left and the other from 45 deg to the right, the wave crests will intersect at 

 90 deg. Since the frequency of each wave train is the same, the wavelengths 

 in both wave trains will be the same. The total pattern of wave crests will 

 appear to be a square grid cocked at 45 deg to the beach and moving normally 

 toward the beach. 



12. If the two wave trains approach the beach at angles that are not as 

 widely separated, say from 10 deg to the observer's left and from 10 deg to 

 the right, the individual wave train crests will still be distinguishable; 

 but the total crest pattern will be elongated in the longshore direction. 

 Instead of being square, the grid pattern will be a rhombus. It will still 

 move normally toward the beach. As the direction separation becomes yet 

 smaller, the rhombus pattern gets more elongated in the longshore direction. 

 Over most of the wave pattern, an observer with a good means of sensing 

 direction would see an almost unidirectional wave train with crests of alter- 

 nating waves aimed in slightly different directions. 



13. Since wave energy moves in the wave propagation direction, the 

 above examples illustrate wave fields where energy is distributed in direction 

 but not frequency. Harmonic (i.e., frequency spectrum) analysis of the time 

 series of sea surface elevation measured at one point in space would show wave 

 energy at only one frequency for all cases. The wave field is thus mono- 

 chromatic in that sense. One could add to the picture more waves of the same 

 frequency but different directions. A graph of wave energy as a function of 

 direction for this set of waves would be called the direction spectrum of wave 

 energy for that frequency. 



14. If the same process is done for waves at all the other frequencies 

 in the wave field, one could construct a three-dimensional diagram of wave 

 energy as a function of both frequency and direction. This type of display is 

 called the frequency-direction spectrum of wave energy. If known completely, 

 it constitutes a complete description of sea state insofar as energy available 

 to do work is concerned. 



15. In general, it is very important to know the directional character- 

 istics of wave energy. If the energy at all frequencies is confined to a very 

 narrow range of directions, then the engineering guidance based on unidirec- 

 tional, irregular seas is sufficient for design work. However, if the energy 

 at one or more frequencies is spread over a broad range of directions, then a 

 host of problems can arise if unidirectional guidance is used. 



