Laboratory Investigations on Air-Sea Interactions 



out-of-phase non-dimensional-pressure-coefficients. The phase 

 angle <p is 



<p = tan' (I) (4) 



The constants a and P were determined by solving an inviscid Orr- 

 Sommerfeld equation which represents the perturbations (caused 

 by the water wave at the interface) to a wind shear-flow described 

 by an assumed logarithmic, mean velocity distribution 



U(y) = U In ;^ (5) 



where y is the vertical distance from the mean water surface and 

 y^j is the roughness height. 



The effect of the impressed aerodynamic pressure P^ on 

 the surface wave can be evaluated by solving Eq, (2). It follows 

 that the complex wave celerity 



2 



2 

 ■0 ' 



where C = (g/k)'^^. Substituting Eq. (6) into Eq. (1) yields 



a=a„exp[ikC„£^(^)'pt] (7) 



w 



where a^ is the amplitude at t = 0. 



It is convenient to measure the growth of wave amplitude as 

 a function of fetch x in a wind- wave channel. The dynamic equi- 

 valence, valid for x » L, is given by Phillips [ 1958] as 



C. 

 X = -^ t , X » L 



where Co/2 is the group velocity of a deep-water wave. Conse- 

 quently, the fetch- dependent amplitude growth a is 



Pa k^ tt2 



^ [ -^^ ^ Uf Px] (8) 



a = a, e.^, p^ - ., 

 where a.^ is now the wave amplitude that would exist without wind 



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