been recognized that a particle in an irrotational, progressive gravity- 

 wave motion will undergo a slow drift at the so-called Stokes' mass 

 transport velocity. For a periodic wave in deep water, this velocity 

 is in the direction of wave celerity and may be expressed as 



7= 2 , -2kZ n\ 



U = a cjke (1) 



where a = wave amplitude 



0) = angular frequency 

 k = wave number 

 Z = Eulerian depth 



In a situation involving the actual sea surface, however, this ex- 

 pression is not directly applicable. The reason for this is, of 

 course, quite obvious since the deep water sea surface cannot be ap- 

 proximated as a periodic motion. In order to derive reasonable esti- 

 mates of wave -induced properties, one should generalize to at least 

 a first order spectrum. A recent study by Chang (1969) has done 

 precisely this for the mean component of Stokes' velocity. A spectral 

 expression of the form 



U = 47^e2("^/g)^S,, Ja.)dc. (2)* 



o 



'l(x)' 



where g - acceleration of gravity 

 5 - Lagrangian depth tag 

 S (oj) = double-ended first order spectrum of the motion 

 l(x/ in the x- direction 



was derived and shown to be applicable through the second order of 

 the perturbed Lagrangian equations of motion. For the deep water 

 case, it was shown that Sw^Wca) could be reasonably approximated 

 by the first order spectrum of wave elevation in the z-direction 

 (i. e., S]^/^;) ("))• This allows an evaluation of U from eq. (2) since 

 estimates of Sw^)^ are, or soon will be, common products of 

 present-day numerical wave forecasting models as described by 

 Pierson, Tick and Baer (1 966). In particular, estimates of the 

 directional-frequency (d-f) spectrum, §(00, 9), are especially use- 

 ful in this context since a direction may be associated with the_mag- 

 nitude andj;hus result in a vector evaluation. Calculations of U fields 

 involving S(co, 9) have recently been completed on a CDC l604 at the 



'Note that eq. (1) is a special case of eq. (2) --namely that which 

 occurs at the initial time (z = - 5) in deep water (kg = i^^) if the 

 x-motion is similar to the z-motion and purely sinusoidal 



(a^ = 4S,, .(a. )) 

 1 (x) ^ o 



399 



