in, which |H| and are defined as the complex transfer function of float 

 position relative to water-particle horizontal motion, and S u is the energy 

 spectrum of horizontal water-particle velocity which can be readily obtained 

 from the spectrum of surface elevation by linear theory. 



and 



S u = S n 3(f) (63) 



cosh 2 k(d - d„) to 2 



3(f) = x (64) 



sinh z kd 



where 



Sri = surface elevation spectrum 



k = wave number 



a) = radian frequency 



d = water depth 



d = depth of float below Stillwater level 



An expression is developed for the spectrum of average drag power of a single 

 float in terms of the wave spectrum -is 



S p = S^g (65) 



Seymour and Hanes (1979) determined that the power consumed in the drag of the 

 float occurs at the expense of the spectrum of incident wave power, which can 

 be expressed per unit of float spacing along the wave crest as 



S w (f) = S n (f) a(f) (66) 



where S (f) is the spectrum of wave power, and S „(f) is the spectrum of 

 surface elevation. Here 



1 

 a(f) = - PgC (f) s (67) 



2 ° 



in which C (f) is the wave group velocity, and s is the float spacing 

 along a wave crest. Seymour and Hanes (1979) analyzed an energy transmission 

 coefficient, ETC, which is the traditional parameter for describing break- 

 water performance. It can be specified in terms of three coefficients: 



(S w - S p ) 1 - [yB(f)] 

 ETC(f)=— - V — = (68) 



Thus, in principle, the performance of a tethered-f loat breakwater can be 

 estimated only if the incident wave field characteristics, breakwater geom- 

 etry, and appropriate values of drag and mass coefficients are known. 



169 



