Pautling 



function of Reynolds number. In applying this concept to the present 

 situation in which we have a periodic fluid motion resulting from the 

 superposition of wave and body motions, we might compute a Reynolds 

 number using the mean absolute velocity, and choose the drag coef- 

 ficient accordingly. The drag term in Eq. (7) should then be a 

 quadratic function of velocity. This, however, destroys the linearity 

 of our analysis, and. in view of the crude approximation involved, it 

 is not worth the added complication. In order to preserve linearity, 

 an equivalent linear drag coefficient is therefore defined, as described 

 in Blagoveshchensky [ 1962] , such that the linear drag force dissipates 

 the same energy per cycle of periodic motion as the nonlinear drag 

 force which is being approximated. 



The derivation of the equivcdent linear drag coefficient is as 

 follows, Assunae a sinusoidal variation of the relative fluid velocity 

 given by 



V = Vq sin cot, (16) 



The linear drag force is given by 



and the nonlinear drag by 



Dn=C,„v". 



The energy dissipated per quarter cycle of motion is given in the 

 linear case by 



and in the nonlinear case by 



Con J -"*' « • 



Equating the two energies enables us to solve for the equiva- 

 lent linear drag coefficient in terms of the assumed nonlinear "coef- 

 ficient. In the case of n = 2 (quadratic drag) the result is 



1096 



