azimuth line. The glitter is brightest where the slope reaches the maximum values, these 

 being the most probable slopes of a sinusoidal wave. Actual conditions are just the 

 opposite. A real glitter pattern as shown in the photograph does not follow any par- 

 ticular azimuth line, and it is brightest in the center, where the required tilt is zero. 

 The observed result is consistent with a continuous two-dimensional spectrum. 



THE SPECTRUM FROM .2 to 200 C/KS 



Most of our work deals with frequencies that are dismissed as D. C. by the radio 

 engineer. For unit frequency we use cycles per 1000 sec, or c/Ks. Fig. 2 shows a 

 typical La Jolla frequency spectrum (non-directional). The ordinate E in cm 2 per 

 c/Ks is referred to as the "Energy density." The range between 50 and 200 c/Ks 

 comprises the ordinary sea and swell spectrum, and has been extensively studied. The 

 remaining part of the spectrum is based on recent work which has not been presented 



FREQUENCY IN c/Ks 



Figure 2. A typical frequency spectrum of the variations in the level of the sea surface above a 



fixed point at La Jolla, California. 



previously. The low frequency records were obtained by means of a sensitive pressure 

 transducer, the Vibrotron. Some analyses have been performed with an analogue 

 computer in England, others with a high speed digital computer in the United States. 1 

 It is encouraging that the results agree. 



Apparently there are five separate bands of high activity. This is a remarkably 

 complex pattern. For comparison, the spectrum of sound background in the sea de- 

 creases monotonically between 10 c/s and 100,000 c/s by roughly 6 db per octave. 



Of course, Fig. 2 is a description, not an explanation. But we have reasons to 

 believe that each of the five peaks involves different physical factors, and that the 

 resolution by frequency is a fruitful one. Also, that each of these bands is a factor in 

 Naval Hydrodynamics when interpreted in its broadest sense. 



The usefulness of the spectral representation has been limited largely to problems 

 where each frequency could be considered as being independent of, and superimposed 

 on, other frequencies; in other words, linear problems. The topic of ocean waves pre- 



1 We are greatly indebted to B. Ferber, D. Shumway and M. Covher of CONVAIR, 

 San Diego, for their part in analyzing many records. 



47 



