356 FOFONOFF [sect. 3 



The equations for the t\\'o-layer ocean can be reduced to 



^uh=-^, (111) 



h dij 



where ^a/h is the potential vorticity and Q is equal to g'h + ^(m^ _|_ ^2) xhe basic 

 difference between these equations for the two-layer ocean and (89) and (90) is 

 that h cannot be considered to be approximately constant. 

 By introducing a volume -transport function ijj such that 



,,;, = ^, vh= -^4' (112) 



dy dx ^ ' 



we obtain relations, analogous to (95) and (96), of the type 



Q = Q{^) (113) 



^ = -^. (114) 



h di/j ^ ' 



We assume that a solution for the transport function for the two-layer ocean 

 can be obtained that is symmetrical with respect to the central meridian of a 

 rectangular ocean. Such a solution requires h, x, Q, Ca, u to be symmetrical and 

 V to be antisymmetrical as in the homogeneous ocean. Charney (1955) and 

 Morgan (1956) have shown that the two-layer equations allow the formation of 

 an intensified accelerating current along the western boundary. From the sym- 

 metry of the equations, we can expect an intense decelerating flow along the 

 eastern boundary. The solutions for the homogeneous ocean lead us to expect 

 an eastward jet joining the two boundary currents. Thus, we anticipate solu- 

 tions for the two-layer ocean that have several features in common with the 

 inertial flow in the homogeneous ocean. Fofonoflf (1954) pointed out that the 

 westward intensification of anticyclonic inertial circulation (poleward flow in 

 the western boundary current) is more pronounced than that of cyclonic 

 circulation. This feature is not present in the homogeneous ocean. The absence 

 of symmetry can be seen from the equations governing Q and ^alh in the 

 boundary region. If we assume the interior flow is westward and slow, we 

 obtain 



iUlhh =filhi (115) 



and 



g'h + l{Ub^ + Vb^) = g'hi (116) 



along a transport line entering the western-boundary region. Solving (115) for 

 the relative vorticity, we obtain 



r iff\ \"'i~"'f>)f 

 tft = -{jb-Ji) 1 Ji 



' (117) 



If f. {Ub^ + Vb^) 



