m wOo 377 



The momentum of the water is dm. (u + u' ) in the horizontal, and dm (w + w* ) in 

 the vertical* Thiis^ the time rate of total horizontal and vertical transport 

 across this area is: 



Dividing through by dAdt^ one obtains the time rate of vertical transfer of 

 horizontal and vertical momentum per unit area_, which is given by: 



and 



f (lA/kr-hU^U -f i^'^Ww'j 



(A-67) 



Taking averages over the period T^ sjid utilizing equations similar to (A-63)^ 

 produces : 



fOr'^'h fi^>'^ s? fa^^ '4'Pujii' (A„68) 



and 



fu^a -hfu'i^ -fai^ -t fdul , 



(A^69) 



The turbvilent transfer quantities are defined as -^Ui^ and -^fci'to' 



Consider the turbulent term^4«ifiu'c This term represents a net transport of 

 horizontal momentum in the vertical by means of a correlation of u' with w" . 

 Correlation exists when _ 



^ - 2. I 1« V it ^ © 



f aw ^ :p -ai^ ^-c -T « ^ (^.^0) 



Note that in the case of ocean v/aves the time vars'ing quantities oscillate 

 and change sign« Thus, there must be an internal systematic relation; e<.g<,, 

 u' is large and negative when to' is large and Gega,tive^ and u' is large and posi- 

 itive when w' is large and positive. 



If u and w are measured at a fixed point beneath the surface of the ocean, 

 and for a given time interval equation (A-75) holds true, one can then conclude 

 that: (1) a much larger or much smaller eddy motion is instmmental in propa- 

 gating moment-'jm downward which the instruments did not detect; or (2) a mecha- 

 nism of stress transfer exists which is unrelated to the Reynolds stress concept o 



A-^IS 



