for a fixed \x, Let this minimum be G (ii). Then (11,33) would be defined as 

 above for 



e^(M.) - TT < e < e^(tx) 



and by zero otherwise. 



The analytic expression determined as outlined above could then be trans- 

 formed to Cartesian coordinates in the c, p plane as described in Part 8. If 

 the function [A(a, p)] so obtained were integrated over a square of the area of 

 one of the squares in the U(r, s) plane the resulting number would then be quite 

 close to the computed values of U(r., s) and it would certainly agree within 

 possible sampling variations with the computed number. However, suclj an 

 analytic expression would still reflect certain features of tlje observed data and 

 the wind field which generated the waves which would be difficult to generalize 

 to other cases. In what follows this point will be discussed in more detail 

 and a simpler analytical expression derived for wave forecasting purposes. 

 P roperties of the directional spectrum 



By means of the data tabulated and graphed so far, in particular by 

 means of Tables 11.6j, ll,l0j, and 11.11 and by means of figures 11,22, 11,26, 

 11.27, and 11,29, certain, properties of the sea generated by the local winds 

 in the area where the data were obtained can be sumimarized. 



These properties are (1) that the integral over direction of the direc» 

 tional spectrum agrees remarkably well as a function of frequency with the 

 theoretical spectrum derived by Neumann for an 18.7 knot wind, (2) that the 

 angular spectrum is concentrated over narrower angular range for long waves 



233 



