The Representation of Oceanic Movements and Kinematics 



373 



Fig. 162a. Two streams of water flowing together. 



Conspicuous phenomena also occur where currents carrying two different water masses flow to- 

 gether and these deserve special attention. If two water masses of different type meet at a sharp land 

 projection or at a motionless water mass there will usually be an appreciable transverse velocity 

 jump at the boundary surface (Fig. 162a). It cannot be expected that separating surfaces of this 

 type will keep for any length of time their simple form, since the state under consideration is highly 

 unstable. Every boundary surface of this sort has a tendency to develop waves and all chance 

 irregularities will thereby grow rapidly and the discontinuity surface will finally dissolve into a 

 number of irregular vortices. These processes are particularly characteristic for the transition from 

 waves to vortices and have been described in detail by Bjerknes (1933) and Prandtl (1942). 

 A boundary surface at which a temporary disturbance of the current field has given rise to a slight 

 bulge is shown in Fig. 1626. This wave-form disturbance will move along the boundary surface with 

 the average of the speeds of the two currents; relative to this wave one of the water masses 

 will move to the right and the other to the left, and with reference to this kind of co-ordinate 

 system the ridges and troughs of the waves will remain in the same place. According to the 

 Bernoulli theory the disturbance in the course of the stream lines will be accompanied by a 

 corresponding transverse pressure disturbance. For a steady state of motion the transverse 

 pressure rise llpidpjds) must be balanced by the centrifugal acceleration c^/r (c denotes the hori- 

 zontal velocity, r the radius of curvature of the stream lines, s the direction of the normal to the stream 

 lines). It becomes obvious that there will be a pressure surplus (+) in the ridges of the waves and a 

 i educed pressure (— ) in the troughs of the wave. This implies that the wave disturbance cannot be 

 stationary but that the water begins to move from the surplus pressure areas to the adjacent areas of 

 reduced pressure; that is, as the wave disturbance becomes stronger it will form current fields similar 

 to those in Fig. 162c, in which the boundary surface will finally be rolled up into vortices, lying one 

 behind the other and all rotating in the same sense. The same phenomenon occurs here in the hori- 

 zontal plane between two water masses with different velocities as in the case of unstable waves at the 

 boundary surface between water masses flowing one above the other (see Vol. n. Chap. XVI, p. 517 

 Internal waves). Examples of cases such as this are the vortex formations at the boundary between the 

 East Greenland Current and the Atlantic Current in the Irminger Sea, or the vortex-formations at the 

 boundary between the Gulf Stream and the Labrador Current south of the Newfoundland Banks (see 

 p. 471). 



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Fig. 1626. Disturbances in the pressure field due to wave-like deformations of a boundary 



surface between two currents. 



