Thus 





E(co)da; . (3-16) 



The spectrum E((jj) permits one to assign specific portions of the 

 total wave energy to specific frequency intervals, to recognize that two 

 or more periods may be important in describing the wave field, and to give 

 an indication of their relative importance. This also permits a first 

 approximation to the calculation of velocities and accelerations from a 

 record of the wave height in a complex wave field. Several energy spectra, 

 computed from coastal zone wave records obtained by CERC, are shown in 

 Figure 3-6. 



The international standard unit for frequency measure is the hertz^ 

 defined as one cycle per second. The units aycZes pev second and radians 

 per second are also widely used. One hertz = 2it radians per second. 



3.24 DIRECTIONAL SPECTRA OF WAVES 



A more complete description of the wave field is required to recognize 

 that not all waves are traveling in the same direction. This may be 

 written as , 



Tj (x, y, t) = 2 a. cos [co-t - 0- - k (x cos fly + y sin 6-^ , (3- 17) 



where k = Ztt/L, and 9^- is the angle between the x axis and the 

 direction of wave propagation, and ^a is the phase of the j^^ wave 

 at t = 0. The energy density E(e,u) represents the concentration of 

 energy at a particular wave direction 6 , and frequency w , therefore 

 the total energy is obtained by integrating E(e,{jo) over all directions 

 and frequencies, thus 



27r oo 



E(0,a))dwd9 . (3-18) 



= // 



The concept of directional wave spectra is essential for advanced 

 wave-prediction models, but technology has not yet reached the point where 

 directional spectra can be routinely recorded or used in engineering design 

 studies. Therefore, directional wave spectra are not discussed extensively 

 here. 



3-13 



