OCEAN TEMPEBATUEES 



391 



upwelling 2 equals 3 . A second approximation to the solution of 



\n 



equation (139) can be found by substituting for its value from 



dy 



the first approximation. The solution is then reduced to 



i 



/a 2 +V k 



- _ . 

 i 7, ~r 



(156) 



where 



tan e., = 



1 i J V 1 \ n ' 



k ' 



2 + (hz) 2 

 If t<; = 0, equation (156) is identical with equation (22). 



Solution for the case in which the flow is a periodic function 



of the time. 



If the vertical velocity equals 



W [l -f-r COS (at ej] 



the -time rate of change of temperature can be obtained from the dif- 

 ferential equation (139) in which the last term is multiplied by 



The new differential equation is therefore 



l 

 dy 



(157) 



Let & be the solution already found when r = 0, and let 8" be the 

 correction due to r, then = 0'-}- 0", and the result of substituting 

 in equation (157) is 



dO" ^ 60" . .60' . .60" 



-^- + A:0"+ w + w r cos (a^ O + uy cos (at ej = 



(158) 



