of the system (Seymour and Isaacs, 1974; Seymour and Hanes, 1979) considers 

 only drag dissipation. Fluid drag, proportional to the square of the veloc- 

 ity, is nonlinear even in steady flows. Since the driving force (wave-field 

 pressure gradient) is always a random broad-spectrum process, the response of 

 a linear oscillator will also be random and broad spectrum; hence, the drag 

 itself is a wide-band random variable. It is therefore difficult to predict 

 the drag in a deterministic sense from some measured parameter such as the 

 water-surface elevation time-history. With random processes, it is more 

 convenient to work with the frequency domain and deal with the statistics of 

 fluid drag. 



Following the usual form for quadratic damping, Seymour and Hanes (1979) 

 defined the drag force in frequency space for a single float as 



F D (f) =- pAC d [U r (f)] 2 (57) 



where 



F Q (f) = drag force in frequency space 



p = fluid density 



A = frontal projected area of a float 



C. = empirically determined drag coefficient 



U (f) = relative velocity between float and fluid particle 



It follows that the drag power of the float, Prj(f), is 



P D (f) = U r (f) F D (f) (58) 



By taking temporal average values 



[U r (f) 3 = S3 /2 (59) 



where the overbar indicates an average value with respect to time, and S is 

 the spectrum of relative velocities. The drag power for a single float then 

 becomes 



1 



N 



P D = - pAC, I [S (nA f )] 3/2 (60) 



"total 2 n=Q 



where NAf is the Nyquist frequency. 



Seymour (1974) showed that the spectrum of relative velocities for a 

 single float, S , can be estimated by 



where 



S r = S u y(f) (61) 



y(f) = 1 + |H| 2 - 2 | H | cos 9 (62) 



168 



