1, 



The average "period" for a partially developed sea can be evaluated 

 in terms of /i^ by the following procedure. Let 2Trf =^ and Zvi. = fj. 

 and let f. = 1/T. ^ 



Then the use of a formula derived by Rice (1944) shows that the average 

 "period" is given by 



or by 



where 



fOD j_ 



2a/ f 



df 



L T 



2 a T 



\ dTl'^2 



Jo T e dT 



a=g2/47r2v2 



(25) 



(26) 



The integrals given in (26) can be integrated by parts until an 

 integral involving the probability integral results. A change in variable 

 under the final integral in order to put it into unit normal form yields, 

 after several operations, the result that 



y"3 



3 Ztt V 



2g 



3e 



2g'TLV47r^2 



2g Tj,/2 7rv -oc^/E 



8T;'gV(2^v) 



doc- 4g2TV(27rv)2 J 



% 



(27) 



The ratio, gT. /Zwv, occurs everywhere in equation (27). This is the 

 ratio of the phase speed of the highest spectral period present to the 

 wind speed. It is usually designated by 



;8,= gTj/2Trv 



(28) 



and then equation (27) yields 



~ V3 2 Try 



2 g 



n'/2 





doc - -4r^ 



(29) 



33 



