15 k 6 



Z(a,6,t) = 6 + S a e cos(k a - oo t) 



m=l 



m m 



14 15 a a _ ^ (k +k )6 



+ Zj 1j (CO +w CO +Cli )e cosHk -k )a-(co -co )t) 



, , , g ^ m m n n ' ^^ n m' ^ n ra' ' 



TTL-l n=m+l " 



14 15 a a (k -k )5 



- 2 Z) CO (oj +00 )e cos({k -k )a-(oj -w )t) (6) 



m=l n=m+l ^ 



The term that is linear in t in eq. (5) can be seen to be a 

 summation of the Stokes' drift effect expressed in eq. (1). The 

 double summation terms in both equations indicate the sum and dif- 

 ference interactions among the 15 waves. One of these terms dies 

 out rapidly with depth. The other does not die out and produces long 

 period, long wavelength, vertical and horizontal oscillations. In a 

 random seaway, groups of high waves separated from other groups 

 by areas where the waves are low produce locally strong Stokes' 

 drifts over dimensions comparable to the size of the group. A meso- 

 scale field of convergences and divergences is established which 

 penetrates to considerable depth. 



As an example of how this effect might manifest itself, consider 

 a weakly stratified portion of ocean initially at rest. At this time, 

 the Eulerian and Lagrangian positions are identical (i. e. , x = a, 

 z = 6, t = 0). Let the temperature distribution be such that every 

 fluid particle at the same depth has the same temperature. If a 

 wave motion is now added and time is set in motion, the particles 

 will begin to move. At time scales on the order of five to twenty 

 minutes, it is not unreasonable to assume that the subsurface fluid 

 particles (say, below -40 meters) have been able to maintain their 

 initial temperature. Therefore, the isotherm initially at some con- 

 stant Eulerian depth will be moved both horizontally and vertically 

 because of the motions of the fluid particles. The spectrum of grid 

 point 13 (6l.9°N, 10.1 "W) of the 4 March case was used as a test to 

 illustrate this effect. The ensemble of 15 waves with approximately 

 the same centered frequencies, wave numbers and amplitudes given 

 by the spectrum were substituted into eqs. (5) and (6) to produce a 

 series of Eulerian positions for various values of a and 6 in the 

 vicinity of the Eulerian origin. The results of this calculation for 

 t = 15 minutes are presented in Figure 5. The Stokes' velocity 

 shear (9U/95) has purposely been masked so that only the vertical 

 features are evident. The important feature to note here is in the 

 vicinity of -40 to -70 meters. The levels that were originally at 

 z = -40, -50, -60, and -70 meters have now been raised and ex- 

 hibit a long wave oscillation due to the wave-induced particle 

 motions. If they are assumed to be isotherms, then a shift in the 

 thermal pattern is indicated. If one now imagines a ship situated 



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