Current velocity is assumed to remain constant alon^ the path. 

 Given the initial latitude and longitude at the starting point, the initial 

 depth of the ocean, the velocity of the current, the initial direction, and 

 the time interval between points , a parcel of water is followed from the 

 initial point Pq to point Pi, using equation (2). The direction (0) of 

 the current will remain constant during the time interval (At), if the time 

 interval is small enough. The parcel of water follows a new direction 

 (01 ) from point Pi to point P2, 0, = (9q+A0/2), where 0q was the direction 

 from Po to Pi, and A0 is determined from equation (10). The above procedure 

 is repeated to find P3, P14, etc. 



Several experimental tests are shown in figures A and 5. The time 

 interval (At) is 10 minutes. Figure 4a shows paths computed with current 

 speeds of one and two m/sec. These speeds are unrealistic, since the actual 

 vertically averaged horizontal speed probably lies between 25 and 50 cm/sec. 

 Using the lower speed of 25 cm/sec, the path of the Gulf Stream was examined 

 bv varying the starting point (figure 4b) and by varying the initial cur- 

 vature (figure 4c). The assumptions for the flow of the Gulf Stream are 

 apparently inadequate. In all of these tests (variation of the mean verti- 

 cally averaged speed, variation of the starting location, and variation of 

 the initial radius of curvature), the calculated paths do not represent 

 observed paths of the Gulf Stream. The predicted position is too far north. 



Since the Gulf Stream current is variable with depth, strongest 

 near the surface and weakest near the bottom, the control of bottom topo- 

 graphy should be weighted in order to account for the difference between 

 the mean flow and the bottom flow. This is accomplished by replacing 

 h/hg in equation (10) by the weighting expression Wg(h-hQ/hQ)+l. For 

 the full effect of the ocean's variable depth, Wg=l; and for no effect, 

 Wg=0. This weighting expression essentially reduces the influence of 

 the topographic gradient along the path. Figure 5 shows a configuration 

 of the Gulf Stream generated with different weights given to bottom 

 topography. The less the influence of the bottom, the more easterly the 

 path of the stream. In the case of a flat-bottomed ocean, the paths 

 become Rossby-type waves. 



75° -,70° 



65° 60°| 





■.j^gs^'vv 



V, 





f-.J 







-^ 











^°^^ 



J- 





\ y^ 







-i£j 



/. . . . 



- 



~-z 



■ ■ ^ 





■f" 



- 

























c. . 

















BOTTOM WEIGHT 













.50 













.25 





■...T.,,r.._ 



...r, ,,!.., r..,;-.. 



• r r r r 1 r . w 



Figure 5. Effects of Bottom Topography on Gulf Stream Path 



-7- 



