Forces and their Relationship to the Structure of the Ocean 

 In the two-dimensional case {x, z) 



and from Stokes's law it follows that 

 a dp = 



dp 

 dx + a ^r- dz 



cz 



r , { C /8a 8p da 8p\ 



f^'^ = ]\ [8xTz-Tz8-xj 



dxdz 



331 



(X.46) 



(X.47) 



If now e and /3 are the angles of the ascendent of the pressure 8plcn and the ascendent 

 of the specific volume 8al8n, respectively, with the .r-axis, then 



da da 



da da 



^ = ^ cos ^, ^ = ^ sin ^, 



8x 8n 



8p 8p 



^ = ^ cos €, 



8x dn 



8z 



dz 



dn 



^dp . 

 ^T Sin e 

 en 



and from equation (X. 47) 



and 



adp =^ 



da dp 

 dn on 



sin (e — P) dx dz 



dC 



~di 



da dp 



-^ ■?- sm (e 



on dn 



iS) dx dz. 



(X.48) 



(X.49) 



The two possible cases are shown graphically in Fig. 136c. If e > j8 then the circulation 

 acceleration dCldt < and produces an anticyclonic circulation. If, on the other hand, 



'1 a'2 a'J 



p p*l p+2 p*3 p*4 p*5 p+6 



Fig. 136c. Cyclonic and anticyclonic circulation movements for different pressure gradients 



and specific volumes. 



e < /8 then dCjdt > and the resultant movement is cyclonic. In the two cases (see 

 Fig. 136c) the circulation proceeds from the ascendent of pressure to the ascendent 

 of specific volume. In oceanography, as a first approximation, the isobaric surfaces 

 are horizontal, i.e. e = 90°, and thus 



dC 

 'dt 



g da 

 a dn 



cos ^ dz 



(X.50) 



A cyclonic circulation is present when ;8 > 90° and thus the isosteres decline towards 



