Integration of equation (5) with respect to time gives: 



C + f C, + f 

 

 T " r » constant (6) 







where Cq , fg and h^ are initial values. The relative vorticity can be 

 expressed by: 



3V V 



where : 



V = the current velocity 



R = the radius of curvature 



V/R = rate of turning by the current 



3V/3n = horizontal velocity shear normal to the current 



Assuming no horizontal shear, which is the same as stating that the 

 current is infinite in width, then OV/3n=0). Starting at an inflection 

 point in the flow, using equation (7), and assuming that 3V/9n=0, equation 

 (6) is simplified: 



C =^fo - f (8) 



Equations (7) and (8) are combined to give: 



£'.-■) 



R = V/(~ f„ - f ) (9) 



>0 



Further, using the mathematical relations: 



AewAS/R 



and 



V = AS/At 



where AS is approximated by a straight line, equation (9) is now written 

 in terms of the change in direction (A0) as the parcel of water moves 

 betwefen two points . 



(}. ") - 



Ae = - fn - f At (10) 



-5- 



