SEAWAY 



79 



# 



Efkg.e) Arbitrary Units 



Fig. 87 Photographs showing statistical phase 

 relations between waves at points separated by 

 2, 9, 18 and 27 ft along a fixed line. Attention is 

 confined to waves of period near 2 sec (from 

 Barber, 1954) 



wind direction was nuicli greater than elsewhere, it is not 

 expected that the curve in Fig. 88 will apply to open 

 water." "The E{kn, 6) curve in Fig. 88 was computed 

 from the last three photographs in Fig. 87. It shows that 

 the highest wa^•es are traveling in the direction 120° to 

 the positive sense of the line joining the instruments. 

 This was, in fact, the direction of the wind at the time of 

 the measurements, so the metliod has given reasonable 

 results." 



It appears that Barber developed the first simple and 

 practical methotl for measuring the directional wa^•e 

 spectrum. By the nature of a mechanical pendulum, he 

 was limited to measuring the directional characteristics 

 of waves near a single frc()uencv coo. Sinuiltancous meas- 

 urements at several frequencies would be possible, how- 

 ever, by using several electronic filters. 



Barber is also the originator of eleven methods for 

 measuring the directional spectrum in the model tank. 

 Since these methods speak of specifically spaced detectors 

 making time histories, certain complications in applica- 

 tion to open-sea work arise. Certain of the methods may 

 conveniently be transformed to spatial systems which 

 suggests the use of aerial stereophotography at sea. It 

 is also possible that a fixed network of probes at sea can 

 be arranged. 



The first four methods deal with line arrays of de- 

 tectors. They are, in the different methods: a) Ro- 

 tated; h) remain fixed but treated with time delays; 



c) remain fixed but modulated by cosine operators; 



d) remain fixed and modulated, but measure horizontal 

 water motions as well. 



Each method results in a set of recoi'ds which is then 

 averaged and filtered. The first metlK)d is in fact the 

 temporal analogy of the method of Marks (1954). Only 



160 



150 \20 90 €0 30 



Pirection of Trovel (0)- Degrees 



Fig. 88 Distribution of wave energy with respect to 

 direction of travel relative to line of instruments. 

 Curve is deduced from records in Fig. 87 (from 

 Barber, 1954) 



the fourth method distinguishes the proper directions of 

 the waves; the others cannot judge whether the waves 

 are coming or going, so to speak. The fourth method 

 uses as few as six double detectors placed in a straight 

 line. 



The remaining .se\'en methods are correlation tech- 

 nicjues which depend on the geometrical orientation of the 

 probes. They require fewer detectors and considerably 

 less computational effort; the results suffer, as a conse- 

 quence. In the words of Barber: "In my opinion, cor- 

 relation methods are likely to be most useful where they 

 aim to use comparatively few measurements to find the 

 outline or general character of the spectrum. Here, they 

 are more powerful than in the case of more orthodox 

 "array" methods. 



"For routine analysis in the Model Basin, an 'array' 

 method would lie best. It could be almost automatic. 

 If the wave directions lie within an arc of 150°, then 

 Methods 2 or )! would serve to give an analysis in about 

 10 minutes. ^lethod 1 would serve if the waves were in 

 an arc of 170° and if a long sample were not necessary. 

 If random waves may come from any direction. Method 

 4 is neces.saiy, but it calls for a detector both for the ver- 

 tical and the horizontal water motion. 



"It may be worth using a correlation method while the 

 apparatus for a more routine method is being l.)uilt." 



Gelci, Cazale, and \'assal (1957) evaluated an energy 

 spectrum by an analysis of ocean swells. These arrived 

 at Dakar and Casablanca from many generating areas 

 with wind velocities at various angles to the direction of 

 the swell propagation. The spectrum, E{T, d), in terms 

 of wave jDcriod, T, and direction 6, was j^resented in the 

 form 



E{T, e) = f{T) ^{d) 



(149) 



where 



,p{e) = 9/4,r = 0.72 

 = 9,'87r = 0.36 

 = 



if < 6* < 20° 

 if 20° < 6> < 00° 

 iie> 60° 



