Water Bodies and Stationary Current Conditions at Boundary Surfaces 469 



density section. Although the axis of the vortex is somewhat inclined towards south, 

 current measurements and the mass distribution suggest a subdivision of the total 

 vortex into two parts or systems. 



(1) The upper system down to 100-150 m depth includes a discontinuity layer at 

 about 25 m. The velocity of the basic current in the top layer is about 15 cm/sec and 

 in the denser lower layer, however, 20 cm/sec. This is thus a strongly stratified cyclonic 

 vortex with a speed of rotation increasing with depth. Under steady conditions the 

 isosteres must therefore dip downwards in the lighter water masses which are con- 

 centrated around the vortex axis. This is shown very clearly by the section given in 

 Fig. 212. 



(2) The lower system extends through the layers below 150 m, where there is a normal 

 increase in density with depth and a steady decrease in the velocity from about 

 20 cm/sec at 200 m to about 6 cm/sec at 800 m. This is therefore a weakly stratified 

 cyclonic vortex with decreasing rotational velocity with depth. The required uplift of 

 the isosteres (accumulation of lower denser water around the vortex axis) is again 

 obvious from Fig. 212. 



Also quantitatively the observed slopes are in a good agreement with that required 

 by theory (equation XIV. 10). Since <^ = 44° 33' N.andtherefore/= 1-023 x lO"* sec-^ 

 equation (XIV. 10) gives for the upper system: a^ = 26-30, q = 15 cm/sec, ag = 26-65, 

 Cg = 25 cm/sec ; the isosteres slope downwards towards the centre by 92 m in 60 km ; 

 observed 70-90 m. For the lower system: ct^ = 26-8, Ci = 20 cm/sec, cto = 27.5, 

 Cg = 6 cm/sec; the isosteres slope upwards towards the centre by 214 m in 100 km; 

 observed 230-290 m. 



The cyclonic vortex performed pulsations, as was indicated by the observations made 

 at the anchor stations. The period of these pulsations corresponded to the period of 

 inertia oscillations (see p. 472). 



Sandstrom (1914, 1918), has carried out laboratory experiments to test the effects 

 of cyclonic and anticyclonic air currents on stratified water masses underneath. 

 Reference is made to these in this connection. 



4. Up- and Down-gliding Surfaces: Pulsations of Stationary Vortices 



In systems of moving water bodies for a stationary position of the boundary 

 surfaces there will be no vertical motions according to equation (XIV. 7). If the equili- 

 brium conditions are not satisfied, accelerations will occur and as a consequence 

 vertical motions are generated which will lead to changes in the position of the dis- 

 continuity surfaces. If the slope angle of the boundary surface is denoted by e and 

 differs from that for its stationary equilibrium y, then e will tend towards its equili- 

 brium slope y. If the boundary surface is steeper inclined than in the equilibrium 

 state (e > y), in order to reduce e the upper lighter water must spread out over the 

 lower heavier water and the lower one will intrude underneath the lighter. Above the 

 boundary surface there will be an up-gliding and below it a down-gliding (up-gliding 

 surface). 



If, on the other hand, for e < y the reverse will apply. In the lighter water type there 

 will be down-gliding and in the heavier up-gliding (down-gliding surface). The processes 

 occurring at the boundary surface can be decisively influenced by the initiated vertical 

 motions. Exner (1924) and J. Bjerknes (1924) have investigated the processes that may 



