Hsu and Yu 



of the experimental data precludes any definite conclusion about 

 possible flow separation. Although a unified theory is needed to 

 describe the relationship between the phase angle <p and ± C/U_ , 

 the experimentally determined phase angles in the inviscid range do 

 indicate a correct trend compared with Miles' theory. 



V. CONCLUSIONS 



The accumulated laboratory experimental evidence obtained 

 at Stanford and elsewhere indicates general support for Miles' 

 inviscid theory of energy transfer between air stream and progressive 

 waves through the phase shift of the aerodynamic pressure at the 

 interface. However, the experimental growth rate is considerably 

 in excess of Miles' prediction, being approximately three times 

 larger. The most fruitful avenue for further study would appear to 

 be to reexamine the necessary simplifying assumptions in the Miles' 

 inviscid model. The incompatibilities near the air-water interface 

 suggest that detailed experimental investigations of this region are 

 essential before an understanding of the energy transfer mechanisms 

 and the conditions under which they occur can be fully established. 

 The effects of turbulence , possible flow separation, ripple super- 

 position and boundary layer development are complex, but could be 

 modelled and fruitfully studied in laboratory simulations. 



REFERENCES 



Benjamin, T. B., "Shearing Flow over a Wavy Boundary," J. Fluid 

 Mech. , 6, 161-205, 1959. 



Bole, J. B. and Hsu, E. Y. , "Response of Gravity Water Waves to 

 Wind Excitation," Stanford Univ. Dept. of Civil Engineering 

 Tech. Rep. No. 79, 1967. 



Chang, P. C. , "Laboratory Measurements of Air Flow over Wind 

 Waves Following the Moving Water Surface," CERu8- 

 69PcC18, Colorado State Univ., 1968. 



Dean, R. G. , "Stream Function Representation of Non-Linear Ocean 

 Waves," J. Geophys. Res., 70, (18), 4651-72, 1965. 



Hires, R. I. , "An Experimental Study of Wind Wave Interactions," 

 Tech. Rep. No. 37, Chesapeake Bay Inst. , Johns Hopkins 

 Univ. , 1968. 



Hsu, E. Y., "A Wind, Water-Wave Research Facility , " Stanford 

 Univ., Dept. of Civil Engineering Tech. Rep. No. 57, 1965. 



Kendall, J. M. Jr. , "The Turbulent Boundary Layer Over a Wall 

 With Progressing Surface Waves," J. Fluid Mech. , 4i_, 

 Pt. 2, 13 April 1970, pp. 259-282. 



34 



