Instruments measuring higher harmonics have a narrower lobe. The directional 

 sensitivity pattern for an instrument measuring the first 6 harmonics is shown in Fig. 4. 



A locally generated sea is unlikely to contain important harmonics above the 

 5th or 6th, and an instrument giving the first six harmonics would therefore be adequate 

 for measuring storm waves. Information approximately equivalent to this can be 

 obtained for a limited range of frequencies using an array of six conventional wave 

 recorders suitably spaced in an L-shaped pattern. The calculation of the spectrum 

 from the recorder outputs requires a rather formidable amount of computation unless 

 automatic equipment is used (see below). 



Swell from a small distant storm may be a very narrow beam, and harmonics 

 up to the 20th or 30th might be required to define it fully. For most purposes, however, 

 a knowledge of the first 5 or 6 angular harmonics will be sufficient. 



The first estimate of directional distribution was made by Arthur (1949). He 

 observed that the high surf activity experienced during the landings in Sicily during 

 World War II could not be accounted for if the wind-generated waves travelled only 

 in the direction of the mean wind, but required that substantial energy be radiated up 

 to 30° to each side of the mean wind direction. 



PRACTICAL METHODS 



At the present time the most practicable method of gaining some directional 

 information is probably the shipborne wave recorder (Tucker, 1955; Cartwright, 1956), 

 which is the basis of some very useful comparisons of ship and wave motion by Cart- 

 wright and Rydill (1956). This instrument may be regarded as measuring the height 

 which the water surface would have near the center of the ship were the ship not there. 

 The directional information is obtained by steaming the ship on a series of different 

 courses (e.g., 12 courses at 30° spacings) and measuring the Doppler shifts of the 

 various frequencies recorded. It is possible to measure only the first harmonic of the 

 angular distribution integrated over all frequencies present, though in the special case 

 where there are two or more separate bands of frequencies (e.g., long period swell and 

 short period locally-generated sea), these can be studied separately. In principle more 

 detail can be obtained, but impossibly long records are required to give sufficient 

 statistical reliability. 



Methods depending on the correlation of the outputs of various measuring 

 devices are practicable with present techniques. The combination of a pressure meas- 

 uring device with a current meter measuring the two horizontal componnts of orbital 

 velocity gives a , a ]f b lt a 2 , b 2 . The same information could be obtained by other 

 similar methods, such as a free floating buoy measuring the three components of its 

 acceleration (Barber, 1946). Barber (1954) has described a method for measuring the 

 two-dimensional spectrum using a number of correctly spaced wave recorders and 

 simple correlating equipment which works directly on the recorder outputs. Using 

 three wave recorders in a limited fetch, Barber observed a "beam width" of ±45°. 

 Barber and Doyle (1956) have described a simplified version of this which measures 

 the mean direction of a narrow beam using just two measuring heads and which is 

 suitable for measuring the direction of approach of swell. 



Another series of methods depends on photography of the sea surface. Since 

 these are instantaneous measurements, they all have a 180° ambiguity, and energy 

 traveling in directions opposed by 180° is added together. Barber (1949) used a 

 photograph of the sea surface as an optical diffraction grating. If the optical density at 

 each point of the photograph were proportional to the elevation of the sea surface, the 

 diffraction pattern would be a 2-dimensional analysis of the wave pattern, with the 

 radius from the center of the pattern being proportional to 1 /wavelength and the 

 intensity being related to E(0,f) in a simple manner. The difficulty is, of course, that 

 the optical density of the photograph is a function of the slope of the surface, the angle 

 of observation and of the distribution of the brightness over the sky. Cox (1955) has 

 examined this problem in more detail, and finds that if a photograph of the sun's 



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