466 Water Bodies and Stationary Current Conditions at Boundary Surfaces 



be expected for extensive vortices. For small vortex sizes, however, it may be as large 

 as 30-40%. A difference from the case for straight flow exists in so far as the slope of 

 the boundary surface depends on the distance from the axis of rotation. In general, 

 when the area immediately around the axis of rotation is disregarded, the oceanic 

 structure of a circular vortex of this type can be readily derived from the rule given 

 above. Four cases can be distinguished (Fig. 210, Northern Hemisphere). 



(o) 



(b) 



Fig. 210. Rotational symmetric stationary vortex in a two-layered ocean (position of the 

 boundary surface and form of the isobaric surfaces, physical sea surface, respectively). 

 a and c, cyclonic and anticyclonic rotation in case of a faster rotation of the upper layer. 

 b and d, cyclonic and anticyclonic rotation in case of a faster rotation of the lower layer 

 (underneath the sections diagram of forces for only one point of the lighter and heavier 

 water mass. G, gradient force; C, Coriolis force; Z, centrifugal force). 



Case a: Ac < 0, for cyclonic rotation Cg < Ci: tan y > 0. The boundary surface 

 rises towards the centre, in fact more rapidly near the vortex axis and less further out; 

 tan ^, on the other hand, is negative in both layers, that is, the pressure surfaces and 

 the physical sea level rise outwards, more so in the upper than in the lower layer. 

 This is the case of a cyclonic vortex with the upper layer rotating more rapidly. Due 

 to the rotational effect the heavier water accumulates around the axis of rotation while 

 the lighter top layer is forced to the outside. In the central area there is a depression 

 in the physical sea level and the isobaric surfaces. 



Case b: Ac > 0, for a cyclonic rotation Cg > Ci: tan y < 0. tan /S is negative in both 

 layers and the boundary surface, the pressure surfaces and the physical sea level rise 

 towards the outside; cyclonic vortex with the lower layer rotating more rapidly. The 

 lighter water masses accumulate around the vortex axis and there, as in the previous 

 case, the physical sea level and the pressure surfaces show a depession. In these cyclonic 

 cases the sum of Coriolis force and the centrifugal force act towards the outside and 

 a larger gradient force is required to balance this combined action. The boundary 

 surface slope must therefore be greater than for water bodies arranged in strips. 



