7 minutes). The amplitude is given in a logarithmic scale 

 as a function of the angle between the two primary swell waves. Amplitudes 

 of about 13 centimeters are obtained if the primary waves are traveling in direc- 

 tions containing an angle of about 60 degrees. The amplitude increases to more 

 than .3 meters for angles of more than 150 degrees, and is only a few centimeters 

 for angles less than 30 degrees. This seems to support the results obtained by 

 K. E. Kenyonll and K. Hasselmannl2 that a narrow directional spectrum of 

 surface waves does not lead to significant internal waves. On the other hand, 

 the figure demonstrates that surface swell which can be described by two surface 

 waves traveling in different directions may create internal waves very rapidly. 

 A swell of that type would be interpreted according to equations (1) to (4) as 

 amplitude-modulated and traveling in a direction given by k-^, because the ampli- 

 tude Aj is much larger than A2 and therefore would govern the swell. 



MEASUREMENTS ON SWELL AND INTERNAL WAVES 



In order to test the theory, simultaneous measurements on surface swell 

 and internal waves were made in October 1966 at the NEL Tower, running from 3 

 October, 1130 to 6 October, 1215- Two wave-height sensors were used to derive 

 the directional spectrum of the swell — one fixed at the NEL Tower, the second 

 at a distance of 39.3 meters toward the west. The voltage output was recorded 

 on punch tape. The temperature fluctuations were measured by means of two 

 vertical thermistor arrays. The spacing between the thermistors was 75 centi- 

 meters, reaching from the bottom up to 2.75 meters below mean sea surface. The 

 two arrays were located in positions along a line from southwest to northeast. 

 The distance between the arrays was 284.4 meters. The temperature fluctuations 

 were recorded on an analog recorder and on punch tape. Simultaneous records 

 of swell and temperature fluctuations were obtained. The complete analysis of 

 these data will be published later. Preliminary results support the theory given 

 above. Figure 3 shows the power spectra of the two wave-height sensors for 

 data from 4 October, 1230—1330. The voltage output of the two sensors has been 

 used directly for these calculations. This output is different for both, and this 

 is the reason for spectrum 2 showing higher intensities than spectrum 1. Other- 

 wise, both spectra coincide quite well. The phase difference changes linearly 

 with frequency as is to be expected. But there occurs a remarkable hole at 

 frequencies of about 0.061 cycle per second, corresponding to&j =0.38 sec"l 

 or 7- = 16.4 sec. The energy decreases in both spectra from about 12 to 1.2 

 (arbitrary units), and the phase differences change from 35° to —70°, which indi- 

 cates that the swell in this spectral range consists of two waves, one with 

 a;2 = 3.9x10'! sec"l traveling in direction 30° and a second one with co-^ = 3.808x 

 lO'l sec'l traveling in a direction of about 270°. The angle between both is 

 about 120°. From figure 2 it follows that within a quarter of an hour these two 

 swell waves would create an internal wave of r = 11.4 minutes with an amplitude 

 of 1.5 meters 



The swell in the vicinity of the NEL Tower therefore seems to be modulated 

 as indicated by figure 3. If the stratification is favorable, that is, if |/j^ — fe,J2/ 

 (a>,ji - cjn)'^ is an eigenvalue, a very intensive energy transfer from the swell 



24 



