about 2 to 3%[Hughes (1956) estimated 2%; Smith (1968) estimated 3.4%]. 



It should be mentioned that empirically estimated ratios should be 

 somewhat higher than those computed here partially because they con- 

 tain not only the Stokes' mass transport effect, but also the Ekman 

 drift and perhaps residual tidal and permanent current effects. 



In regions of less wind variability such as the Trades, the 

 statistic becomes more significant. A ratio on the order of less than 

 one percent seems to be indicated. 



In contrast with the first statistic, the direction statistic proved 

 to be relatively easy to interpret. The results of the 4 March analy- 

 sis are presented in Figure 4 in a histogram. The central peak in 

 the distribution reinforces the idea of a wave-induced current apart 

 from the Ekman mechanism since the peak is not to the right of the 

 wind direction. Basically, the distribution reflects the tendency for 

 wave energy to be situated in the general wind direction. The particle 

 motions produced by these waves will then be in these directions. 

 This may account for some of the variability found in conventional 

 current measurements. In particular, the components in the wind 

 direction would be especially susceptible to this explanation. 



The bar on the far right in Figure 4 indicates an interesting feature. 

 In this particular case, approximately 2% of the grid points showed a 

 mean Stokes' drift against the wind. 



THERMAL UNDULATIONS CAUSED BY STOKES' MASS TRANSPORT 



Since the influence of surface waves reaches to a depth of approxi- 

 mately half their wavelength, it may be expected that particle motions 

 are effective to considerable depths. In order to investigate this effect, 

 a long-crested nonlinear Lagrangian model proposed by Pierson (1961) 

 was used. Two of the solutions derived in this formulation were a set 

 of second order equations for determining the Eulerian position (X,Z) 

 of a fluid particle as a function of the Lagrangian tags a, 5, and time,t. 

 If these equations are written in terms of 15 waves, they form 



15 k 5 



X(a,6,t) = a - S a e s in(k a - oj t) 



rn=l "^ ra m ' 



3 2 



14 15 a a /jj +co \ (k +k )6 



^ V mn/m n\n m' ■ m i \ t \t\ 



- 2 S ( e sin((k -k )a-(oo -u )t) 



1 .igVco-oo/ ^^nm'^n m' ' 



m=l n=m+l ^ V n nV 



14 i5aa (k-k)5 



+ S S (oj +00 )c;j e sin((k -k )a-(w -(^)t) 



m=ln=Ai+l g ' n m^ n ^^ n m' ^ n m' ' 



15 2 ^^^m^ 



+ i:a^Goke"^t (5) 



, m m m 

 m=l 



403 



