Hsu and Yu 



The dearth of systematic measurements taken under controlled 

 conditions closely comparable to those of Miles' model was a moti- 

 vation for our research program at Stanford University. In order 

 to examine the applicability of Miles' inviscid theory, experiments 

 were designed for measuring the wave induced perturbation pressure 

 or inviscid Reynolds stress under steady- state and unsteady- state 

 conditions. Other experiments were also devised for measuring the 

 growth of mechanically generated waves subjected to wind action. 

 From these measured wave growths, the growth factor of Miles was 

 calculated. The objectives of this paper are to present a summary 

 of our experimental data in the inviscid range, to compare our data 

 and other existing data to the theory and the ocean observations, 

 and to suggest specific and fruitful avenues for further study. 



II. A BRIEF REVIEW OF THE THEORY 



To facilitate presentation and discussion of the experimental 

 data, a brief outline of the assumptions, key equations and results 

 of Miles' inviscid, shear-flow theory are presented below. 



The deep-water, wave profile is assumed to be a progressive, 

 sinusoidal wave, expressed as 



T) = a exp [ ik(x - Ct)] , ka « 1 (1) 



where a is the amplitude, k = 2it/L is the wave number, L is the 

 wave length, and C is the wave celerity. The assumptions of irro- 

 tational, incompressible water motion lead to the existence of 

 velocity potential. By substituting the velocity potential in the 

 linearized Bernoulli equation and evaluating the result at the free 

 surface, one obtains the equation of motion governing the propaga- 

 tion of a small amplitude, surface wave 



where g is the acceleration caused by gravity, p^ is the mass 

 density of water, and p is the aerodynamic pressure caused by 

 the wind stream. 



Miles [ 1957] assumed the aerodynamic pressure p^ has 

 the form 



p^= {a + iP)p^ufkii (3) 



where pg is the mass density of the air, U| is a reference speed 

 for the air, and a and P are, respectively, the in- phase and 



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