Water Bodies and Stationary Current Conditions at Boundary Surfaces 467 



Case c: Ac > 0, for anticyclonic rotation |ci| > [ca]. As long as the term in brackets 

 in (XIV. 10) remains positive, which is always true except in extreme cases, then 

 tan y < and the boundary surface rises towards the outside. Tan ^ is positive in 

 both layers and the slope of the pressure surfaces is less in the heavier water body than 

 in the lighter: anticyclonic vortex with the top layer rotating more rapidly and a central 

 dome-like uplift of the pressure surfaces and of the physical sea level. The rotation 

 gives rise to an accumulation of the lighter water masses around the rotational axis. 



Case d: Finally, it is possible in an anticyclonic rotation to have /Ic < and then 

 kal > kil- The slope of the boundary surface rises towards the centre since tany is 

 positive (with the same restriction as in case c). The pressure surfaces also rise towards 

 the centre but in this case more strongly in the heavier than in the lighter water layer : 

 anticyclonic vortex with the lower layer rotating more rapidly and a central dome- 

 like uplift of the sea level and the isobaric surfaces. Here the lower heavier water 

 accumulates around the vortex axis. Since in the sea the current velocity almost always 

 decreases with depth, cases a and c will predominate. In a cyclonic vortex the deep 

 water is hfted close to the surface and if the vertical velocity gradient is sufficiently 

 large the boundary layer may reach the surface. Then the vortex centre will be filled 

 with deep water. In an anticyclonic vortex, on the other hand, there is an accumulation 

 of the hghter upper water around the vortex axis that may extend downwards to con- 

 siderable depth. 



The actual stratification in the sea seldom consists of only two layers; the same laws 

 apply, however, also to a continuously stratified ocean (see Chap. XV). The boundary 

 surface slope is then replaced by the slope of the isosteres and in place of sharp kinks 

 there appears a steady curvature in the isobars. Also here, due to the low velocities 

 and the large radia of curvature of the current trajectories, the centrifugal force is of 

 little importance compared with the Coriolis force for an estimate of the mass field 

 adjustment. Figure 21 1 shows dynamic sections through such cyclonic and anticyclonic 



Fig. 211. Mass and pressure distribution in rotationally symmetric layered vortices with a 

 decreasing rotational velocity with depth, {a) Cyclonic; {b) anticyclonic rotation. 



circular vortices in a stratified ocean; in both cases it is assumed that the velocity of the 

 current decreases with depth; for a two-layered ocean they correspond to the cases 

 a and c of Fig. 210. 



Charts of ocean currents often show more or less extensive vortices in the top 

 layers. They are found mostly in those areas where the wind field also indicates 



