376 



FOFONOFF 



[sect. 3 



{We+ Wx)l2. We can consider either the mean vertical velocity or the mean 

 meridional temperature gradient, but not both, as unknown. Integration of the 

 linearized equation yields 



^^MJo 2 ^'-^^' 2 = ^ 



(193) 



and, from (189), 





&d\!;,\ for ^ > 0, a; < 



JO 



(194) 



= + &d\^\ for ^ < 0, :c > 0. 



If W does not change sign with depth {we, w, Wod > 0), we can approximate 

 W and & by 



W = lfoo + (lfe-lFao)e-2l^l/^ (195) 



^ = ^oe-2l?l/^. (196) 



Substitution of (196) into (194) yields 



JO 



&dm = Mol2. 



(197) 



The boundary conditions become 



..,'!)„ ^ -^ -^ <f 





2{We-Woo) 



L 



\ for ^ > 



(198) 



and 



m\ _2Mo_ 



ldW\ ^ -liWe-Woo) 



\ for ^ < 0. 



By substituting (197) and (198) or (199) into (194), we obtain 

 We- Woo ^ ^oi>2/4 = kv'~&o^lq*'- 

 and, from (193), 



2q* + {We+Wao)&0+^T,{We-Wo,) = 0. 



(199) 



(200) 



[201) 



If we assume that We, Woo and q* are given, we can calculate d-Q from (200) and 

 T) from (201) provided we consider ky as known. On the other hand, if we 

 use Robinson's and Stommel's assumption that We, &o and Ti are known, 



