PART II: NOTATION AND SEMANTICS OF DIRECTIONAL SPECTRA 



39. A system of notation is necessary to conununicate ideas and organize 

 data for use in mathematical models and computer-controlled physical models. 

 This notation applies to wave energy spectra, corresponding sea surface 

 descriptions, and their interrelationships. Since several types of spectra 

 were mentioned in the introduction, a graphic display is useful so the reader 

 can picture what the notation means. In this section a (conventional) 

 notation is defined, and some pictorial examples of wave spectra are 

 presented. 



Review of Basic Definitions 



40. The basis for all analysis used in this report is linear (or Airy) 

 wave theory. Its properties are described and further references given in the 

 SPM (1984) . In this theory, a complex wave field is approximated by a number 

 of individual wave components or trains. Each wave train is a simple sinusoi- 

 dal displacement of the sea surface from a reference (still) water level 

 propagating in one direction along a horizontal plane with a certain speed. 



If rj is the water surface,* x and y are horizontal coordinates, and t 

 is time, a single wave train can be represented by 



r7(x,y,t) = a cos(27rft - kx cos 6' - ky sin 9' + 4>) (1) 



where, relative to a straight reference coastline, 



x = shore-normal coordinate, originating at sea and increasing 

 toward land 



y = longshore coordinate, increasing to the right of an observer 

 looking seaward 



a = wave amplitude or half the wave height in linear theory 



f = 1/T, wave frequency with 



For convenience, symbols and abbreviations are listed in the Notation 

 (Appendix B) . 



18 



