- -p < 9 < -^ and zero otherwise (i. e. waves traveling against the mean 

 local wincT are not considered). The actual values of S(oj, 9) rarely 

 coincide ■with this form because simple fully developed seas are not 

 frequent in the North Atlantic. 



The calculation of U now becomes a matter of applying eq. (2) 

 to each d-f interval. The resulting magnitude is then assigned (as 

 a first approximation) the centered direction of the band in which it 

 is situated. By convention, the direction is taken as "from" the 

 centered direction of the band--in the sense of Figure 1. When the 

 procedure has been applied to all the d-f components in turn, a set 

 of component vectors is produced. The vector sum is an approxi- 

 mation of the mean Stokes' velocity at the grid point. The magnitude 

 evaluation is essentially all contained in a subroutine called UDRIFT. 

 The logic behind it can be seen by examining eq. (2) in the form 



U.. = 2J ^e"^" '«^"S,,((^,9)dca (4) 



where (^i+i - upper limit of a particular frequency band 

 w. = lower limit of the same frequency band. 



Since S. .(oo, 9) = E. .(w, 9) /(cu. , , - w.) and E..(w,9) 



has previously been estimated as constant in the interval, Si;((jj,9) 

 may be approximated as constant with respect to co in the interval 

 and taken out of the integral as a constant. For a specified 6, the 

 remaining integral can then be seen to yield a constant. The pro- 

 duct of these two quantities produces the desired component magnitude. 



It should be noted that the right-hand side of eq. (2) has apparently 

 been halved in the transition to eq. (4). This is to account for the 

 fact that Si(2)(<^) Is a double-ended spectrum while §(oj, 9) is a 

 single-ended estimate. 



The results presented in the next section are confined to the 

 free surface (6 = 9) although, in principle, the computational 

 procedure may be used for any acceptable* value of 6 or to get 

 a drift averaged over a range of depths. The basic effect of in- 

 creasing depth (5 becoming more negative) is a function of the sur- 

 face spectrum. That is, with increasing depth, the resultant vector 

 will exhibit greater direction and magnitude persistence if the energy 



'Longuet-Higgins (1969) has shown that a component of secondary 

 vorticity is generated in a thin layer of thickness (vT)'2 adjacent 

 to the surface and that this vorticity propagates into the interior 

 of the fluid. These effects must be considered in future work. 



401 



