Global Wave Forecasts Using Spacecraft Data 



ral profile assuming She 

 to construct the original wind field as in 



Vn(z) = v(z; Cio), (13) 



the ratio 



R = 



d2v(z)/dz2 dvM(z)/dz 



^ (14) 



dv(z)/dz d2v^(z)/dz2 



can be evaluated at Zf. to get FB(v, f), which will replace B(v, f) in Eq. (7). 



Stable conditions will probably make R near one for high frequencies and 

 less than one for low frequencies because the greatest variation in the wind pro- 

 file is near the surface. Unstable conditions will probably make R greater than 

 one over the whole frequency range. 



The effect will be to produce more rapidly developing seas in unstable air, 

 but the fully developed spectrum will not be changed. Whether or not this cor- 

 responds to all aspects of reality is open to question. Present data do not seem 

 to show any dependence of the fully developed spectrum on air sea temperature 

 difference (5). 



The papers at the International Symposium on Turbulence in the Boundary 

 Layer held at Kyoto, Japan, in September 1966 (lUGG-IUTAM) provided many 

 new concepts for the integration of the pressure field with the boundary layer. 

 In particular, we hope to be able to use the ideas of Dr. Swinbank, Dr. Priestly, 

 and Prof. Lettau in the further development of the preceding concepts. 



Dissipation 



The spectral components traveling against the wind will not receive energy 

 from the wind and must undergo some form of dissipation. This dissipation in 

 our model is governed by the height of the wind sea. With S^ = X s,^,(fi), 



SpCfj-^j) f-ys.^f.X (15) 



So(fi.^j) " \ / • 



where Sg ( f . , 6?^ ) is a component traveling against the wind, s^ ( f . , 6'. ) is the 

 component after 2 hours of dissipation, and N = 4 if f. is opposite to the wind, 

 N = 3.5 if e. is ±15° to the wind, N = 3 if 6^j is ±30° to the wind, and so on. 



For a spectral component of 0.10 sec"^ traveling opposite to a fully devel- 

 oped 30 -knot- wind sea, 



Sd(0-10.^) ^-0.1248 



So(0.10, 77) " ^ 



511 



