To compute the growth function, a curve fitting program was designed 

 for the computer so that the end product was a 3-hourly final growth 

 table showing wind speeds at 2-knot intervals from 10 to 60 knots versus 

 the E-values (Table 3). Here E is in units of (ft) and represents a 

 number twice the variance of the spectral density. The new growth 

 assumes that a partially developed spectrum has the same shape as the 

 fully- developed spectrum for the lower wind speed that would produce the 

 same significant height waves. This assunrption yields a much more reason- 

 able spectrum during periods of wave growth and propagation than do other 

 assumptions. 



Another study at New York University led to the conclusion that the 

 high-frequency end of the wave spectriun could be simply represented 

 within the limits of forecast accirracy as a function of wind speed alone. 

 Thus, the machine program could be modified to assume full development 

 for all waves with periods less than 7 seconds. A further consequence 

 of this idea was the assimption that all waves with periods below J 

 seconds dissipated immediately if the wind decreased. With these assump- 

 tions the machine programming was considerably simplified. 



In a test of the original machine program it was found that the waves 

 at a point did not dissipate as fast as they should because the pro- 

 grammed dispersion was too low. To remedy this an empirical dissipation 

 function was developed and tested. The form of the dissipation function 

 ■vreis 



(10) a2 {f, 9) -. Af (f, 0) .[exp [C3 fV-5lj''^ ^'^ 



where A-^if, 9 ) = spectral energy of component after (with) dissipation 



A^(f, 9 ) = spectral energy of coaqponent before (without) dis- 

 sipation 

 f = center frequency of spectral component 

 B = center direction of spectral component 

 Cq = 3^5 -Oj a constant 



E = ^r Aj(f, 9)d£di9 - total energy in spectrum 



•' r 1 = X& - wind direction/ 



andK(/(Ji<75°) =0 



K(75 < /?.|<105°) = 1.5 



K(105°</(91/ 1135°) = 3.0 



K(l35°</|l/< 165°) = h.3 



K(i65°</^yii8oo) = 6 



By using this empirical dissipation factor a solution was found for the 

 problem of shifting wind directions and decreasing wind speeds. 



Thus, when the original program had been modified by using a new 

 spectral model, a new growth function, a new dissipation factor, and a 

 specification only for the long period end of the spectrum, then the 

 results compaxed favorably with wave observations in most of the situations. 



27 



