All-101 



&^ 



Appendix 2, i"ep;lect of t he i^.on -'.lnnpr Terns. 



Consider the integrated eqUFtions of iiotion of section 



3. 



'n A„. 



-h 



912-' .^z .. 

 dt "^ ■ 



u' lii' dz + v' M^6.z - By 

 -h J -h ^ 



' v'dz 



-h 



= - 2 D -^ + A 

 6:: 



Au' dz + Tx 



(1) 



at 



dz + P u' 9v' ,i2 + f"^ V' IZ'dz + Pyf^ u'd 



-h 



dx 



-h 



9y 



L/ -h 



g B ^ 4- A 

 9y 



Av' dz + "^y 



-h 



(2) 



where v/e have linearized the pressure term in eccordanco vith 

 reiiarl's to be I'.ade later in sectic^.s 3 p'<'^<^'- 5. 't^„j t^„ are now 



X y 

 the wind-stress components of section 3 divided by p. Assume 



.kz 



u' = u(x,y,t) e " , v' = v(x,y,t) 



.kz 



i.e. tl:? velocities decay exponentially \/ith depth. 



Then, 



au „kz 

 dt ^ 



1 - 8u p21:z 



2 ~: 



-h 



-h 



+ Iv Q^ o21-.z 

 2 ay ^ 



-a 



2Q sin(-5i) V e 



Kz 



- D ^ k + A A u e" ''^^ 

 9:: 



-h 



+ T k (3) 



» -h 



