sents important non-linear problems, such as the breaking of ocean waves. The pre- 

 vious speaker, Dr. Lighthill, has been particularly successful in coming to grips with 

 non-linear problems. But as far as we know, all such work has been confined to mono- 

 chromatic, one-directional waves. What is the situation for a continuous spectrum? 

 Not even the limits for the linear approximation have been stated explicitly. For the 

 monochromatic case one simply assumes that the height-length and height-depth ratios 

 must be small. Is the equivalent requirement that the rms slope must be small, or would 

 infrequent occurrence of steep slopes change the situation materially. These remarks 

 are in part directed at Professor Stoker, the chairman of this session. Is it safe to apply 

 any of the work on the formation of bores to the actual ocean unless we understand 

 more about the effect of non-linearity for continuous spectra? 



RIPPLES 



The tiny peak to the right of Fig. 2 represents enhanced activity for waves a 

 mm or so in length. The result is preliminary, and numerical values of energy density 

 are not yet available. It is based on work by Charles Cox. In this range of the spectrum, 

 capillary forces are more important than gravity. Some of this activity must be related 

 to tiny wavelets on the lee side (forward) of wave crests. An oil slick will wipe out 

 this part of the spectrum. 



It has been shown by Eckart (1953) and others that sound waves or electro- 

 magnetic waves impinging on the sea surface will be backscattered by ocean waves of 

 about half the wavelength of the incident radiation. The problem of RADAR sea 

 return and acoustic surface reverberation involves this high-frequency spectrum. 



The visibility of objects beneath the surface from an observer above the surface 

 also appears to be critically related to this part of the spectrum (Duntley, 1950). 



SEA AND SWELL 



This part of the spectrum is closely related to meteorologic activity. Sea is 

 generated by local winds, swell by distant winds. In La Jolla we usually have a peak 

 at about 65 c/Ks (period 15 s ), presumably due to swell arriving from generating areas 

 5000 miles to the south. More often than not there is a second peak due to meteorologic 

 activity in the Northern Hemisphere. Numerical values in the figure represent typical 

 conditions. On occasion the energy might be 10 times higher or 10 times lower. The 

 cutoff to the right is drawn as E oc /~ 6 in accordance with Neumann's proposed formula 

 (Neumann, 1954) for the spectrum of a fully developed sea. 



It is a strange, if you wish an unhappy circumstance, that this peak is associated 

 with wave lengths of dimensions commensurate with those of ships. We shall return 

 to this subject later. 



SURF BEAT 



This band was discovered several years ago by means of wave recorders tuned 

 to low frequency (Munk, 1949; Tucker, 1950). At a depth of 20 to 30 feet the energy 

 of the surf beat band is about 1 per cent of the sea-swell band; at greater depths and 

 large distances offshore this band appears to be considerably reduced. The mechanism 

 of generation is not clear, but some kind of non-linear interaction of the sloping bottom 

 with the incoming groups of waves appears to be involved. Obviously our pressure 

 mines, which are tuned to frequencies lower than the swell, must not be triggered by 

 surf beat. 



SURGES 



These differ greatly from locality to locality, depending critically on offshore 

 topography. Some of the activity is in the form of trapped modes, with the continental 



48 



