a wave height record for a complex wave field. Since wave period is pro- 

 portional to the reciprocal of frequency, important wave periods are also 

 identified. Thompson (1980) provides further interpretations of coastal wave 

 spectra. 



The international standard unit for frequency measure is the hevtZy 

 defined as one cycle per second. The unit radians per second is also widely 

 used. One hertz is equivalent to 2Tr radians per second. 



4. Directional Spectra of Waves. 



A more complete description of the wave field must recognize that not all 

 waves are traveling in the same direction. This may be written as 



n(x,y,t) = Z a . cos [w -t - 



*. 



-k • (x cos 



*. 



is the angle between the x 



e . + y sin e 



r'] 



(3-19) 



th 



axis and the direction of 



where k •= 2ti/L. , ^ 



wave propagation, and 6- is the phase of the j"" wave at t = . The 



energy density E(9,(jo) represents the concentration of energy at a particular 



wave direction 

 by integrating 



9 and frequency to ; therefore, the total energy is obtained 

 E(e,a)) over all directions and frequencies. Thus 



-;/ 



E(6,a))da) d9 



(3-20) 



The directional spectrum E(9,(jo) can be used to identify prominent frequen- 

 cies and propagation directions; when these represent individual wave trains, 

 they provide important information for many coastal engineering applications. 



The concept of directional wave spectra is essential for advanced wave 

 prediction models. Such models estimate wave growth, decay, and propagation 

 under varying wind conditions in terms of directional spectra. Directional 

 spectra are becoming increasingly available from gage measurements through the 

 use of multiple, closely spaced pressure or staff gages; a pressure gage in 

 combination with velocity measurements in the horizontal plane; or measure- 

 ments of pitch and roll in a floating buoy. Remote sensing techniques for 

 estimating directional spectra from imagery obtained by satellite are also a 

 promising source of directional spectra. 



5. Comparability of Wave Height Parameters . 



The wave height parameters discussed in Chapter 3, Sections 11,1 and 2 

 based on statistics of the heights of individual waves in a record, may be 

 referred to as "statistical-based" parameters. Wave height parameters intro- 

 duced in Chapter 3, Section II, 3 are defined in terms of the standard 

 deviation of sea-surface elevations as represented by all data values in the 

 wave record. These parameters represent a fundamentally different class 

 called "energy-based" parameters. 



A third class of wave height parameters is defined in terms of idealized 

 waves of uniform height and period. These "monochromatic-based" parameters 



3-14 



