676 BARBER AND TUCKER [CHAP. 19 



Until it is possible to base predictions on an adequate physical theory of wave 

 generation, it seems unlikely that there will be any major improvement in their 

 accuracy. 



5. Waves from Distant Storms 



Waves do not die away immediately the wind ceases to blow. On the contrary, 

 the waves from a storm occurring somewhere in a wide ocean spread outward 

 rather like ripples from a stone thrown into a pond. The wave height grows less 

 as the energy spreads over an increasing area. Some energy is lost in creating 

 white-caps and the shorter choppy waves disappear fairly soon, but the longer 

 waves can travel as low undulations to great distances. In tracing this progress 

 one cannot, of course, follow individual wave crests ; attention is directed to the 

 arrival of wave groups, and different wave groups are distinguished by the 

 period or frequency of their waves. 



The first waves that come from a distant storm have a low frequency, 

 sometimes as low as 50 c/ks, a period of 20 sec, and have outrun the rest because 

 of their higher group velocity. They are sometimes called "ground swell" 

 because they are such low undulations as to escape observations at sea and are 

 obvious only where they have gained height over shallow ground or in the surf 

 in the manner indicated later in Fig. 8. Wave groups of higher frequency travel 

 more slowly and arrive later. By keeping a watch on the period of the incoming 

 waves at a coastal station, one can deduce the distance of the storm that 

 caused them. From formula (4) for the group velocity it is seen that the time 

 taken for a group of waves of frequency/ (or 1/T) to travel a distance D is 



t = 47rfDlg. 



The waves received from a short-lived distant storm should therefore show a 

 frequency that increases linearly with time, and the distance is given by 



D = gl{47Tdfldt). 



In round figures this is 100 sea miles for every hour of the interval needed for 

 the frequency to increase by 15 c/ks. The linear increase in frequency suggests 

 that, at some instant prior to the observations, the wave frequency should 

 have been zero. This is the time at which the storm occurred. 



Storm distances can sometimes be deduced from the slow change in frequency 

 of swell breaking on the shore. But such observations are frequently interrupted 

 by the arrival of waves from other storms or by waves raised by local winds, 

 and it is desirable to have a means of distinguishing waves of different fre- 

 quencies. Digital computers working on the signals from underwater pressure 

 detectors are currently being used with great success to detect swell arriving on 

 the Californian coast from storms many thousands of miles away (Munk and 

 Snodgrass, 1957). Earlier workers used an analogue machine (Barber et al., 

 1946) to resolve wave records into a "spectrum" and Fig. 5 indicates a series of 

 wave spectra got from records of wave detectors off the coast of Cornwall, 

 England (Barber and Ursell, 1948). It can be seen that, at very low frequencies, 



